US20130092785A1 - System and method for guiding and controlling a missile using high order sliding mode control - Google Patents
System and method for guiding and controlling a missile using high order sliding mode control Download PDFInfo
- Publication number
- US20130092785A1 US20130092785A1 US12/501,395 US50139509A US2013092785A1 US 20130092785 A1 US20130092785 A1 US 20130092785A1 US 50139509 A US50139509 A US 50139509A US 2013092785 A1 US2013092785 A1 US 2013092785A1
- Authority
- US
- United States
- Prior art keywords
- target
- lateral
- acceleration
- missile
- attitude
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F41—WEAPONS
- F41G—WEAPON SIGHTS; AIMING
- F41G7/00—Direction control systems for self-propelled missiles
- F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
- F41G7/22—Homing guidance systems
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F41—WEAPONS
- F41G—WEAPON SIGHTS; AIMING
- F41G7/00—Direction control systems for self-propelled missiles
- F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
- F41G7/22—Homing guidance systems
- F41G7/2213—Homing guidance systems maintaining the axis of an orientable seeking head pointed at the target, e.g. target seeking gyro
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F41—WEAPONS
- F41G—WEAPON SIGHTS; AIMING
- F41G7/00—Direction control systems for self-propelled missiles
- F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
- F41G7/22—Homing guidance systems
- F41G7/2253—Passive homing systems, i.e. comprising a receiver and do not requiring an active illumination of the target
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F41—WEAPONS
- F41G—WEAPON SIGHTS; AIMING
- F41G7/00—Direction control systems for self-propelled missiles
- F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
- F41G7/22—Homing guidance systems
- F41G7/2273—Homing guidance systems characterised by the type of waves
- F41G7/2293—Homing guidance systems characterised by the type of waves using electromagnetic waves other than radio waves
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/12—Target-seeking control
Definitions
- the present invention relates to the control of missile trajectories homing to collide with a maneuvering target. More particularly, the use of a High Order Sliding Mode (HOSM) control adapted to the control of one or more functional subsystems of the homing missile, including the guidance, seeker, and autopilot subsystems.
- HOSM High Order Sliding Mode
- the interceptor has a perfect dynamic response and perfect control of its acceleration
- U.S. Pat. No. 6,244,536 B1 uses a modified formulation of PN called PRONAV and Riccati Equation. While the use of Riccati equation reduces the divert effort, it is predicated on the availability of good state models.
- U.S. Pat. No. 7,185,844 B2 and also Ref 1 introduces PN with a so called “parallel” navigation additional term proportional to the cube of the line-of-sight rate and additional term proportional to relative longitudinal acceleration, not easy to estimate very accurately and account for interceptor acceleration. The compensation for such effects is beneficial. Its explicit compensation as proposed in U.S. Pat. No. 7,185,844 B2 is only as good as the estimation/measurement of corresponding terms.
- Neoclassical Guidance in reference 3 does not require estimating target acceleration and tgo, but since it is based on adjoint techniques, it requires a good dynamical model of the interceptor flight control system and does not apply to the case of dual concurrent lateral controls.
- ZMD Zero Miss distance
- Reference 5 includes in the observer a set of maneuver patterns that enhance the prediction of target kinematics and a method based on differential game theory to adjust the gains of the guidance.
- the degree to which actual target maneuvers must “match” the models makes this approach not very realistic.
- the quest for better prediction of target maneuvers in Ref. 6 leads to use banks of filters with typical maneuvers and maneuver detectors.
- the problem is that the detection of a maneuver of change thereof takes some time if one wants to have enough confidence in the decision made and also the “mathematical” separation of the maneuvers may not be evident.
- the use of a Kalman Filter transition matrix with a ZEM based guidance in Ref. 7 helps in reducing the effects of delays but is only applicable for longer range exo-atmospheric guidance.
- Kalman Filtering has been a technique of choice for estimating target motion. While it produces good estimations, its relatively slow convergence may cause it to be ineffective at the end-game when rapid target maneuvers are encountered. Reference 8 showed that Higher Order Sliding Mode Observers can provide faster and yet more accurate estimations than traditional Kalman Filter.
- U.S. Pat. No. 6,532,454, B1 uses adaptive techniques to estimate an interceptor model. While this approach works well when given enough time for the estimation process to settle, it cannot handle the case where rapid disturbances are created by the interaction between the firing of thrusters and the aerodynamic flow around the missile as described in Ref. 9. Another important issue is to achieve interceptor maneuverability as large as possible. This calls for operations in the endo-atmospheric domain for combined operation of several divert mechanisms, possibly several control surfaces.
- U.S. Pat. RE37,331 E where a forward placed thruster and tail (fin control) are used jointly to initiate a lateral maneuver faster and without non-minimum phase effects.
- a short fall associated with the use of first order sliding mode control is that it achieves its robustness by high frequency (infinite switching rate) or eventually can be approximated by a sub-performing high gain approximation.
- Reference 11 proposes a Multiple Input Multiple Output solution to steer the angle of attack and pitch rate to satisfy a Lateral acceleration condition. It uses a Variable Structure Solution; unfortunately, it uses Euler Angles and its generalization to a Quaternion solution would be very difficult.
- U.S. Pat. Nos. 6,611,823 B1 and 7,080,055 B2 both address the problems associated with actuator nonlinearities as encountered with on-off thrusters and come up with complex neural network solutions requiring some “learning” hardly an option with missile systems.
- High Order Sliding Mode (HOSM) control techniques are applied to the Guidance Control (G&C) of a interceptor missile in which velocity may be steered by combination of main thrust, aerodynamic lift and lateral on-off divert thrusters, and attitude may be steered by either continuous or by on-off actuators.
- Methods include the pointing of the seeker, its associated estimation processes, a guidance law that uses concurrent divert mechanisms, and an attitude autopilot.
- the insensitivity of the controller to matched disturbances allows the concurrent usage of the divert mechanisms without adverse effect on the accuracy.
- the controller also allows the de-coupling of the control of roll, pitch and yaw channels, and quaternions to represent body attitude and it provides control perfect robustness. While it is conceivable to design separately the components of the G&C method, it is widely accepted that designing them in an integrated fashion usually produces a better result.
- the guidance and control methods of the present invention are applied to a very challenging missile configuration.
- the interception can take place in the exo-atmospheric domain, after the end of boost with lateral divert accelerations being achieved by the firing of on-off divert thrusters.
- the interception can occur while still boosting.
- lateral divert accelerations are achieved by orienting the missile body with respect to the velocity, and in such case when the interception occurs in the endo-atmospheric domain, lateral acceleration also includes aerodynamic lift.
- interceptor attitude during autonomous Kill-Vehicle flight can be steered by the firing of on-off attitude thrusters and during the boost phase by the continuous TVC control or aerodynamic control surfaces.
- the methods presented can also be applied to simpler missile configurations operating in a single exo vs. end atmospheric domains.
- a good example of this type of problem is the interaction of aerodynamic flow with divert attitude control thrusters placed on the sides of the missile as shown in FIG. 1 .
- the jet flow coming out of the thrusters creates an obstacle to the airflow, thereby modifying the system of shock waves around the body and thus, aerodynamic forces.
- thruster flow expansion governed by the external pressure will differ different depending whether or not thrusters are being fired.
- These interactions may affect aerodynamic lift up to 30% in relative term and the effective forces of the thrusters by similar amount as indicated in the work of Kennedy 9 (Ref. 9.)
- Typical durations of thruster firing of 10-20 msec show that the effect is clearly a non-steady state effect.
- Sliding Mode Control of r th order is said to exist if ⁇ , ⁇ dot over ( ⁇ ) ⁇ , . . . ⁇ (r ⁇ 1) ⁇ 0 in finite time and stay there thereafter.
- the sliding variable and its derivatives up to ⁇ (r ⁇ 1) are continuous as illustrated by FIG. 2 .
- Higher Order Sliding Mode Control laws are based on the property that some families of differential equations converge to zero in the presence of bounded right hand side of the equations as exemplified hereafter by the so called “super-twist” algorithm.
- f(y,t) represents the nominal response other than caused by control term bu and d represents the effects of unknown disturbances and (n) represents the relative degree of the sliding surface dynamical model that is, the number of successive time-differentiation required for the control term to appear explicitly in the right-hand side.
- a first important contribution of this invention is to allow concurrent use of various divert mechanisms such the firing of lateral divert thrusters, aerodynamic lift, main booster/sustainer by orienting the missile body.
- divert mechanisms and conventional control techniques are used the two main possible approaches are:
- Control techniques require the number of inputs, i.e. controlled variables and outputs, i.e. actuator command to be the same.
- actuator command i.e. a command to be the same.
- the usual remedy is to include internal models that estimate, in real-time, what is the contribution of each divert mechanism. For example when aerodynamic lift and divert thrusters are used, the internal model will estimate what would have been the lateral acceleration produced by aerodynamic lift, had it been used alone. In practice this is difficult because those are transient response models and in most of the case divert responses are not de-coupled as discussed before.
- failure to account exactly for the effects of each actuator will have a strong adverse effect on control accuracy and may even lead to unstable conditions.
- the missile commanded acceleration may be achieved using combination more than one of divert mechanisms such as orientation of main/sustainer thrust with respect to velocity vector, aerodynamic lift and divert thrusters.
- divert mechanisms such as orientation of main/sustainer thrust with respect to velocity vector, aerodynamic lift and divert thrusters.
- Setting several sets of actuators (control outputs) to achieve a single input (guidance law) requires when conventional control techniques to have accurate explicit knowledge of the effects of each set of actuators and to set a control allocation strategy.
- the usage of higher order sliding mode control allows overcoming this limitation.
- one the divert mechanisms is defined as the primary control.
- the choice of primary control is based on the response time of said control, the smallest the better and requires said control for achieving a sufficient share of total control effort, typically larger than 1 ⁇ 3; in a missile application the divert thrusters is the preferred choice.
- the present HOSM method illustrated hereafter allows using several divert mechanisms without resorting to complicated and eventually uncertain model, without any loss of performance and with a much simpler architecture.
- the interception strategy (for the pitch and the yaw channels) is represented by a sliding surface function of several variables that must be steered to zero and kept null thereafter.
- f (.) is a function that will be compensated explicitly and g (.) a bound unknown disturbance to be compensated implicitly and ⁇ (.) represent the command of divert thrusters (assumed to be continuous in this illustration for simplicity sake).
- HOSM technique gives the designer considerable latitude in the choosing of which terms should be compensated explicitly and which should be compensated implicitly.
- ⁇ ( . ) 1 b _ ⁇ ⁇ f ⁇ ( . ) + ⁇ 1 ⁇ ⁇ ⁇ ( . ) ⁇ 2 / 3 ⁇ ⁇ sign ⁇ ( ⁇ ( . ) ) + ⁇ 2 ⁇ ⁇ ⁇ ⁇ ( . ) ⁇ 1 / 3 ⁇ ⁇ sign ⁇ ( ⁇ ( . ) ) ⁇ ⁇ ⁇ ⁇ ( 8 )
- Equation (9) represents another family of differential equations that guarantees simultaneous convergence of ⁇ (.) , ⁇ dot over ( ⁇ ) ⁇ (.) ⁇ 0 in the presence of bounded unknown right hand side term, provided that ⁇ 1 , ⁇ 2 have been selected taking in to consideration the bounding condition for the derivative of the disturbing term ⁇ (t) (.) .
- ⁇ ( t ) (.) g (.) ⁇ (.) + ⁇ tilde over (f) ⁇ (.) (10)
- such secondary control in claim 3 creates a “cooperative” disturbance that reduces the initial magnitude of the bound disturbance as
- the cooperative disturbance needs not to be calculated to match exactly commanded acceleration nor do inaccuracies thereof have any adverse effect on the performance accuracy of the guidance.
- the response time of cooperative disturbance needs not match the dynamics of the target maneuver as this is the case when aerodynamic lift is used as secondary control and slower response thereof has no adverse effect on the performance accuracy of the guidance.
- a second important contribution of this invention is the slewing of the bore-sight and design of associated HOSM based estimators of the target motion that provides shorter settling times than traditional Kalman Filters together with better accuracy.
- a third contribution of the present invention is a method for guiding the missile.
- Most missile guidance is based on some form of Proportional Navigation (PN) or some of its derivatives such as Augmented Proportional Navigation (APN) or Zero Effort Miss (ZEM) that are based on assumptions discussed before.
- PN Proportional Navigation
- APN Augmented Proportional Navigation
- ZAM Zero Effort Miss
- the proposed method consists in regulating a linear combination of the target relative position error perpendicular to the bore-sight and the corresponding velocity conducive to setting the interceptor in collision course in a prescribed time using a HOSM control law which, by its inherent insensitivity to matched disturbances, also compensates implicitly for other uncertainties and alleviates the need for additional explicit terms accounting inter-alia for the variation of interceptor longitudinal velocity.
- a fourth contribution of the invention is the HOSM quaternion based autopilot.
- the interceptor considered has two modes: the first mode during boost phase where attitude motion is steered by continuous TVC control, and the second mode used during autonomous KV flight where attitude is controlled by the on-off firing of PWM attitude thrusters.
- the methods could apply to a missile only operating with one type of attitude control.
- the use of quaternions avoids using Euler Angles.
- Liquid thrusters can be continuously throttled from a minimum to a maximum value. Solid thrusters are preferred, in many applications for their easier handling and storage. Their simpler mode of operation is on-off. Several seconds before intercept a gas generator is ignited which produces. The gas can be ejected through several valves, the opening and closing thereof is defined according to the direction in which the force must be produced, typically up/down, left/right. In the case where no force is required the four valves are opened simultaneously. This is an on-off operating mode, which is PWM modulated by the duration of the opening sequence.
- the present invention has application in endo and exo-atmospheric and combined endo & exo-atmospheric missiles.
- FIG. 1 illustrates an exemplary missile to be controlled by the control system of the present invention.
- FIG. 2 illustrates the convergence of multiple time derivatives of the sliding surface.
- FIG. 3 illustrates the relation of Earth Centered Inertial (ECI) axes and North East Down (NED) axes.
- ECI Earth Centered Inertial
- NED North East Down
- FIG. 4 illustrates the relation of NED axes with body axes.
- FIG. 5 illustrates control architecture in accordance with the present invention.
- FIG. 6A illustrates an exemplary seeker configured with a fixed and rotating mirror.
- FIG. 6B illustrates an exemplary dither signal applied to the Pulse Width Modulation.
- FIG. 7 represents exemplary azimuth bore-sight pointing error for a simulated seeker subsystem in accordance with FIG. 6A .
- FIG. 8 represents exemplary pulse width modulated torques applied to the intermediate mirror of FIG. 6A .
- FIG. 9 represents the target lateral distance with respect to bore-sight.
- FIGS. 10( a ) and 10 ( b ) represents the tracking performance of target normal relative velocity.
- FIG. 11 represents the tracking performance of target normal acceleration.
- FIG. 12 represents the interception geometry in the vertical plane.
- FIG. 13 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 0.6 Hz.
- FIG. 14 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 0.8 Hz.
- FIG. 15 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.0 Hz.
- FIG. 16 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.25 Hz.
- FIG. 17 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.5 Hz.
- FIG. 18 represents the comparison of target and interceptor accelerations.
- FIG. 19 represents attitude quaternion parameters errors
- FIG. 20 represents autopilot angle errors
- FIG. 21 represents attitude rate errors
- FIG. 22 represents multiplicative disturbances applied upon the actuators.
- FIG. 23 represents the comparison between normalized pitch and actual responses thereof.
- the present invention relates to the control of missile trajectories homing to collide with a maneuvering target.
- Missile considered includes a seeker with its associated process used for keeping the seeker pointed in the direction of the target and for estimating target motion; guidance law which calculates commanded acceleration conducive to interception and an automatic pilot process which translates the commands into adequate actuator commands.
- the missile is equipped with Inertial Navigation Sensors (INS) and their associated process that calculates interceptor kinetics, attitude and attitude rate which is outside the scope of this invention.
- INS Inertial Navigation Sensors
- the system achieves perfect robustness of the design as long as the disturbances are within bounding conditions.
- the system allows to not representing explicitly part of system dynamics thereby enabling significant architectural simplifications.
- the system as a non-linear control method can generate either continuous commands to continuous actuators such as control surfaces or to on-off discontinuous actuators without major design changes and loss of performance.
- the system achieves finite time convergence, the effect of which is that when nested loops are used, the convergence of the inner loop makes it to become an identity as seen from the outer loop, which as a beneficial impact on reducing the settling time of control loops.
- Higher Order Sliding mode Control allows implicit compensation for disturbing effects such as bending modes or minor orienting motors bias and random walk.
- the usage of higher order sliding mode control techniques allows to implicitly compensating for terms disturbing the guidance law, and in particular the effects of target acceleration or errors in the estimation thereof.
- FIG. 1 illustrates an exemplary missile to be controlled by the control system of the present invention.
- FIG. 1 shows an interceptor 102 having divert thrusters 104 , attitude thrusters 106 , and thrust vector control (TVC) 108 , wherein the primary acceleration thrust 122 may be directed off axis 109 at a thrust vectoring angle 124 .
- the divert thrusters typically apply divert thrust 116 or 114 at or near the center of gravity (CG) of the interceptor to cause a lateral divert motion and create a disturbing attitude moment with a maximum magnitude typically less than 10% of the maximum attitude moment achievable by means of attitude controls and thus without substantially affecting the control of the attitude angle of attack 110 .
- the interceptor 102 attitude may be steered by moments created by TVC or by attitude thrusters.
- Divert and attitude thrusters may be proportional control thrusters producing a thrust continuously adjustable between minimum and maximum values; or on-off thrusters that provide full thrust or nothing are typically lower cost.
- Attitude thrusters apply a pitch 120 or yaw 118 moments or alternatively the deflections of TVC deflection or the deflection of aerodynamic surfaces creates a pitch or yaw moment.
- aerodynamic angles 110 produce aerodynamic lift applied at the Center of Pressure (CP) and an aerodynamic moment that combines with the moments generated by the controls.
- the total moment produces angular accelerations around the CG that modify the body axis 109 .
- the sum of lift forces with thruster forces and gravity forces also modify the orientation and magnitude of the velocity vector 111 .
- Aerodynamic angle is the angle between the body axis 109 and the velocity vector 111 .
- the magnitude of acceleration produced by aerodynamic effects can be up to twice the magnitude of the acceleration produced by divert thrusters, but conversely the response time is slower.
- HOSM autopilot allows considerably increasing the total lateral acceleration of the missile while retaining the short response of the divert thruster.
- the present invention utilizes concepts related to sliding mode control to achieve improved control of the missile.
- Sliding mode control is a form of variable structure control where the control structure switches between multiple control laws. Each control law always moves toward the switching condition, which defines the sliding surface.
- High order sliding mode control further improves single order sliding mode control by driving the system not only to zero the sliding surface, but one or more successive time derivatives of the sliding surface. This can provide smooth continuous operation even with the use of discontinuous controls such as switching controls.
- FIG. 2 illustrates the convergence of multiple time derivatives of the sliding surface.
- the system has an initial condition at point 208 .
- FIG. 3 illustrates an exemplary relation of Earth Centered Inertial (ECI) axes and North East Down (NED) axes.
- Earth Centered Inertial frame is composed as follows. They originate from the center of Earth, the first I axis is oriented along the direction of Aries, the third axis K is oriented along the polar line and second axis J forms with the two other an orthogonal frame.
- Earth Center Inertial axes do not rotate with Earth's daily rotation.
- North East Down axes are centered on the vehicle CG.
- the down axis is along the local vertical to the center of Earth, the North axis is parallel to the local meridian G (longitude) and the East axis parallel the local parallel Lat (latitude).
- FIG. 3 illustrates the principle components of each coordinate system. Numerous variations and detail considerations may be included in a complete coordinate system definition.
- FIG. 4 illustrates the relation of NED axes with body axes.
- the first rotation is around the Down axes and is called yaw angle w; the rotation defines an intermediate reference X1, Y1, Down.
- a second rotation around Y1 of the pitch angle ⁇ defines a second intermediate reference X2, Y2, Z2.
- a third rotation around X2 of angle ⁇ leads to the body axes.
- the present invention relates to a missile control system and several subsystems of the missile control system as implemented together or separately. It should be understood that the total system represents at least one embodiment, and that each subsystem comprising the seeker observer block, the guidance block, the attitude command block, and/or the autopilot block may be used separately or in combination with one or more of the other blocks and may be used in combination with conventional blocks replacing one or more of the other blocks. As should be understood by the following disclosure that certain synergistic benefits and efficiencies may be achieved by combining two or more of the blocks herein described.
- FIG. 5 is a functional block diagram of an exemplary missile control system in accordance with the present invention.
- the missile control system 500 comprises the seeker observer 502 , the guidance 504 , the attitude command 506 , and the quaternion autopilot 508 .
- the autopilot 508 controls the vehicle control actuators of an interceptor 510 (alternatively referred in its terminal autonomous configuration as a kill vehicle (KV)).
- Typical control actuators include but are not limited to lateral thrusters, attitude thrusters, thrust vector control servos (TVC) and other devices.
- the interceptor 10 then responds according to a kinematic response, which may include aerodynamic responses.
- the kinematic response is measured by Inertial Navigation System (INS) 512 .
- INS Inertial Navigation System
- the INS comprises Inertial Measurement System (IMS); a set of gyroscopic and accelerometer sensors and possibly other sensors and a set of processes combining the measurements of said sensors for calculating interceptor position, velocity, and attitude to the attitude command block 506 and body attitude and roll rates to the autopilot 508 .
- IMS Inertial Measurement System
- Estimated interceptor positional and angular dynamics are used in seeker 502 .
- the missile control system main functional blocks are:
- the seeker observer block 502 performs the estimation of the target-interceptor relative motion as well as steering of the bore-sight line in the target direction in an integrated fashion that considerably reduces seeker noise effects.
- Block 502 uses seeker measurement of target angular error with respect to bore-sight, and interceptor body rate measurements bore-sight direction and estimations by the interceptor Inertial Measurement Unit (IMU) of its position, velocity, and acceleration.
- IMU Inertial Measurement Unit
- Block 502 includes an observer that estimates the components of target relative location parallel and perpendicular to the bore-sight, as well as the corresponding components of target velocity and acceleration.
- the inputs are the outputs of observer block 502 .
- the Guidance block 504 calculates commanded normal and transversal acceleration.
- the guidance block 502 has access to target range and range rate either through uplinks and dead-reckoning or with range sensors.
- Attitude Command Block 506
- the attitude command block 506 calculates the prescribed transformation matrix from body frame to reference frame used (i.e., ECI). Two modes are considered. In the boosting mode, changes in body attitude are commanded to achieve desired normal/transverse acceleration. This mode is also used during Kill Vehicle, KV flight when there is enough dynamic pressure to achieve substantial divert acceleration. The second mode aligns the body with the velocity frame during KV autonomous flight when the dynamic pressure is too small or any other prescribed body attitude with respect to interceptor velocity.
- the commands generated are the prescribed quaternion representing the rotation from reference axis to the body axes, the associated transformation matrix, its time-derivative, and the prescribed attitude rate in body axes.
- the autopilot 508 steers the body attitude as prescribed and commanded by the attitude command block 506 .
- the quaternion error is used to calculate attitude errors (referred to as “integral errors”).
- integrated errors referred to as “integral errors”.
- PWM Pulse Width Modulated
- TVC Thrust Vectoring Commands
- KV endgame three roll, pitch and yaw on-off attitude thrusters are used.
- the same autopilot is used during boost and KV endgame. The only difference is that control of the TVC continuous actuators used in the boost phase whereas the control of on-off thrusters during the KV endgame they applied to on-off thrusters.
- INS Inertial Navigation System
- ⁇ circumflex over (Q) ⁇ ECI body ⁇ circumflex over (Q) ⁇ M estimated value of the quaternion defining body attitude with respect to reference, and estimated attitude rate ⁇ circumflex over ( ⁇ ) ⁇ M , represented by 524 .
- a feature of this design is that during the KV flight the guidance block generates the commands 522 for the divert thrusters using the inputs 514 from the seeker. At the same time the guidance block generates an attitude command 518 that will result in the autopilot commanding attitude thrusters to assist the divert thrusters through aerodynamic lift effects.
- This assistance effect is handled by the guidance algorithm as a bounded “cooperative” disturbance relative to the control command 522 for the divert thrusters.
- the invariance property of the HOSM controller design to matched disturbance allows the guidance control to take into consideration the effects of this “cooperative disturbance” without having to estimate the effect explicitly as conventional control techniques require.
- a collision condition refers to the combined velocity and direction of the interceptor and target such that, without further control of the interceptor or maneuver of the target, the two will remain on a collision course.
- the guidance objective is to first guide to a collision condition and then to maintain the collision condition to intercept in the presence of disturbances.
- the control command is issued directly from the guidance to the divert thrusters in a more efficient way than proposed in previous works [15-16] where a commanded trajectory is calculated from the guidance command, where a trajectory autopilot tracks that intermediate trajectory command and generates direct actuator commands
- FIG. 6A illustrates an exemplary interceptor 602 with a seeker configured with a fixed mirror 604 and a rotating minor 606 .
- Two types of seeker mounts are typically used in a missile; the first one places the seeker sensor, i.e. focal plane array on a gimbaled gyroscopically stabilized platform, the second, strap-down mount employs a rotating minor which reflects the incoming ray from the target onto the focal plane array fixed onto the missile structure as shown in FIG. 6 .
- the objects of FIG. 6A are not necessarily drawn to scale relative to one another.
- the seeker subsystem is severable and may be used alone or in combination with one or more of the other subsystems of the present disclosure.
- Different element of this method either compensate implicitly or explicitly for disturbing terms, the integrated design by accounting for the effects of multiple sources of uncertainty across different elements of the guidance suite, does a better job than a collection of separate designs because it accounts for such effects coherently.
- the focal plane array 608 does not measure directly the target elevation and azimuth angles because the field of view is much too small, but rather measures the offset 610 and 611 of the target from a bore sight line representing the center of the focal plane array as directed by the moving minor 606 .
- Either the gimbaled platform or minor is slewed such as to maintain the spot representing the incoming direction of the rays centered on the focal plane array.
- the exemplary moving minor configuration used in this application represents the more challenging case compared with the gimbaled seeker because the measurements are directly affected by the attitude motion of the interceptor, which makes the technical challenge more difficult.
- Seeker mounted on gyroscopically stabilized platforms or with intermediate minors is not new and this new method is not about a new specific hardware design thereof.
- This method is about a new algorithm for controlling the slewing of the bore-sight in the direction of the target.
- gyroscopic and accelerometer sensors By mounting gyroscopic and accelerometer sensors onto the gimbaled platform one can measure the accelerations and attitude rate to which the gimbaled platform is subjected.
- the angular rate of the platform provided that the target spot is maintained on the center of the focal plane array, can be used by the guidance law.
- the focal plane array rotates with the missile body, and the rotation angle of the mirror 606 is half the angle between the Line of Sight (LOS) 613 and the longitudinal axis 618 of the missile body.
- the rotation of the bore-sight line 612 is then, going to be the sum of the angular rate of the missile body 618 +twice the rotation rate of the minor 606 with respect to the missile body 618 .
- the bore-sight frame is defined as shown FIG. 6A by axes x-bore 612 , y-Bore 614 , z-Bore 616 respectively the bore-sight direction, horizontal vector orthogonal the x-bore and a third vector in the z-plane to for a direct reference.
- axes x-bore 612 , y-Bore 614 , z-Bore 616 respectively the bore-sight direction, horizontal vector orthogonal the x-bore and a third vector in the z-plane to for a direct reference.
- the quaternion representing the transformation from bore-sight-axes/LOS to some reference is represented by:
- the present method applies HOSM control techniques for achieving the combined slewing and estimation of target motion.
- the algorithm achieves:
- attitude and divert thrusters creates longitudinal and rotational accelerations, and thus a very noisy reading for the accelerometers and gyroscopic sensors.
- the proposed design integrates the slewing process and the target acceleration such as to account for those spiky readings in a coherent fashion.
- Kalman Filter has been the preferred control technique used for the last decades.
- the Kalman filter works well when the different components of the dynamic noise and of measurement noise are well known and well modeled.
- the dynamic measurement noise is affected by angular accelerations created by the on-off firing of attitude thrusters that create spiky angular missile body accelerations, creating at the level of the seeker a wide-band noise.
- the seeker slewing is designed to be very fast, but one can anticipate nonetheless that the seeker readings will be contaminated by some of the residual noise.
- the dynamic measurement noise creates a number of problems:
- the present invention includes a seeker subsystem for integrated seeker slewing and target estimation.
- the seeker subsystem includes a Higher Order Sliding Mode observer based on a noise and uncertainty bound that does not include and does not require detailed dynamic state models and noise models and thereby circumvents much of the difficulty discussed above.
- the first element of the method is the design of an estimator that will estimate the bore-sight error and the target relative and absolute motion perpendicular to the bore-sight. Additional related background material may be found in works by Shtessel, Shkolnikov and Levant in Ref 12, Levant in Ref 13.
- the second element is the steering of the platform such as to have the center of the spot representing the target in the focal plane array continuously in the centre thereof.
- a fourth order sliding mode observer is used to estimate target relative velocity orthogonal to boresight and target acceleration perpendicular to boresight in the presence to disturbing attitude motion of said interceptor body without the need for explicit accurate representation of said disturbing effects. This estimation is achieved by
- the Lipshitz constant L must bound ⁇ (4) the 4 th derivative of the disturbing term, that is
- the outputs of the estimator are ⁇ circumflex over ( ⁇ ) ⁇ (.) the azimuth and elevation components of the bore-sight error, ⁇ circumflex over (V) ⁇ ⁇ (.) represents the components of target relative acceleration perpendicular to bore-sight; ⁇ circumflex over ( ⁇ ) ⁇ (.) T represent the components of target acceleration perpendicular to bore-sight.
- the difference ⁇ circumflex over ( ⁇ ) ⁇ (.) ⁇ ⁇ between measured and estimated bore-sight errors indicates how well the estimation converges.
- unlike Kalman Filter asymptotic convergence the difference goes literally to zero in finite time. Since in this case we have a measurement noise, we expect the residual difference to be significantly under the noise level.
- the bore-sight line is steered by applying torques on the platform or the mirror.
- the mirror dynamics is governed by second order model with a moment of inertia, a dampening term, a spring term and an applied torque. Assuming that the inertial term is small compared to the other terms, we have a transfer function
- FIG. 7 shows pitch 704 and yaw 702 seeker slewing error for a simulated flight. Note that the controller achieves well its objective of driving the bore-sight error into the measurement noise level as shown in FIG. 7 .
- the estimated ( 704 ) and actual slewing errors in azimuth is about 20 micro rad, it increases during the KV segment to 40 micro radians.
- FIG. 8 shows seeker torque 802 driving the seeker moving mirror for a portion of the simulated flight of FIG. 7 .
- the amplitude of the torque varies significantly, during the pulse.
- the pulse widths vary due to the PWM.
- FIG. 9 shows the exemplary simulated tracking performance of target estimated and actual relative position error 902 with respect to bore-sight in the horizontal plane, with pointing errors less than 5 m at the beginning of the interception and decreasing linearly function of the range.
- FIG. 10A and FIG. 10B show the comparison of target true 1002 and ⁇ circumflex over (V) ⁇ ⁇ y estimated 1004 velocity with respect to bore-sight for the exemplary simulated case.
- the HOSM estimation ⁇ circumflex over (V) ⁇ ⁇ y 1004 follows well the true 1002 values.
- the estimator tracks well the relative velocity with velocity errors of few meters/sec.
- FIG. 11 shows the simulated estimation of target transversal acceleration.
- the estimator performs well again regarding tracking of target transversal acceleration â Y T 1102 where estimated acceleration signal 1104 is passed by a second order low pass filter 1106 with a characteristic frequency of 25 rad/sec.
- the total lag is about 100 microseconds.
- the third embodiment is HOSM guidance.
- Guidance is the process that provides acceleration commands to the autopilot process.
- the guidance process begins by generating a guidance strategy.
- the guidance strategy defines the sensor inputs, control outputs and the objectives for each of one or more phases of intercept.
- One exemplary guidance strategy may endeavor to minimize a line of sight rate.
- Another guidance strategy may endeavor to minimize time to intercept.
- Still another guidance strategy may minimize control effort. Any guidance strategy may be used with the present invention.
- a sliding surface for a high order sliding mode control is established to enforce the selected guidance strategy.
- the guidance controller drives the system to the simultaneous sliding condition for the sliding surface and one or more derivatives of the sliding surface, whereupon the simultaneous sliding condition is maintained until intercept, thereby maintaining the guidance strategy until intercept.
- the guidance strategy is to achieve and maintain a collision condition.
- a collision condition is the set of interceptor and target position and velocity states that, without further maneuver, will result in a collision intercept. It is desired to establish a collision condition and thereafter to maintain the collision condition in the presence of disturbances.
- the disturbances may include target maneuvers and system measurement errors and noises.
- system modeling errors resulting from simplification of system design models and control algorithms are included in the total system disturbance budget.
- a high order (second order or higher) sliding mode control law is selected that achieves the high order sliding condition in finite time, i.e., before intercept, in the presence of disturbances less than a Lipschitz bound in accordance with the system disturbance budget.
- the guidance strategy reduces the interceptor maneuver advantage, i.e., minimizes the ratio of interceptor acceleration perpendicular to the bore-sight line over corresponding target acceleration.
- the interceptor only needs to “mimic” target acceleration, that is with a maneuver advantage barely over one.
- This guidance strategy is especially desirable for re-entry intercepts. When re-entry target maneuvers are considered, target maneuverability peaks at the end (lowest altitude for the target), while at this stage interceptor maneuverability is minimum (highest altitude for the interceptor).
- FIG. 12 represents interception geometry in the vertical plane. A similar figure could be easily drawn in the horizontal plane.
- target 1204 and interceptor 1202 velocities are constant, the collision condition may be written as
- PN Augmented Proportional Navigation, where the control Eq. (20) is augmented with estimated value of target acceleration perpendicular to LOS as
- the guidance strategy is defined as:
- ⁇ (.) is defined as a “sliding variable.”
- a Second Order Sliding Mode Controller (SSOMC) control law is used to drive ⁇ (.) , ⁇ dot over ( ⁇ ) ⁇ (.) ⁇ 0 and thereby drive sliding variable to the sliding surface and thus set the missile, into collision condition in finite time and in the presence of unknown bounded disturbance, and where V ⁇ (.) and Z T ⁇ (.) respectively target relative velocity and position with respect to boresight tgo max and tgo min chosen such as to achieve desired reaching time to the collision time and such as to avoid excessive gains close to the origin.
- SSOMC Second Order Sliding Mode Controller
- bounded disturbing term f(t) represents all other dynamical effects; which can be separated into target acceleration and other terms as:
- ⁇ (.) represents the terms other than target acceleration that will be compensated explicitly.
- the smooth control u that drives ⁇ , ⁇ dot over ( ⁇ ) ⁇ 0 (smooth second order sliding mode) in finite time:
- the estimation of target acceleration ⁇ circumflex over ( ⁇ ) ⁇ 2 ⁇ (.) T may be achieved by a smooth observer:
- the target estimation by the seeker ⁇ circumflex over ( ⁇ ) ⁇ 1 ⁇ (.) T is matches better actual target acceleration ⁇ circumflex over ( ⁇ ) ⁇ ⁇ (.) T .
- v ( . ) deadBand ⁇ [ sign ⁇ ( u ( . ) ) + a ⁇ ⁇ sin ⁇ ( ⁇ _ ⁇ ⁇ t ) , b ] ( 29 )
- ⁇ ⁇ ( . ) ⁇ V ⁇ ( . ) tgo min - V ⁇
- Equation (25) can now be written as
- the guidance performance is compared to widely used and proven guidance techniques, namely, PN, APN.
- FIG. 14 is a comparison of simulated target and interceptor accelerations.
- FIG. 14 shows that the interceptor literally “mimics” the target, which means that the interceptor lateral acceleration capability does not outmaneuver the target in order to successfully intercept it.
- HOSM guidance only requires a “maneuver advantage ratio” close to unity.
- the smooth line 1406 represents target acceleration.
- FIG. 15 , FIG. 16 , FIG. 17 show that with maneuvers frequencies 1, 1.25, 1.5 Hz, HOSM miss-distance cumulative distributions 1502 , 1602 , 1702 outperform traditional guidance laws represented by 1504 - 1506 , 1604 - 1606 , 1704 - 1706 by 20-40% probability.
- this shorter-lag unsmooth “Super-Twist” observer causes some degradation in the distribution of small miss-distances ⁇ 0.15 as shown by comparison of curves 1302 - 1402 obtained with the smooth observe Eq. (28) against target maneuvers at 0.6-0.8 Hz compared with curves 1502 - 1602 - 1707 obtained using the “Super-Twist” observer against targets maneuvering at 1-1.25-1.5 Hz.
- the fourth embodiment is HOSM quaternion autopilot.
- the autopilot typically needs to steer the missile attitude to achieve some desired lateral acceleration.
- attitude may be directly commanded.
- Commanded attitude may be a directly commanded attitude such as at launch and shortly thereafter or before impact, or such as to enhance collision effectiveness as this could be done after interceptor booster burn-out and when dynamic pressure is small enough.
- Commanded attitude may be calculated in the autopilot subsystem such to achieve some prescribed lateral acceleration calculated by the guidance.
- Said prescribed lateral acceleration may the primary acceleration command, as this may be the case with an interceptor which divert is solely achieved by aerodynamic lift, orientation of main booster/sustainer body orientation or combination thereof or may be the secondary cooperative disturbance acceleration.
- the relation of the autopilot with other elements of architecture in the present invention can be better understood by examining FIG. 5 .
- the first step of the method is the calculation in the attitude command block 506 of prescribed body attitude represented by a quaternion and the corresponding commanded body attitude rate 518 .
- the second step comprises calculating in the block automatic pilot 508 the three sliding variables, and thereafter the calculation by the HOSM autopilot actuator commands 520 required to driving the three surfaces to zero.
- commanded acceleration from the HOSM guidance are used to calculate the desired angles of attack, in the pitch and yaw planes, taking into consideration the aerodynamic lift gradient and the thrust using
- the pitch and yaw lead angles are calculated as follows. First we calculate the LOS frame. Its first vector I x is the bore-sight direction and the two other axes are calculated by
- rI is the local vertical unit-vector. Then, the velocity frame is calculated with the first vector J x in the direction of the interceptor velocity vector and two other axes calculated by
- the transformation matrix represented desired body attitude is calculated using rotation matrices defined as follows
- T ⁇ ( ⁇ , e ) [ cos ⁇ ( ⁇ ) + ( 1 - cos ⁇ ( ⁇ ) ) e ⁇ ⁇ 1 ⁇ e ⁇ ⁇ 1 ( 1 - cos ⁇ ( ⁇ ) e ⁇ ⁇ 1 ⁇ e ⁇ ⁇ 2 + sin ⁇ ( ⁇ ) e ⁇ ⁇ 3 ( 1 - cos ⁇ ( ⁇ ) e ⁇ ⁇ 1 ⁇ e ⁇ ⁇ 3 - sin ⁇ ( ⁇ ) e ⁇ ⁇ 2 ( 1 - cos ⁇ ( ⁇ ) e ⁇ ⁇ 1 ⁇ e ⁇ ⁇ 2 - sin ⁇ ( ⁇ ) e ⁇ ⁇ 3 cos ⁇ ( ⁇ ) + ( 1 - cos ⁇ ( ⁇ ) ) e ⁇ ⁇ 2 ⁇ e ⁇ ⁇ 2 ( 1 - cos ⁇ ( ⁇ ) e ⁇ ⁇ 3 ⁇
- the axes of the required body attitude are obtained by a first rotation of ⁇ yaw around J z .
- Prescribed roll, pitch and yaw rates can be defined from the time derivative of the prescribed quaternion as
- Introducing the angle error ⁇ I wherein the quaternion attitude errors in a 4 component quaternion space errors (Q* body/(.) ⁇ Q body/(.) ) are mapped to 3 component body axes as:
- each body component being a linear combination of four quaternion components.
- ⁇ represents actual rotation rate in body axes and wherein characteristic frequencies ⁇ p , ⁇ q , ⁇ r are chosen to achieve desired settling time of roll, pitch and yaw.
- Equation (51) projects the 4-vector of sliding variables in quaternion space into a 3-vector of sliding variables in body axes.
- Equation (51) projects the 4-vector of sliding variables in quaternion space into a 3-vector of sliding variables in body axes.
- the dynamics of the sliding variables after the two successive time derivations required to have the control appearing explicitly in the right hand side are represented by:
- [ ⁇ ⁇ p ⁇ ⁇ q ⁇ ⁇ r ] [ g p + b p ⁇ u p g q + b q ⁇ u q g r + b r ⁇ u r ] ( 52 )
- [ ⁇ ⁇ p ⁇ ⁇ q ⁇ ⁇ r ] [ ⁇ p ⁇ ( p . * - p . ) + p ⁇ * - p ⁇ ⁇ q ⁇ ( q . * - q . ) + q ⁇ * - q ⁇ ⁇ r ⁇ ( r . * - r . ) + r ⁇ * - r ⁇ ] ( 53 )
- the third step of the fourth embodiment is the design of the HOSM controller that will drive sliding variables Eq. (50) to zero.
- the attitude motion is achieved using a continuous TVC actuator.
- Related background material may be found in Shtessel, Shkolnikov and Levant in Ref 12, Levant in Ref 13, Shtessel and Tournes in Ref 16.
- We introduce auxiliary Proportional-Derivative surfaces designed to reduce the relative degree, Since the Second Order Sliding Mode controller is designed to operate with systems of relative degree 1.
- ⁇ ′ (.) c ⁇ (.) + ⁇ dot over ( ⁇ ) ⁇ (.) (59)
- the corresponding controller is
- the Lipshitz constant L must be g (.) (2) the 2 nd derivative of the disturbing terms,
- g (.) (2) ⁇ L, (.) p, q, r
- the Nonlinear Filter with Pulse Width Modulation controller is designed directly as
- the four quaternion parameter errors are shown FIG. 19 .
- One can also notice the brief transient at t 55 1902 as the autopilot switches from one mode to the next.
- the quaternion parameter errors are less than 0.001 during most of the flight.
- Attitude angular errors are ⁇ 1.5 mrad.
- Attitude angular rate errors 2102 shown FIG. 217 are also very small; about 1 deg/sec in the first segment they are noisier, about 4 deg/sec during the KV terminal flight segment. The reason is that during this phase lateral divert is achieved by on-off firing of divert thrusters. Each firing creates a brief and large acceleration pulse. Since the divert thrusters are not placed exactly at the center of gravity which moves during the flight, this creates a brief intense moment disturbance.
- the HOSM design of the autopilot does not require values for interceptor control characteristics other than a very broad estimation of the upper bound of the disturbances.
- multiplicative disturbances to the magnitude of the thrusters. Applying this disturbance, as shown in FIG. 22 , it is possible for the maximum magnitude of a thruster to be as some point in time 1.3 times the nominal value and 50 msec after to be 0.8 times this value.
- FIG. 22 shows the multiplicative disturbance 2202 applied to each commanded thruster actuation to simulate a thruster with this degree of unknown thrust. In the inventor's experience, such a rapid and large amplitude variation of the thrust level cannot be estimated in real-time by a disturbance accommodating controller.
Abstract
Description
- This application claims the benefit of U.S.
Provisional Application 61/129,676, titled “High order sliding mode (HOSM) control method,” Filed Jul. 11, 2008, which is incorporated herein by reference in its entirety. - This invention was made with Government support under Contract HQ0006-08-C-7824 awarded by Missile Defense Agency. The Government has certain rights in the invention.
- The present invention relates to the control of missile trajectories homing to collide with a maneuvering target. More particularly, the use of a High Order Sliding Mode (HOSM) control adapted to the control of one or more functional subsystems of the homing missile, including the guidance, seeker, and autopilot subsystems.
- Missile guidance and control has received considerable attention in the last 50 years. Proportional Navigation (PN) and its multiple variants has been the preferred guidance technique. It is unfortunately based on the following assumptions:
- (i) The target has zero acceleration;
- (ii) The interceptor has a perfect dynamic response and perfect control of its acceleration;
- (iii) The interceptor is launched on a near collision condition;
- (iv) The interceptor has no longitudinal acceleration;
- One or more of said assumptions is not applicable in challenging interception situations.
- U.S. Pat. No. 6,244,536 B1 uses a modified formulation of PN called PRONAV and Riccati Equation. While the use of Riccati equation reduces the divert effort, it is predicated on the availability of good state models. U.S. Pat. No. 7,185,844 B2 and also
Ref 1 introduces PN with a so called “parallel” navigation additional term proportional to the cube of the line-of-sight rate and additional term proportional to relative longitudinal acceleration, not easy to estimate very accurately and account for interceptor acceleration. The compensation for such effects is beneficial. Its explicit compensation as proposed in U.S. Pat. No. 7,185,844 B2 is only as good as the estimation/measurement of corresponding terms. In the present invention compensates for such effects without complex modeling of the effects and without being subjected to the effects of possible estimation errors. A number of works have addressed the problem of highly maneuvering targets and proposed solutions that require additional information. The so-called optimal law ofreference 2 is applicable to first order interceptor response, requires good estimation of target maneuver and of tgo (time to go). Neoclassical Guidance inreference 3 does not require estimating target acceleration and tgo, but since it is based on adjoint techniques, it requires a good dynamical model of the interceptor flight control system and does not apply to the case of dual concurrent lateral controls. The claim that Neoclassical Guidance can force Zero Miss distance (ZMD) against any bounded target maneuver is questioned in Ref. 4.Reference 5 includes in the observer a set of maneuver patterns that enhance the prediction of target kinematics and a method based on differential game theory to adjust the gains of the guidance. The degree to which actual target maneuvers must “match” the models makes this approach not very realistic. The quest for better prediction of target maneuvers in Ref. 6 leads to use banks of filters with typical maneuvers and maneuver detectors. Here the problem is that the detection of a maneuver of change thereof takes some time if one wants to have enough confidence in the decision made and also the “mathematical” separation of the maneuvers may not be evident. The use of a Kalman Filter transition matrix with a ZEM based guidance in Ref. 7 helps in reducing the effects of delays but is only applicable for longer range exo-atmospheric guidance. - Kalman Filtering has been a technique of choice for estimating target motion. While it produces good estimations, its relatively slow convergence may cause it to be ineffective at the end-game when rapid target maneuvers are encountered.
Reference 8 showed that Higher Order Sliding Mode Observers can provide faster and yet more accurate estimations than traditional Kalman Filter. - To be effective, a guidance law must be supported by a good autopilot. Most autopilot design are based on classical control techniques or on state feedback techniques that rely on internal mathematical models are only as good as the internal models. Further, the internal models are more and more expensive and difficult to develop as the domain of utilization of the missiles becomes larger and larger and as the accuracy is more than often questionable, which then degrades the accuracy of the guidance and control (G&C). Their validation using wind tunnels is also becoming increasingly difficult due to the cost of the energy required for simulating missile flights in the atmosphere at several thousand of meters per second. Most of the numerical codes calculating the flow around the missile and most of the wind tunnel experiments simulate steady state conditions that is, their governing equations do not include or model partial derivatives with respect to time. This assumption was reasonable up to now but is becoming increasingly questionable as missile with greater and greater agility and shorter time constants are designed. Working with non steady state computational fluid codes of designing non-steady state wind tunnel experiments increases dramatically the difficulty in generating realistic missile models. Thus, there is a need for more robust control systems and methods that are tolerant of complex and unpredictable interactions and adapt to changing dynamics resulting from effects such as hypersonic aerodynamics and interactions. Such hypersonic effects are described in Ref. 9. Such robust control must be able to work with nonlinear thrusters, to be insensitive to model variations caused by variations of altitude, mass, center of gravity, and other effects difficult to model or predict and that by not being dependent of missile specific mathematical model to allow a greater reuse of previous designs on new missiles.
- U.S. Pat. No. 6,532,454, B1 uses adaptive techniques to estimate an interceptor model. While this approach works well when given enough time for the estimation process to settle, it cannot handle the case where rapid disturbances are created by the interaction between the firing of thrusters and the aerodynamic flow around the missile as described in Ref. 9. Another important issue is to achieve interceptor maneuverability as large as possible. This calls for operations in the endo-atmospheric domain for combined operation of several divert mechanisms, possibly several control surfaces. U.S. Pat. RE37,331 E where a forward placed thruster and tail (fin control) are used jointly to initiate a lateral maneuver faster and without non-minimum phase effects. One of the potential problems associated with this approach is that it requires accurate estimation of lateral divert and angular motion effects of each control that are by definition not measurable separately. A similar approach is described in
Reference 10 where a dual control missile is fitted with the canard, primarily used to achieve the miss-distance and the tail for “trimming” the pitch attitude; the two surfaces are controlled with first order sliding mode controls approximated by high gain saturation which unfortunately cause the controllers to lose some of their robustness. U.S. Pat. No. 6,341,249 control satellite attitude using a Lyapunov Controller or a first order sliding mode controller. A short fall associated with the use of first order sliding mode control is that it achieves its robustness by high frequency (infinite switching rate) or eventually can be approximated by a sub-performing high gain approximation. Reference 11 proposes a Multiple Input Multiple Output solution to steer the angle of attack and pitch rate to satisfy a Lateral acceleration condition. It uses a Variable Structure Solution; unfortunately, it uses Euler Angles and its generalization to a Quaternion solution would be very difficult. U.S. Pat. Nos. 6,611,823 B1 and 7,080,055 B2 both address the problems associated with actuator nonlinearities as encountered with on-off thrusters and come up with complex neural network solutions requiring some “learning” hardly an option with missile systems. - Thus, there is a need for more robust control systems and methods that are tolerant of complex and unpredictable interactions and adapt to changing dynamics resulting from effects such as hypersonic aerodynamics and interactions
- High Order Sliding Mode (HOSM) control techniques are applied to the Guidance Control (G&C) of a interceptor missile in which velocity may be steered by combination of main thrust, aerodynamic lift and lateral on-off divert thrusters, and attitude may be steered by either continuous or by on-off actuators. Methods include the pointing of the seeker, its associated estimation processes, a guidance law that uses concurrent divert mechanisms, and an attitude autopilot. The insensitivity of the controller to matched disturbances allows the concurrent usage of the divert mechanisms without adverse effect on the accuracy. The controller also allows the de-coupling of the control of roll, pitch and yaw channels, and quaternions to represent body attitude and it provides control perfect robustness. While it is conceivable to design separately the components of the G&C method, it is widely accepted that designing them in an integrated fashion usually produces a better result.
- The guidance and control methods of the present invention are applied to a very challenging missile configuration. For one, the interception can take place in the exo-atmospheric domain, after the end of boost with lateral divert accelerations being achieved by the firing of on-off divert thrusters. Further, the interception can occur while still boosting. In such case, lateral divert accelerations are achieved by orienting the missile body with respect to the velocity, and in such case when the interception occurs in the endo-atmospheric domain, lateral acceleration also includes aerodynamic lift. Likewise interceptor attitude, during autonomous Kill-Vehicle flight can be steered by the firing of on-off attitude thrusters and during the boost phase by the continuous TVC control or aerodynamic control surfaces. The methods presented can also be applied to simpler missile configurations operating in a single exo vs. end atmospheric domains.
- A good example of this type of problem is the interaction of aerodynamic flow with divert attitude control thrusters placed on the sides of the missile as shown in
FIG. 1 . The jet flow coming out of the thrusters creates an obstacle to the airflow, thereby modifying the system of shock waves around the body and thus, aerodynamic forces. Conversely, thruster flow expansion, governed by the external pressure will differ different depending whether or not thrusters are being fired. These interactions may affect aerodynamic lift up to 30% in relative term and the effective forces of the thrusters by similar amount as indicated in the work of Kennedy9 (Ref. 9.) Typical durations of thruster firing of 10-20 msec show that the effect is clearly a non-steady state effect. - Sliding Mode Control of rth order is said to exist if σ, {dot over (σ)}, . . . σ(r−1)→0 in finite time and stay there thereafter. The sliding variable and its derivatives up to σ(r−1) are continuous as illustrated by
FIG. 2 . Higher Order Sliding Mode Control laws are based on the property that some families of differential equations converge to zero in the presence of bounded right hand side of the equations as exemplified hereafter by the so called “super-twist” algorithm. -
{dot over (x)}+ω 1 |x| 1/2sign(x)+ω 2∫sign(x)dτ=ξ(t) (1) - One can demonstrate that x,{dot over (x)}→0 converge to the origin in finite time in the presence of unknown and bounded right-hand side term ξ(t). The terms
ω 1,ω 2 are calculated based on the upper bound |{dot over (ξ)}(t)|≦L of the first time derivative of the unknown right-hand side term as -
- The finite convergence time {tilde over (t)}r is given by
-
- The design of a control law can then proceed as follows. The dynamics of the sliding surface is represented as
-
σ(n) =f(y,t)+d−bu (4) - where f(y,t) represents the nominal response other than caused by control term bu and d represents the effects of unknown disturbances and (n) represents the relative degree of the sliding surface dynamical model that is, the number of successive time-differentiation required for the control term to appear explicitly in the right-hand side.
The algorithm used as example, shown here applies to systems of relative degree n=1. Finally using the insensitivity property discussed before it is possible to treat the combined effects of f(x,t)+d as the disturbing term ξ(t) in Eq. (3) and to design accordingly the continuous control as -
u=ω 1|σ|1/2sign(σ)+ω 2∫sign(σ)dτ (5) - This means that one can design an accurate control with required knowledge of the plant barely limited to the so called Lipchitz bounding constant L in Eq. (2) and the approximate knowledge
b of term b in Eq. (3). With b=b +{tilde over (b)} one can rewrite Eq. (3) as -
{dot over (σ)}=f(y,t)+d−{tilde over (b)}u−b u (6) - and treat the term {tilde over (b)}u as part of the disturbing term f(y,t)+d−{tilde over (b)}u.
Higher Order Sliding Mode Control is able to drive the sliding variable and its n−1 consecutive derivative to zero in finite time while the sliding variable dynamics given by a generalized version of eq. (4) that uses a differential inclusion terminology: -
σ(n) ε[−C,C]−[K m ,K M ]u - where |f(y,t)+d|≦C and Km≦b≦KM, C>0, 0<Km<KM.
Higher Order Sliding Mode control techniques represent a paradigm shift, in the sense that -
- 1. HOSM is an output control technique that does not rely on a dynamical model of the system's response and as such is perfectly robust.
- 2. The gain are based on inequality relations, therefore the control works perfectly as long as the magnitude of the disturbing term is within the bounds used to calculate the gains as per Eq. (2).
- A first important contribution of this invention is to allow concurrent use of various divert mechanisms such the firing of lateral divert thrusters, aerodynamic lift, main booster/sustainer by orienting the missile body. When several divert mechanisms and conventional control techniques are used the two main possible approaches are:
-
- 1. Nested control loops where the outer-loop set the effect to be produced and the inner loop manages to achieve that effect. For example an outer; guidance loop will calculate the commanded lateral acceleration and calculate the required angle of attack required. The inner loop will track said angle of attack. It is a good design practice to have the characteristic frequency(ies) of inner loop to have a magnitude at least three times the magnitude of outer-loop characteristic frequencies. Since inner loops responses are inevitably limited, this staging adversely affects the response of the outer-loop.
- 2. Multiple input-Multiple Output (MIMO) designs are organized with a single multiple variable feedback but require modal decompositions the accuracy of which becomes questionable as the order of the system exceeds 5-6 even with good models and are very strongly adversely affected by model errors.
Here by concurrent use of several divert mechanisms we mean that two control loops controlling separate divert mechanisms can be designed independently one from another, and yet achieve effective cooperative operation of the diverts, with their responses not being hampered by the necessary staging of the eigenvalues in nested loops or by the robustness issues of large MIMO designs
- Control techniques require the number of inputs, i.e. controlled variables and outputs, i.e. actuator command to be the same. With conventional control methods, when several divert mechanisms are used concurrently to achieve lateral divert acceleration, it is necessary to design separate control laws, one per independent divert mechanism, yet there only one output available which is the lateral acceleration. The usual remedy, is to include internal models that estimate, in real-time, what is the contribution of each divert mechanism. For example when aerodynamic lift and divert thrusters are used, the internal model will estimate what would have been the lateral acceleration produced by aerodynamic lift, had it been used alone. In practice this is difficult because those are transient response models and in most of the case divert responses are not de-coupled as discussed before. Evidently, failure to account exactly for the effects of each actuator will have a strong adverse effect on control accuracy and may even lead to unstable conditions.
- In one embodiment of the invention, the missile commanded acceleration may be achieved using combination more than one of divert mechanisms such as orientation of main/sustainer thrust with respect to velocity vector, aerodynamic lift and divert thrusters. Setting several sets of actuators (control outputs) to achieve a single input (guidance law) requires when conventional control techniques to have accurate explicit knowledge of the effects of each set of actuators and to set a control allocation strategy. The usage of higher order sliding mode control allows overcoming this limitation. For that matter one the divert mechanisms is defined as the primary control. The choice of primary control is based on the response time of said control, the smallest the better and requires said control for achieving a sufficient share of total control effort, typically larger than ⅓; in a missile application the divert thrusters is the preferred choice.
- The present HOSM method, illustrated hereafter allows using several divert mechanisms without resorting to complicated and eventually uncertain model, without any loss of performance and with a much simpler architecture.
- The interception strategy (for the pitch and the yaw channels) is represented by a sliding surface function of several variables that must be steered to zero and kept null thereafter.
-
{dot over (σ)}(.) =f (.) +g (.) −bΔ (.); (.)=pitch, yaw (7) - where f(.) is a function that will be compensated explicitly and g(.) a bound unknown disturbance to be compensated implicitly and Δ(.) represent the command of divert thrusters (assumed to be continuous in this illustration for simplicity sake). The use of HOSM technique gives the designer considerable latitude in the choosing of which terms should be compensated explicitly and which should be compensated implicitly. It is possible to have all the effects compensated implicitly in which case f(.)=0 or conversely try to model or estimate all the effects, for them to be compensated implicitly, in such case the g(.) will only compensate for {tilde over (f)}(.)=f(.)−{circumflex over (f)}(.) the estimation errors of f(.).
- The direct smooth guidance law based on another family of HOSM differential equations is given by:
-
- Where
b represents the estimated maximum dynamical effect of normalized divert control Δ(.). At the same time attitude command δ(.)=h(bΔ(.)), function of desired acceleration is applied to the autopilot producing acceleration ΔΓ(δ(.)).
Equation (7) can be written as -
{dot over (σ)}(.)+α1|σ(.)|2/3sign(σ(.))+α2∫|σ(.)|1/3sign(σ(.))dτ=ξ(t)(.) (9) - Equation (9) represents another family of differential equations that guarantees simultaneous convergence of σ(.),{dot over (σ)}(.)→0 in the presence of bounded unknown right hand side term, provided that α1, α2 have been selected taking in to consideration the bounding condition for the derivative of the disturbing term ξ(t)(.).
-
ξ(t)(.) =g (.)−ΔΓ(.) +{tilde over (f)} (.) (10) - The right side disturbance equals the initial disturbance g(.)+the estimation error {tilde over (f)}(.)=f(.)−{circumflex over (f)}(.) minus ΔΓ(.), the effect of the attitude maneuver.
- This shows that additional divert mechanisms (the orientation of the main thrust and possibly aerodynamic lift reduce the magnitude of the disturbance |ξ(.)|<|g(.)| thereby permitting effective guidance that may not have been achievable solely with divert thrusters.
- Stated alternatively, such secondary control in
claim 3 creates a “cooperative” disturbance that reduces the initial magnitude of the bound disturbance as -
g 2 (.) =g (.)−ΔΓ(.) - Allowing engaging targets engaging in lateral acceleration exceeding maximum divert capability
b achievable by principal control alone. The cooperative disturbance needs not to be calculated to match exactly commanded acceleration nor do inaccuracies thereof have any adverse effect on the performance accuracy of the guidance. The response time of cooperative disturbance needs not match the dynamics of the target maneuver as this is the case when aerodynamic lift is used as secondary control and slower response thereof has no adverse effect on the performance accuracy of the guidance. - A second important contribution of this invention is the slewing of the bore-sight and design of associated HOSM based estimators of the target motion that provides shorter settling times than traditional Kalman Filters together with better accuracy.
- A third contribution of the present invention is a method for guiding the missile. Most missile guidance is based on some form of Proportional Navigation (PN) or some of its derivatives such as Augmented Proportional Navigation (APN) or Zero Effort Miss (ZEM) that are based on assumptions discussed before.
- The proposed method consists in regulating a linear combination of the target relative position error perpendicular to the bore-sight and the corresponding velocity conducive to setting the interceptor in collision course in a prescribed time using a HOSM control law which, by its inherent insensitivity to matched disturbances, also compensates implicitly for other uncertainties and alleviates the need for additional explicit terms accounting inter-alia for the variation of interceptor longitudinal velocity.
- A fourth contribution of the invention is the HOSM quaternion based autopilot. The interceptor considered has two modes: the first mode during boost phase where attitude motion is steered by continuous TVC control, and the second mode used during autonomous KV flight where attitude is controlled by the on-off firing of PWM attitude thrusters. Clearly the methods could apply to a missile only operating with one type of attitude control. The use of quaternions avoids using Euler Angles. A first inconvenient of Euler Angles is their singularity of pitch angle θ=±π/2 encountered with vertical launches. Another inconvenient their coupling, whereas a pitch torque only creates a pitch acceleration, but roll or yaw torques create roll, and yaw accelerations.
- Liquid thrusters can be continuously throttled from a minimum to a maximum value. Solid thrusters are preferred, in many applications for their easier handling and storage. Their simpler mode of operation is on-off. Several seconds before intercept a gas generator is ignited which produces. The gas can be ejected through several valves, the opening and closing thereof is defined according to the direction in which the force must be produced, typically up/down, left/right. In the case where no force is required the four valves are opened simultaneously. This is an on-off operating mode, which is PWM modulated by the duration of the opening sequence.
- With conventional control techniques and on-off thrusters, a continuous control law is first designed assuming that proportional continuous thrusters are used. The continuous control law is then re-designed to be used with on-off thrusters. For that matter the redesigned on off law is designed to produce equivalent effects than the original continuous law. Said “equivalent” law is predicated on “ideal” rectangular pulses. The departure from this assumption leads to severe degradation of performance accuracy or even to the control stability. In practice with short thruster firings, actual thruster accelerations are far from their predicated “ideal” shapes and thus, such PWM control laws exhibit poor performance.
- In order to overcome this hurdle, continuous throat able solid thrusters have been developed in particular by Aerojet Corp. Since the thrusters have to produce a thrust proportional to the command, with good scale and linearity performance, their design is significantly more complex than the simpler on-off design presented before. Owing to its nonlinear nature HOSM control works equally well with on-off actuators as with continuous actuators and allow usage of simpler and much less expensive thrusters without sacrificing performance.
- The present invention has application in endo and exo-atmospheric and combined endo & exo-atmospheric missiles.
- The present invention is described with reference to the accompanying drawings. In the drawings, like reference numbers indicate identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears.
-
FIG. 1 illustrates an exemplary missile to be controlled by the control system of the present invention. -
FIG. 2 illustrates the convergence of multiple time derivatives of the sliding surface. -
FIG. 3 illustrates the relation of Earth Centered Inertial (ECI) axes and North East Down (NED) axes. -
FIG. 4 illustrates the relation of NED axes with body axes. -
FIG. 5 illustrates control architecture in accordance with the present invention. -
FIG. 6A illustrates an exemplary seeker configured with a fixed and rotating mirror. -
FIG. 6B illustrates an exemplary dither signal applied to the Pulse Width Modulation. -
FIG. 7 represents exemplary azimuth bore-sight pointing error for a simulated seeker subsystem in accordance withFIG. 6A . -
FIG. 8 represents exemplary pulse width modulated torques applied to the intermediate mirror ofFIG. 6A . -
FIG. 9 represents the target lateral distance with respect to bore-sight. -
FIGS. 10( a) and 10(b) represents the tracking performance of target normal relative velocity. -
FIG. 11 represents the tracking performance of target normal acceleration. -
FIG. 12 represents the interception geometry in the vertical plane. -
FIG. 13 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 0.6 Hz. -
FIG. 14 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 0.8 Hz. -
FIG. 15 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.0 Hz. -
FIG. 16 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.25 Hz. -
FIG. 17 represents the comparison of HOSM guidance with conventional guidance for target maneuvers at 1.5 Hz. -
FIG. 18 represents the comparison of target and interceptor accelerations. -
FIG. 19 represents attitude quaternion parameters errors -
FIG. 20 represents autopilot angle errors -
FIG. 21 represents attitude rate errors -
FIG. 22 represents multiplicative disturbances applied upon the actuators. -
FIG. 23 represents the comparison between normalized pitch and actual responses thereof. - The present invention relates to the control of missile trajectories homing to collide with a maneuvering target. Missile considered includes a seeker with its associated process used for keeping the seeker pointed in the direction of the target and for estimating target motion; guidance law which calculates commanded acceleration conducive to interception and an automatic pilot process which translates the commands into adequate actuator commands. The missile is equipped with Inertial Navigation Sensors (INS) and their associated process that calculates interceptor kinetics, attitude and attitude rate which is outside the scope of this invention. Up to now the laws controlling different processes where designed taking into consideration or included internal mathematical models of the dynamic response of the process; and the performance of the control law was only as good as the model. The present invention is based on the use of a novel control technique, called Higher Order Sliding Mode control HOSM), that allows circumventing therein the use of said mathematical models which are difficult and expensive to develop.
- In accordance with the present invention, multiple benefits and features are realized including:
- The system achieves perfect robustness of the design as long as the disturbances are within bounding conditions.
- The system allows to not representing explicitly part of system dynamics thereby enabling significant architectural simplifications.
- The usage of higher order sliding mode control techniques allows treating terms of the interceptor attitude dynamic response as unknown bounded disturbances and thereby avoiding the development of complex and error prone non-linear coupled dynamical models.
- The system as a non-linear control method can generate either continuous commands to continuous actuators such as control surfaces or to on-off discontinuous actuators without major design changes and loss of performance.
- The system achieves finite time convergence, the effect of which is that when nested loops are used, the convergence of the inner loop makes it to become an identity as seen from the outer loop, which as a beneficial impact on reducing the settling time of control loops.
- The usage of higher order sliding mode control techniques allow concurrent usage of multiple divert mechanisms without a complex control coordination strategy.
- The usage of higher order sliding mode control techniques allows controlling attitude motion either using continuous actuators such as thrust vectoring or aerodynamic control surfaces of on-off discontinuous actuators with minor design modifications and without loss of accuracy performance.
- The usage of Higher Order Sliding mode Control allows implicit compensation for disturbing effects such as bending modes or minor orienting motors bias and random walk. The usage of higher order sliding mode control techniques allows to implicitly compensating for terms disturbing the guidance law, and in particular the effects of target acceleration or errors in the estimation thereof.
-
FIG. 1 illustrates an exemplary missile to be controlled by the control system of the present invention.FIG. 1 shows aninterceptor 102 having divert thrusters 104,attitude thrusters 106, and thrust vector control (TVC) 108, wherein the primary acceleration thrust 122 may be directed offaxis 109 at a thrust vectoring angle 124. The divert thrusters typically apply divert thrust 116 or 114 at or near the center of gravity (CG) of the interceptor to cause a lateral divert motion and create a disturbing attitude moment with a maximum magnitude typically less than 10% of the maximum attitude moment achievable by means of attitude controls and thus without substantially affecting the control of the attitude angle ofattack 110. Theinterceptor 102 attitude may be steered by moments created by TVC or by attitude thrusters. Divert and attitude thrusters may be proportional control thrusters producing a thrust continuously adjustable between minimum and maximum values; or on-off thrusters that provide full thrust or nothing are typically lower cost. - Attitude thrusters apply a pitch 120 or yaw 118 moments or alternatively the deflections of TVC deflection or the deflection of aerodynamic surfaces creates a pitch or yaw moment. When the dynamic pressure is sufficient,
aerodynamic angles 110 produce aerodynamic lift applied at the Center of Pressure (CP) and an aerodynamic moment that combines with the moments generated by the controls. The total moment produces angular accelerations around the CG that modify thebody axis 109. The sum of lift forces with thruster forces and gravity forces also modify the orientation and magnitude of thevelocity vector 111. Aerodynamic angle is the angle between thebody axis 109 and thevelocity vector 111. - In general with sufficient dynamic pressure, the magnitude of acceleration produced by aerodynamic effects can be up to twice the magnitude of the acceleration produced by divert thrusters, but conversely the response time is slower. HOSM autopilot allows considerably increasing the total lateral acceleration of the missile while retaining the short response of the divert thruster.
- The present invention utilizes concepts related to sliding mode control to achieve improved control of the missile. Sliding mode control is a form of variable structure control where the control structure switches between multiple control laws. Each control law always moves toward the switching condition, which defines the sliding surface. High order sliding mode control further improves single order sliding mode control by driving the system not only to zero the sliding surface, but one or more successive time derivatives of the sliding surface. This can provide smooth continuous operation even with the use of discontinuous controls such as switching controls.
-
FIG. 2 illustrates the convergence of multiple time derivatives of the sliding surface.FIG. 2 illustrates a states space with a first hyper-plane sliding surface 202 representing σ=0, second hyper-plane sliding surface representing {dot over (σ)}=0 and possible additional surfaces representing σ(2)=0, . . . σ(n)=0, the intersection of the sliding variables is theline 206 that represents σ={dot over (σ)}=0. The system has an initial condition atpoint 208. The control structure drives simultaneously σ, {dot over (σ)}, σ(2)=0, . . . σ(n)→0 to 212 whereupon the simultaneous solution is maintained thereafter in the presence of unknown, bounded disturbances. -
FIG. 3 illustrates an exemplary relation of Earth Centered Inertial (ECI) axes and North East Down (NED) axes. Earth Centered Inertial frame is composed as follows. They originate from the center of Earth, the first I axis is oriented along the direction of Aries, the third axis K is oriented along the polar line and second axis J forms with the two other an orthogonal frame. Earth Center Inertial axes do not rotate with Earth's daily rotation. North East Down axes are centered on the vehicle CG. The down axis is along the local vertical to the center of Earth, the North axis is parallel to the local meridian G (longitude) and the East axis parallel the local parallel Lat (latitude).FIG. 3 illustrates the principle components of each coordinate system. Numerous variations and detail considerations may be included in a complete coordinate system definition. -
FIG. 4 illustrates the relation of NED axes with body axes. One can note that the first rotation is around the Down axes and is called yaw angle w; the rotation defines an intermediate reference X1, Y1, Down. A second rotation around Y1 of the pitch angle Θ defines a second intermediate reference X2, Y2, Z2. A third rotation around X2 of angle φ leads to the body axes. - The present invention relates to a missile control system and several subsystems of the missile control system as implemented together or separately. It should be understood that the total system represents at least one embodiment, and that each subsystem comprising the seeker observer block, the guidance block, the attitude command block, and/or the autopilot block may be used separately or in combination with one or more of the other blocks and may be used in combination with conventional blocks replacing one or more of the other blocks. As should be understood by the following disclosure that certain synergistic benefits and efficiencies may be achieved by combining two or more of the blocks herein described.
-
FIG. 5 is a functional block diagram of an exemplary missile control system in accordance with the present invention. Referring toFIG. 5 , themissile control system 500 comprises theseeker observer 502, theguidance 504, theattitude command 506, and thequaternion autopilot 508. Theautopilot 508 controls the vehicle control actuators of an interceptor 510 (alternatively referred in its terminal autonomous configuration as a kill vehicle (KV)). Typical control actuators include but are not limited to lateral thrusters, attitude thrusters, thrust vector control servos (TVC) and other devices. Theinterceptor 10 then responds according to a kinematic response, which may include aerodynamic responses. The kinematic response is measured by Inertial Navigation System (INS) 512. The INS comprises Inertial Measurement System (IMS); a set of gyroscopic and accelerometer sensors and possibly other sensors and a set of processes combining the measurements of said sensors for calculating interceptor position, velocity, and attitude to theattitude command block 506 and body attitude and roll rates to theautopilot 508. Estimated interceptor positional and angular dynamics are used inseeker 502. - The missile control system main functional blocks are:
- The
seeker observer block 502 performs the estimation of the target-interceptor relative motion as well as steering of the bore-sight line in the target direction in an integrated fashion that considerably reduces seeker noise effects.Block 502 uses seeker measurement of target angular error with respect to bore-sight, and interceptor body rate measurements bore-sight direction and estimations by the interceptor Inertial Measurement Unit (IMU) of its position, velocity, and acceleration.Block 502 includes an observer that estimates the components of target relative location parallel and perpendicular to the bore-sight, as well as the corresponding components of target velocity and acceleration. - The inputs are the outputs of
observer block 502. TheGuidance block 504 calculates commanded normal and transversal acceleration. Theguidance block 502 has access to target range and range rate either through uplinks and dead-reckoning or with range sensors. - The
attitude command block 506 calculates the prescribed transformation matrix from body frame to reference frame used (i.e., ECI). Two modes are considered. In the boosting mode, changes in body attitude are commanded to achieve desired normal/transverse acceleration. This mode is also used during Kill Vehicle, KV flight when there is enough dynamic pressure to achieve substantial divert acceleration. The second mode aligns the body with the velocity frame during KV autonomous flight when the dynamic pressure is too small or any other prescribed body attitude with respect to interceptor velocity. The commands generated are the prescribed quaternion representing the rotation from reference axis to the body axes, the associated transformation matrix, its time-derivative, and the prescribed attitude rate in body axes. - The
autopilot 508 steers the body attitude as prescribed and commanded by theattitude command block 506. The quaternion error is used to calculate attitude errors (referred to as “integral errors”). During the boost phase and initial KV autonomous flight, on-off Pulse Width Modulated (PWM) roll actuator and continuous pitch and yaw Thrust Vectoring Commands (TVC) are used. During the KV endgame, three roll, pitch and yaw on-off attitude thrusters are used. The same autopilot is used during boost and KV endgame. The only difference is that control of the TVC continuous actuators used in the boost phase whereas the control of on-off thrusters during the KV endgame they applied to on-off thrusters. - Continuous lines in
FIG. 5 represent data transmission, whereas the dashed lines represent kinematic returns. - From the seeker to the guidance: missile ECI position, target parallel component and perpendicular components of the velocity with respect to bore-sight, respectively {circumflex over (r)}, {circumflex over (v)}∥, {circumflex over (v)}⊥, Target estimated velocity {circumflex over (v)}∥ T,{circumflex over (v)}⊥ T and acceleration components v{circumflex over (Γ)}
| T ,{circumflex over (Γ)}⊥ T with respect to bore-sight represented by 514.
From guidance to attitude command block: The two components of commanded acceleration perpendicular to missile velocity, represented by 516.
From attitude command block to autopilot bloc: Quaternion defining prescribed body orientation Q*ECI body=Q*M of body axes with respect to reference frame i.e. (ECI) as well as the prescribed body rate Ω*M represented by 518.
From autopilot to actuators δ={δ1,δm,δn} roll, pitch and yaw actuator commands as represented by 520. During the boost phase the command respectively the roll on-off actuator and pitch and yaw continuous actuators. During terminal KV flight they command roll, pitch and yaw on-off actuators.
From guidance to divert actuators: Δ={Δm,Δn} respectively normal and transversal divert on-off thrusters, represented by 522.
From Inertial Navigation System (INS) to autopilot: {circumflex over (Q)}ECI body={circumflex over (Q)}M estimated value of the quaternion defining body attitude with respect to reference, and estimated attitude rate {circumflex over (Ω)}M, represented by 524.
From INS to attitude command: {circumflex over (r)}M, {circumflex over (v)}M respectively missile estimated ECI position, velocity and represented by 526.
From INS to seeker: {circumflex over (r)}M, {circumflex over (v)}M, {circumflex over (Γ)}M respectively missile estimated ECI position, velocity and acceleration represented by 531. - From missile airframe to INS: Sensed acceleration and rotation rate, represented by 528.
From missile airframe to seeker: Missile position and missile attitude represented by 530. - A feature of this design is that during the KV flight the guidance block generates the
commands 522 for the divert thrusters using theinputs 514 from the seeker. At the same time the guidance block generates anattitude command 518 that will result in the autopilot commanding attitude thrusters to assist the divert thrusters through aerodynamic lift effects. This assistance effect is handled by the guidance algorithm as a bounded “cooperative” disturbance relative to thecontrol command 522 for the divert thrusters. The invariance property of the HOSM controller design to matched disturbance allows the guidance control to take into consideration the effects of this “cooperative disturbance” without having to estimate the effect explicitly as conventional control techniques require. The net effect will be that the cooperative disturbance or sum thereof will alleviate the control that the divert thrusters have to accomplish in order to steer the missile into a collision condition. A collision condition refers to the combined velocity and direction of the interceptor and target such that, without further control of the interceptor or maneuver of the target, the two will remain on a collision course. The guidance objective is to first guide to a collision condition and then to maintain the collision condition to intercept in the presence of disturbances. Here the control command is issued directly from the guidance to the divert thrusters in a more efficient way than proposed in previous works [15-16] where a commanded trajectory is calculated from the guidance command, where a trajectory autopilot tracks that intermediate trajectory command and generates direct actuator commands - The second embodiment is illustrated in
FIG. 6A .FIG. 6A illustrates anexemplary interceptor 602 with a seeker configured with a fixedmirror 604 and arotating minor 606. Two types of seeker mounts are typically used in a missile; the first one places the seeker sensor, i.e. focal plane array on a gimbaled gyroscopically stabilized platform, the second, strap-down mount employs a rotating minor which reflects the incoming ray from the target onto the focal plane array fixed onto the missile structure as shown inFIG. 6 . Note that the objects ofFIG. 6A are not necessarily drawn to scale relative to one another. One should appreciate that the seeker subsystem is severable and may be used alone or in combination with one or more of the other subsystems of the present disclosure. Different element of this method, either compensate implicitly or explicitly for disturbing terms, the integrated design by accounting for the effects of multiple sources of uncertainty across different elements of the guidance suite, does a better job than a collection of separate designs because it accounts for such effects coherently. - Referring to
FIG. 6A , thefocal plane array 608 does not measure directly the target elevation and azimuth angles because the field of view is much too small, but rather measures the offset 610 and 611 of the target from a bore sight line representing the center of the focal plane array as directed by the movingminor 606. Either the gimbaled platform or minor is slewed such as to maintain the spot representing the incoming direction of the rays centered on the focal plane array. The exemplary moving minor configuration used in this application represents the more challenging case compared with the gimbaled seeker because the measurements are directly affected by the attitude motion of the interceptor, which makes the technical challenge more difficult. Seeker mounted on gyroscopically stabilized platforms or with intermediate minors is not new and this new method is not about a new specific hardware design thereof. This method is about a new algorithm for controlling the slewing of the bore-sight in the direction of the target. - By mounting gyroscopic and accelerometer sensors onto the gimbaled platform one can measure the accelerations and attitude rate to which the gimbaled platform is subjected. The angular rate of the platform, provided that the target spot is maintained on the center of the focal plane array, can be used by the guidance law.
- With strap-down mounts, as shown in
FIG. 6A , the situation is a little bit more complicated. For one, the focal plane array rotates with the missile body, and the rotation angle of themirror 606 is half the angle between the Line of Sight (LOS) 613 and thelongitudinal axis 618 of the missile body. The rotation of the bore-sight line 612 is then, going to be the sum of the angular rate of themissile body 618+twice the rotation rate of the minor 606 with respect to themissile body 618. - The bore-sight frame is defined as shown
FIG. 6A by axes x-bore 612, y-Bore 614, z-Bore 616 respectively the bore-sight direction, horizontal vector orthogonal the x-bore and a third vector in the z-plane to for a direct reference. Likewise, we have traditional body axesx-Body 618, y-Body 620, z-Body 622 as represented inFIG. 6A . - The quaternion representing the transformation from bore-sight-axes/LOS to some reference (in this case Earth Centered Inertial) is represented by:
-
- where ζ, v are the rotations in pitch and yaw respectively. When a gimbaled platform is used, the formulation is simpler:
-
- The present method applies HOSM control techniques for achieving the combined slewing and estimation of target motion. The algorithm achieves:
- a. The slewing of the bore-sight line towards the target.
b. The estimation of the rotation rate of the bore-sight line.
c. The estimation of target acceleration. - The rapid sequence of brief firings of attitude and divert thrusters, creates longitudinal and rotational accelerations, and thus a very noisy reading for the accelerometers and gyroscopic sensors. For that matter, the proposed design integrates the slewing process and the target acceleration such as to account for those spiky readings in a coherent fashion.
- A Kalman Filter has been the preferred control technique used for the last decades. The Kalman filter works well when the different components of the dynamic noise and of measurement noise are well known and well modeled.
- In this particular case, regarding the measurement noise, one must understand that the dynamic measurement noise is affected by angular accelerations created by the on-off firing of attitude thrusters that create spiky angular missile body accelerations, creating at the level of the seeker a wide-band noise. The seeker slewing is designed to be very fast, but one can anticipate nonetheless that the seeker readings will be contaminated by some of the residual noise. The dynamic measurement noise creates a number of problems:
-
- 1. This is a noise that occurs mostly when thrusters are fired. Since the thruster firing is on-off the amplitude of this noise will be either maximum, or null. This type of noise differs significantly from the basic Kalman Filter assumption that the noise is constant and is governed by Gaussian distribution.
- 2. This noise is also unfortunately correlated to some of the state variables used in the Kalman filter which complicates the design of the filter. Some special formulations of the Kalman Filter allow handling the case where dynamic noise and measurement noise are correlated, but the formulation of the filter is much more complicated. Moreover the disturbing effects of each thruster must be taken into account separately increases considerably the complexity of the filter.
- 3. The development of good dynamic model of target maneuver is difficult, in particular in the exo-atmospheric domain when targets engage in voluntary and involuntary maneuvers and include multiple causes of uncertainty and noises not necessarily Gaussian.
- The present invention includes a seeker subsystem for integrated seeker slewing and target estimation. The seeker subsystem includes a Higher Order Sliding Mode observer based on a noise and uncertainty bound that does not include and does not require detailed dynamic state models and noise models and thereby circumvents much of the difficulty discussed above.
- The first element of the method is the design of an estimator that will estimate the bore-sight error and the target relative and absolute motion perpendicular to the bore-sight. Additional related background material may be found in works by Shtessel, Shkolnikov and Levant in
Ref 12, Levant in Ref 13. The second element is the steering of the platform such as to have the center of the spot representing the target in the focal plane array continuously in the centre thereof. - Let us assume that
ε (.),Ω (.),ā(.); (.):az, el respectively the bore-sight error (ε,μ) in (610,611)FIG. 6A , the components along bore-sight axes y-Bore, z-Bore of the rotation rate of the bore-sight and measured acceleration. A fourth order sliding mode observer is used to estimate target relative velocity orthogonal to boresight and target acceleration perpendicular to boresight in the presence to disturbing attitude motion of said interceptor body without the need for explicit accurate representation of said disturbing effects. This estimation is achieved by -
- In the formulation above interception motion is represented by interceptor measured body rate
Ω (.); (.)=y, z seeker axes, interceptor measured acceleration ā(.) M; - (.)=y, z seeker both of which may differ from actual values and without need for corresponding dynamical state model.
- The Lipshitz constant L must bound φ(4) the 4th derivative of the disturbing term, that is |φ(4)|≦L. The outputs of the estimator are {circumflex over (ε)}(.) the azimuth and elevation components of the bore-sight error, {circumflex over (V)}⊥(.) represents the components of target relative acceleration perpendicular to bore-sight; {circumflex over (α)}(.) T represent the components of target acceleration perpendicular to bore-sight. The difference {circumflex over (ε)}(.)−
ε between measured and estimated bore-sight errors indicates how well the estimation converges. We must note that unlike Kalman Filter asymptotic convergence here the difference goes literally to zero in finite time. Since in this case we have a measurement noise, we expect the residual difference to be significantly under the noise level. - Design of the Controller Slewing the Bore-Sight Line:
- The bore-sight line is steered by applying torques on the platform or the mirror. The mirror dynamics is governed by second order model with a moment of inertia, a dampening term, a spring term and an applied torque. Assuming that the inertial term is small compared to the other terms, we have a transfer function
-
- We assume that the control is achieved by applying elevation and azimuth angular accelerations ζ, υ. Since our controls are on-off, we introduce an integration, which makes the magnitude of the torques w(.) to increase linearly with the duration of the pulse. If we denote the control signals u(.) we have
-
- We also assume the existence of random Gaussian multiplicative disturbances, set in the simulations at 1% of the nominal values of the torques. The sliding variable is defined as σ(.)={circumflex over (ε)}(.).
An on-off Nonlinear Filter with Pulse Width Modulation controller is designed directly as The relative degree=2, The Nonlinear Filter with Pulse Width Modulation controller is designed directly as -
-
- Where the dither signal d(t) is represented in
FIG. 6B . where for the exemplary simulated case, the gains are set to -
-
FIG. 7 shows pitch 704 andyaw 702 seeker slewing error for a simulated flight. Note that the controller achieves well its objective of driving the bore-sight error into the measurement noise level as shown inFIG. 7 . During initial part of the interception the estimated (704) and actual slewing errors in azimuth is about 20 micro rad, it increases during the KV segment to 40 micro radians. -
FIG. 8 shows seeker torque 802 driving the seeker moving mirror for a portion of the simulated flight ofFIG. 7 . One can appreciate inFIG. 8 that due to the large disturbance level introduced, the amplitude of the torque varies significantly, during the pulse. One can only note that the pulse widths vary due to the PWM. -
FIG. 9 shows the exemplary simulated tracking performance of target estimated and actualrelative position error 902 with respect to bore-sight in the horizontal plane, with pointing errors less than 5 m at the beginning of the interception and decreasing linearly function of the range. -
FIG. 10A andFIG. 10B show the comparison of target true 1002 and {circumflex over (V)}⊥y estimated 1004 velocity with respect to bore-sight for the exemplary simulated case. One can note that after the transient response during the 5 first seconds, the HOSM estimation {circumflex over (V)}⊥y 1004 follows well the true 1002 values. One also can note that the values of the target relative velocity are large until time=42, where the missile reaches the collision condition. From time=50 sec to the end, one can note that the simulated target engages in sinusoidal maneuvers. One can note on the zoomed portionFIG. 10B that notwithstanding target rapid maneuvers, the estimator tracks well the relative velocity with velocity errors of few meters/sec. -
FIG. 11 shows the simulated estimation of target transversal acceleration. The estimator performs well again regarding tracking of targettransversal acceleration â Y T 1102 where estimatedacceleration signal 1104 is passed by a second orderlow pass filter 1106 with a characteristic frequency of 25 rad/sec. The total lag is about 100 microseconds. - The third embodiment is HOSM guidance. Guidance is the process that provides acceleration commands to the autopilot process.
- The guidance process begins by generating a guidance strategy. The guidance strategy defines the sensor inputs, control outputs and the objectives for each of one or more phases of intercept. One exemplary guidance strategy may endeavor to minimize a line of sight rate. Another guidance strategy may endeavor to minimize time to intercept. Still another guidance strategy may minimize control effort. Any guidance strategy may be used with the present invention. In accordance with one embodiment of the present invention, a sliding surface for a high order sliding mode control is established to enforce the selected guidance strategy. Upon initiation, the guidance controller drives the system to the simultaneous sliding condition for the sliding surface and one or more derivatives of the sliding surface, whereupon the simultaneous sliding condition is maintained until intercept, thereby maintaining the guidance strategy until intercept.
- In one embodiment, the guidance strategy is to achieve and maintain a collision condition. A collision condition is the set of interceptor and target position and velocity states that, without further maneuver, will result in a collision intercept. It is desired to establish a collision condition and thereafter to maintain the collision condition in the presence of disturbances. The disturbances may include target maneuvers and system measurement errors and noises. In one embodiment of the invention, system modeling errors resulting from simplification of system design models and control algorithms are included in the total system disturbance budget. A high order (second order or higher) sliding mode control law is selected that achieves the high order sliding condition in finite time, i.e., before intercept, in the presence of disturbances less than a Lipschitz bound in accordance with the system disturbance budget.
- By doing so the guidance strategy reduces the interceptor maneuver advantage, i.e., minimizes the ratio of interceptor acceleration perpendicular to the bore-sight line over corresponding target acceleration. As once the collision condition is achieved, then for sustaining of the collision condition, the interceptor only needs to “mimic” target acceleration, that is with a maneuver advantage barely over one. This guidance strategy is especially desirable for re-entry intercepts. When re-entry target maneuvers are considered, target maneuverability peaks at the end (lowest altitude for the target), while at this stage interceptor maneuverability is minimum (highest altitude for the interceptor).
-
FIG. 12 represents interception geometry in the vertical plane. A similar figure could be easily drawn in the horizontal plane. Whentarget 1204 andinterceptor 1202 velocities are constant, the collision condition may be written as -
- where x, y are the horizontal and vertical interceptor to target and vx,vy relative velocities along x and y axes. If the bore-sight frame is not rotating {dot over (λ)}*=0 the collision condition is ZT
⊥ =0, if the bore-sight frame 1206 is rotating the we have -
- where r is the range; in this case ZT
⊥ +V⊥tgo=0
The Proportional Navigation requires the normal acceleration to be -
Γ⊥ M =−N V∥ {dot over (λ)}; N=3−5. (20) - If the guidance is not initiated in collision, collision condition will only occur at the end, missile will be maneuvering continuously and the acceleration will peak at the end. A variant of PN is Augmented Proportional Navigation, where the control Eq. (20) is augmented with estimated value of target acceleration perpendicular to LOS as
-
- Both PN and APN formulations require missile constant longitudinal velocity, and assume a perfect response of the interceptor. We have also the Zero Effort Miss formulation using the time to go, tgo
-
- Here the accuracy of the formulation requires tgo to be accurate and a perfect response of the interceptor. Proportional Navigation and APN are known to yield reasonable miss-distance against non-maneuvering and moderately maneuvering targets.
- The method proposed here, acknowledges that the variation of longitudinal velocity and of target acceleration have adverse effects on PN and APN guidance, but instead of trying to compensate explicitly for such effects with a compensation that is only as good as the estimation of said effects as most methods described above do; it takes advantage of the insensitivity of HOSM to matched disturbance, to compensate implicitly for said effects. In accordance with the present invention, the guidance strategy is defined as:
-
Z T⊥ ω+V ⊥=0; ω=1/t reach ; t reach <tgo (23) - Designed, when ZT
⊥ ≠0 to drive ZT⊥ to zero first, and for maintaining collision condition thereafter. For that matter we define the guidance strategy: -
- where σ(.) is defined as a “sliding variable.” A Second Order Sliding Mode Controller (SSOMC) control law is used to drive σ(.),{dot over (σ)}(.)→0 and thereby drive sliding variable to the sliding surface and thus set the missile, into collision condition in finite time and in the presence of unknown bounded disturbance, and where V⊥(.) and ZT
⊥(.) respectively target relative velocity and position with respect to boresight tgomax and tgomin chosen such as to achieve desired reaching time to the collision time and such as to avoid excessive gains close to the origin. - With this choice of surfaces, we force the missile into collision early in the game and at the end of the end game we avoid the singularity of Eq. (24) when tgo→0. In the intermediate regime, we adjust ω to the current value of tgo.
- In one aspect of this third embodiment, we use a HOSM formulation to drive σ(.){dot over (σ)}(.)→0 in finite time, i.e., before intercept.
- Thus, we represent the dynamics of the system as
- Where u represents commanded lateral acceleration and unknown, bounded disturbing term f(t) represents all other dynamical effects; which can be separated into target acceleration and other terms as:
-
- where η(.) represents the terms other than target acceleration that will be compensated explicitly. Here we have the choice of using Target acceleration {circumflex over (Γ)}1⊥(.) T estimated by the seeker as discussed previously or {circumflex over (Γ)}2⊥(.) T calculated by an observer embedded with guidance which not only estimates target acceleration but effects of disturbance terms such as errors in terms V⊥(.), tgo and V∥{dot over (λ)}. The smooth control u that drives σ,{dot over (σ)}→0 (smooth second order sliding mode) in finite time:
-
- The estimation of target acceleration {circumflex over (Γ)}2⊥(.) T may be achieved by a smooth observer:
-
- Here the target estimation by the seeker {circumflex over (Γ)}1⊥(.) T is matches better actual target acceleration {circumflex over (Γ)}⊥(.) T. Conversely the term {circumflex over (Γ)}2⊥(.) T calculated by the estimator estimates not only {circumflex over (Γ)}⊥(.) T, but the errors in the estimation of {tilde over (η)}(.)={circumflex over (η)}(.)−η(.) and other disturbance in Eq. (25). The gains achieved by selecting {circumflex over (Γ)}2⊥(.) T over {circumflex over (Γ)}1⊥(.) T are few percent better scores against 0.3 and 0.5 miss-distances. Here what is important is to compensate for all disturbing terms which target acceleration is only part of.
- In this example L=1000. When on-off thrusters are used, their command is derived from the continuous and smooth control u.
-
- Equation (25) can now be written as
-
{dot over (σ)}(.)+α1|σ(.)|2/3sign(σ(.))+α2∫|σ(.)|1/3sign(σ(.))dτ={tilde over (Γ)} ⊥(.) T+{tilde over (η)}(.) =g (.) (31) - Considering the boundedness of ġ(.) the first term {tilde over ({dot over (Γ)}⊥(.) T is evidently bounded, but this is not necessarily the case of {tilde over ({dot over (η)}(.) as tgo→0. Considering Eq. (25); when tgo<tgomin assuming perfect estimation of target acceleration exact compensation of η(.) we have
-
- When tgo→0, Z⊥(.)≈0; σ(.)≈V⊥(.) if we represent {circumflex over (V)}⊥(.)=(1−ε)V⊥(.); |ε|<<1, Eq. (32) after (only) compensating {circumflex over (η)}(.) becomes
-
- which is mildly unstable if ε<0. For that matter a multiplicative factor k is applied before in {circumflex over (η)}(.) in Eq. (27); one can see that k−1>|ε| guarantees the strict stability. Corresponding control law becomes
-
- The guidance performance is compared to widely used and proven guidance techniques, namely, PN, APN.
- In the engagement scenario chosen half of the interceptions take place between 20000 and 35000 meters where the target 0.6 Hz sinusoidal maneuvers result in accelerations peak amplitudes in the 50-100 m/sec2. The initial target altitude, flight path angle and azimuth, its ballistic coefficient are randomized, as well as the launch delay. Statistics established with 500 Monte Carlo runs, presented in
FIG. 13 show that HOSMguidance 1302outperforms PN 1304 andAPN 1306. Considering the objective maximum miss-distances of 0.5 m, HOSM guidance achieves the desired result in 99.8% of the cases compared with 78 and 66% for PN and APN. With an objective of 0.3 m, numbers become 98% compared with 74% and 63% respectively. -
FIG. 14 is a comparison of simulated target and interceptor accelerations. Referring toFIG. 14 ,FIG. 14 shows that the interceptor literally “mimics” the target, which means that the interceptor lateral acceleration capability does not outmaneuver the target in order to successfully intercept it. In other terms, HOSM guidance only requires a “maneuver advantage ratio” close to unity. One can note the sinusoidal pattern of theinterceptor acceleration 1404 achieved by the attitude maneuver and the acceleration spikes 1402) representing the firing of divert thrusters. Thesmooth line 1406 represents target acceleration. - When target maneuver frequencies increase beyond 0.8 Hz, in the 1-1.5 Hz we have a situation where the observer lag of embedded observer, Eq. (28) that achieves the smoothness of the control law is about 0.1 sec, is responsible for about 10-30% misses. Considering the interception of rapidly maneuvering targets we use an alternative “Super-Twist” design and the guidance law becomes
-
- with Lipshitz constant L that bounds φ(2) the 2nd derivative of the disturbing term, that is |φ(2)|≦L=10000. This reduces very significantly the embedded observer lag and allows achieving excellent performance against targets maneuvering in the 1-1.5 Hz range. Considering maneuvers beyond 1.5 Hz, as the metric amplitude of target oscillations decreases as Γmax T/ωT 2 maneuver amplitudes become then small enough to still constitute significant problem, i.e. at frequencies of 2.5 Hz, the amplitude of the target lateral motion is only 0.45 m. This observer is noisier than previous one, however on average it achieves a better compensating performance.
- Results
FIG. 15 ,FIG. 16 ,FIG. 17 show that withmaneuvers frequencies 1, 1.25, 1.5 Hz, HOSM miss-distancecumulative distributions - The fourth embodiment is HOSM quaternion autopilot. Here the autopilot typically needs to steer the missile attitude to achieve some desired lateral acceleration. Alternatively, attitude may be directly commanded. Commanded attitude may be a directly commanded attitude such as at launch and shortly thereafter or before impact, or such as to enhance collision effectiveness as this could be done after interceptor booster burn-out and when dynamic pressure is small enough. Commanded attitude may be calculated in the autopilot subsystem such to achieve some prescribed lateral acceleration calculated by the guidance. Said prescribed lateral acceleration may the primary acceleration command, as this may be the case with an interceptor which divert is solely achieved by aerodynamic lift, orientation of main booster/sustainer body orientation or combination thereof or may be the secondary cooperative disturbance acceleration.
- The relation of the autopilot with other elements of architecture in the present invention can be better understood by examining
FIG. 5 . The first step of the method is the calculation in theattitude command block 506 of prescribed body attitude represented by a quaternion and the corresponding commandedbody attitude rate 518. The second step comprises calculating in the blockautomatic pilot 508 the three sliding variables, and thereafter the calculation by the HOSM autopilot actuator commands 520 required to driving the three surfaces to zero. - In the first step, commanded acceleration from the HOSM guidance are used to calculate the desired angles of attack, in the pitch and yaw planes, taking into consideration the aerodynamic lift gradient and the thrust using
-
- The cos(α) in the denominator, that takes into account that the aerodynamic lift is calculated iteratively.
- The pitch and yaw lead angles are calculated as follows. First we calculate the LOS frame. Its first vector Ix is the bore-sight direction and the two other axes are calculated by
-
- Where rI is the local vertical unit-vector. Then, the velocity frame is calculated with the first vector Jx in the direction of the interceptor velocity vector and two other axes calculated by
-
- And we have
-
- This formulation is exactly the same regardless of the reference chosen provided that vectors rI, Jx are expressed in the selected reference frame. The quaternion may be defined relative to a variety of references such as for example, ECI, NED and a variety of other references provided that commanded and actual references are the same.
- The transformation matrix represented desired body attitude is calculated using rotation matrices defined as follows
-
- The axes of the required body attitude are obtained by a first rotation of αyaw around Jz. We obtain intermediate axes:
-
J2x =T[α yaw ,J z ]J x ; J2y =T[α yaw ,J z ]J y (41) - Followed by a rotation αyaw around J2y
-
JB x =T[α pitch ,J2y ]J2x ; JB y =T[α pitch ,J2y ]J2y ; JB z =JB x ×JB y. (42) - The matrix TECI body=[JBx JBy JBz] formed by the three body axes column vectors represent the transformation from body to ECI. (Note we could have used any other reference instead, such as NED) Corresponding quaternion is then calculated using the following formulae. Given a transformation matrix R the corresponding quaternion first, scalar parameter q0 is calculated as in Ref. 17 as:
-
4q 0 2=1+R 1,i +R 2,2 +R 3,3 (43) - and the three vector parameters:
-
- This can also be written as:
-
- This formulation of the quaternion may unfortunately become singular when q0 approaches zero. The rotation becomes a simple reflection and the vector e becomes undefined. The approach for overcoming this difficulty is to assume that the quaternion representing the rotation is now q1, q2 or q3 and to calculate them choosing one of the four possible formulations of Eq. (44) and Eq. (45) in Ref [17]. It should be noted that the problem seemingly posed by the initiation of a quaternion using a rotation/transformation matrix is solved by the iteration of the calculation. Once the initial quaternion has been calculated it suffices to update the quaternion and it does not matter anymore whether cos(φ/2) becomes zero thereafter.
- Prescribed roll, pitch and yaw rates can be defined from the time derivative of the prescribed quaternion as
-
- Alternatively we can calculate prescribed attitude rate wherein the quaternion attitude rate errors in 4 component quaternion space errors ({dot over (Q)}*body/(.)−{dot over (Q)}body/(.)) are mapped to 3 component body axes, wherein prescribed body rate errors are derived from the time derivative {dot over (T)}*body/(.) of transformation matrix T*body/(.) that represents prescribed attitude with respect to chosen reference. The prescribed attitude rate is:
-
- Where the time derivatives of the components of T*body/(.) are obtained using a HOSM exact differentiator as per Ref [13].
-
- z0i,j=Ti,j, z1i,j=T(1) i,j, z2i,j=T(2) i,j, z3i,j=T(3) i,j, z4i,j=T(4) i,j is achieved in finite time that can be made very short relative to dynamics of the differentiated signal.
Introducing the angle error ΔΩI wherein the quaternion attitude errors in a 4 component quaternion space errors (Q*body/(.)−Qbody/(.)) are mapped to 3 component body axes as: -
- With each body component being a linear combination of four quaternion components.
- In the second step of the fourth embodiment, we set the desired Proportional-Integral error response. Three proportional integral sliding variables define the desired behavior of the error-response is represented as
-
- Where Ω represents actual rotation rate in body axes and wherein characteristic frequencies ωp, ωq, ωr are chosen to achieve desired settling time of roll, pitch and yaw.
- Interestingly, when ω=ωp=ωq=ωr Eq. (50) can be represented as
-
- The term (ωΔQ+Δ{dot over (Q)}) represents a 4-vector of sliding variables in quaternion space. Equation (51) projects the 4-vector of sliding variables in quaternion space into a 3-vector of sliding variables in body axes. The dynamics of the sliding variables after the two successive time derivations required to have the control appearing explicitly in the right hand side are represented by:
-
- (i) {umlaut over (p)}*, {umlaut over (q)}*, {umlaut over (r)}* and {dot over (p)}*, {dot over (q)}*, {dot over (r)}* could be calculated numerically using a HOSM differentiator.
(ii) The calculation of {dot over (p)}, {dot over (q)}, {dot over (r)} would be as follows -
- And the torque commands are given by:
-
- then Eqs. (54-55, 57) are derived with respect to time. As this is done the time derivatives of δl, δm, δn are
-
- Clearly, the expansion of Eq. (53) transforms the three Single-Input-Single-Output control problems in a Multiple-Input-Multiple-Output control problem much more difficult to solve. With this HOSM design we lump together all effects other than the direct effect of roll, pitch and yaw actuator as g(.); (.)=p, q, r, without having explicit ting the complex terms represented in Eqs. (54-58) and without incurring the risk of introducing inevitable model errors. We do not define all the variables in Eqs. (54-58) since we do use them in the HOSM design.
wherein g(.); (.)=p, q, r represent unknown but yet bounded effects of all the dynamics with the exception of {circumflex over (b)}(.)u(.); (.)=p, q, r and wherein {circumflex over (b)}(.)u(.) represents the effects that roll, pitch and yaw command to either continuous or on-off commands would have on roll, pitch and yaw sliding surface dynamics. - In one embodiment, the effects represented by b(.)u(.); (.)=p, q, r and modeled effects {circumflex over (b)}(.)u(.) used in the design of the controller may differ by relative {tilde over (b)}(.)u(.) errors as large as 30% in relative terms without any adverse effect on controller performance as they are implicitly accounted for in the unknown bounded term g(.); (.)=p, q, r.
- The third step of the fourth embodiment is the design of the HOSM controller that will drive sliding variables Eq. (50) to zero.
- During the first part of the interceptor flight, the attitude motion is achieved using a continuous TVC actuator. Related background material may be found in Shtessel, Shkolnikov and Levant in
Ref 12, Levant in Ref 13, Shtessel and Tournes inRef 16. We introduce auxiliary Proportional-Derivative surfaces designed to reduce the relative degree, Since the Second Order Sliding Mode controller is designed to operate with systems of relative degree=1. -
σ′(.) =cσ (.)+{dot over (σ)}(.) (59) - The corresponding controller is
-
U (.)=α1|σ′(.)|2/3signσ′(.)+α2∫|σ′(.)|1/3sign(σ′(.))dτ+z1(.); (.)=q,r -
ż 0 =v 0 +U (.) ; v 0=−3|L| 1/3 |z 0−σ′(.)|2/3sign(z 0−σ(.))+z 1 -
ż 1 =v 1 ; v 1=−2|L| 1/2sign(z 1−υ0)|z 1−υ0|1/2 +z 2 -
ż 2=υ2; υ2=−1.5 |L|sign(z 2−υ1) (60) - The Lipshitz constant L must be g(.) (2) the 2nd derivative of the disturbing terms, |g(.) (2)<L, (.)=p, q, r
- The control of pitch and yaw attitude motion during KV autonomous flight and the control of roll motion during boost and KV flight are achieved by means of on-off PWM thrusters. Corresponding control laws are designed as follows:
- The relative degree=2, The Nonlinear Filter with Pulse Width Modulation controller is designed directly as
-
-
- Where the dither signal d(t) is represented in
FIG. 6B . - The four quaternion parameter errors (the difference between the prescribed value of the quaternion parameters and actual values) are shown
FIG. 19 . One can also notice the brief transient at t=55 1902 as the autopilot switches from one mode to the next. The quaternion parameter errors are less than 0.001 during most of the flight. - The same observation can be made regarding angular errors shown 2002
FIG. 206 . Attitude angular errors are <1.5 mrad. - Attitude
angular rate errors 2102 shownFIG. 217 are also very small; about 1 deg/sec in the first segment they are noisier, about 4 deg/sec during the KV terminal flight segment. The reason is that during this phase lateral divert is achieved by on-off firing of divert thrusters. Each firing creates a brief and large acceleration pulse. Since the divert thrusters are not placed exactly at the center of gravity which moves during the flight, this creates a brief intense moment disturbance. - As indicated before and as shown in the formulae presented before, the HOSM design of the autopilot does not require values for interceptor control characteristics other than a very broad estimation of the upper bound of the disturbances. To demonstrate even further the inherent robustness of the design we have applied multiplicative disturbances to the magnitude of the thrusters. Applying this disturbance, as shown in
FIG. 22 , it is possible for the maximum magnitude of a thruster to be as some point in time 1.3 times the nominal value and 50 msec after to be 0.8 times this value.FIG. 22 shows themultiplicative disturbance 2202 applied to each commanded thruster actuation to simulate a thruster with this degree of unknown thrust. In the inventor's experience, such a rapid and large amplitude variation of the thrust level cannot be estimated in real-time by a disturbance accommodating controller. - Likewise, the modeling of such effects would require very complex codes that account for the combination of the effects of the multiple simultaneous causes of such disturbances which not only include the fast variation of the maximum thrust, but also a slow sinusoidal modulation for the disturbances caused by slowly varying effects such as air density or velocity change.
- The present invention has been described above with the aid of functional building blocks illustrating the performance of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Any such alternate boundaries are thus within the scope and spirit of the claimed invention. One skilled in the art will recognize that these functional building blocks can be implemented by discrete components, application specific integrated circuits, processors executing appropriate software and the like or any combination thereof.
- While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the appended claims and their equivalents.
-
-
CG Center of gravity (in body axes) CP Center of pressure (in body axes) CG Center of gravity along x-axis CP Center of pressure along x-axis Lat, G, SG Latitude, Longitude, Sidereal angle NED North, East Down ECI Earth Centered Inertial Ta/b Transformation matrix from frame a to frame b Qa/b Quaternion representing the transformation matrix from frame a to frame b κ[.] Lead angle around y-body and z-body L Lipshitz constant r, v, Γ Position, velocity and acceleration vectors u(.); (.) (ζ = pitch), η = yaw Normalized seeker commands uδ, uΔ, uζ Attitude, Divert and TVC normalized controls, with δ = [δp, δq, δr] roll, pitch and yaw commands Δ = [Δx, Δy, Δz] x, y, z (body) divert commands ζ = [ζ = pitch, υ = yaw] moments around y-body, z-body Ω, ΩI Vector of body rates, vector of angles ΔΩ = Ω* − Ω Vector of body rate errors ΔΩI Vector of body (position errors) = “integral errors” ΔΩ = Δ{dot over (Ω)}I but ΔΩI ≠ ∫ΩIdτ ψ, θ, φ Euler's yaw, pitch and roll angles α, γ, q Angle of attack, flight path angle, pitch rate ε(.); (.) = az, el Target angular error with respect to boresight, also εaz = ε; εel = μ ω Characteristic frequency rad/sec ζ, υ Pitch, yaw rotation of boresight (.) Generic variable (.)* Prescribed, commanded value of variable (.) ( . )Measured value of variable (.) ({circumflex over (.)}) Estimated value of variable (.) ({tilde over (.)}) = ({circumflex over (.)}) − (.) Error in estimation of variable (.) ({tilde over (.)}) = ( . ) − (.)Error in measurement of variable (.) (.)∥, (.) ⊥[.] Component of variable (.) along boresight and [.] along y-boresight and z-bore-sight (.)T, (.)M; (.)T, (.)M Variable (.) applied to target, interceptor t, tgo Current time, time to go sec. s Laplace variable rad/sec d; l + d Disturbance, multiplicative disturbance λ Line of sight angle λ* Boresight angle Lat Latitude G Longitude M Mach number press Atmospheric pressure S Reference (cross) sectional area CLα Lift gradient m Current missile mass F Thrust magnitude
Appendix II Contains reference cited in this disclosure. All of the following references are incorporated herein by reference in their entirety. -
- U.S. Pat. No. 6,244,536 B1, issued June 2001 to Cloutier;
- U.S. Pat. No. 7,185,844 B2 issued March 2007 to Yanushevsky;
- U.S. Pat. No. 6,532,454 B1 issued March 2003 to Werbos;
- U.S. RE37,331 E issued August 2001 to Schroeder;
- U.S. Pat. No. 6,341,249 B1 issued January 2002 to Xin et al.;
- U.S. Pat. No. 6,611,823 B1 issued July 2003 to Selmic et al.; and
- U.S. Pat. No. 7,080,055 B2 issued July 2006 to Campos et al.
-
- 1. R. T., Yanushevsky and W. J., Bond, “New Approach to Guidance Law Design,” AIAA Journal of Guidance Control and Dynamics, Vol. 27, no. 4 July, August 2004 issue, pp. 1-5.
- 2. P. Zarchan, “Tactical and Strategic Missile Guidance” AIAA Progress in Astronautics and Aeronautics, Vol. 157, AIAA Reston VA, pp. 25-43.
- 3. P. Gurfiel., M. Jodorovsky., and M. Guelman, “Neoclassical Guidance for Homing Missiles,” AIAA Journal of Guidance Control and Dynamics, Vol. 24, no. 3 May, June, 2001 issue, pp. 452-459.
- 4. S. Gutman., “Can Lead-Guidance Compensator Guarantee Zero Miss Distance” AIAA Journal of Guidance Control and Dynamics, Vol. 31, no. 3 May, June 2008 issue, pp. 779-782.
- 5. R. T. Chen., J. L, Speyer. and D. Lianos., “Homing missile Guidance and Estimation Under Agile Target acceleration,” AIAA Journal of Guidance Control and Dynamics, Vol. 30, no. 6 November, December 2007 issue, pp. 1577-1589.
- 6. D. Dionne., H. Michalska., and J. Shinar., and Y. Oshman., “Decision-Directed Adaptive Estimation and Guidance for an Interception Endgame,” AIAA Journal of Guidance Control and Dynamics, Vol. 29, no. 4 July, August 2006 issue, pp. 970-980.
- 7. H. Hablani., “Endgame Guidance and Relative Navigation of Strategic Interceptors with Delays” AIAA Journal of Guidance Control and Dynamics, Vol. 29, no. 1 January, February 2006 issue, pp. 82-94.
- 8. I. Shkolnikov, Y. B. Shtessel, P. Zarchan, D. Lianos “Simulation Study of the Homing Interception Guidance Loop with Sliding Mode Observers Versus Kalman Filters,” Proceedings of 2001 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2001-4216.
- 9. Kennedy, W. B., and Mikelsen, C, “AIT Real Gas Divert Jet Interactions; Summary of Technology,” AIAA Paper 98-5188, 1998, pp. 225-234.
- 10. M. Idan., T. Shime., and O. M. Golan., “Integrated Sliding Mode Autopilot Guidance for Dual-Control Missiles,” AIAA Journal of Guidance Control and Dynamics, Vol. 30, no. 4 July, August 2007 issue, pp. 1081-1089.
- 11. M. S. Bhat., D. S. Bai., A. A. Powly., K. N. Swamy., and D. Ghose., “Variable Structure Controller Design with Application to Missile Tracking,” AIAA Journal of Guidance Control and Dynamics, Vol. 24, no. 4 July, August 2001 issue, pp. 859-862.
- 12. Shtessel Y., Shkolnikov, I., and Levant A., “Smooth Second Order Sliding Modes: Missile Guidance Application,” Automatica, Vol. 43, No. 8, 2007, pp. 1470-1476.
- 13. Levant, A., “Higher-order sliding modes, differentiation and output-feedback control”. International Journal of Control, 76, 9/10, 2003, 924-94
- 14. Shkolnikov I., Shtessel Y., and Lianos D. Integrated Guidance-Control System of a Homing Interceptor: Sliding Mode Approach, Proceedings of 2001 AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2001-4218.
- 15. C. Tournes, Y. B. Shtessel, I. Shkolnikov, “Autopilot for Missiles Steered by Aerodynamic Lift and Divert Thrusters,” AIAA Journal of Guidance Control and Dynamics, Vol. 29, no. 3, May, June 2006 issue, pp. 617-625.
- 16. Y. B. Shtessel, C. Tournes, “Integrated Higher-Order Sliding Mode Guidance & Autopilots for Dual-Control Missiles,” AIAA Journal of Guidance Control and Dynamics, Vol. 32, no. 1 January, February 2009 issue, pp. 74-94
- 17. B. L. Stevens, F. L. Lewis, “Aircraft Control and Simulation,” J. Willey and sons, pp. 42,-43, New York, 1992
Claims (43)
{dot over (σ)}(.) =f (.) +g (.) −
g2(.) =g (.)−ΔΓ(.) ; |g2(.) |<|g (.)|;
U (.)=α1|σ′(.)|2/3signσ′(.)+α2∫|σ′(.)|1/3sign(σ′(.))dτ+z1(.); (.)=q,r
ż 0 =v 0 +U (.) ; v 0=−3|L| 1/3 |z 0−σ′(.)|2/3sign(z 0−σ(.))+z 1
ż 1 =v 1 ; v 1=−2|L| 1/2sign(z 1−υ0)|z 1−υ0|1/2 +z 2
ż 2=υ2; υ2=−1.5 |L|sign(z 2−υ1),
{dot over (σ)}(.)+α1|σ(.)|2/3sign(σ(.))+α2∫|σ(.)|1/3sign(σ(.))dτ={tilde over (Γ)} ⊥(.) T+{tilde over (η)}(.) =g (.)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US12/501,395 US8436283B1 (en) | 2008-07-11 | 2009-07-10 | System and method for guiding and controlling a missile using high order sliding mode control |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US12967608P | 2008-07-11 | 2008-07-11 | |
US12/501,395 US8436283B1 (en) | 2008-07-11 | 2009-07-10 | System and method for guiding and controlling a missile using high order sliding mode control |
Publications (2)
Publication Number | Publication Date |
---|---|
US20130092785A1 true US20130092785A1 (en) | 2013-04-18 |
US8436283B1 US8436283B1 (en) | 2013-05-07 |
Family
ID=48085346
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US12/501,395 Active 2031-12-13 US8436283B1 (en) | 2008-07-11 | 2009-07-10 | System and method for guiding and controlling a missile using high order sliding mode control |
Country Status (1)
Country | Link |
---|---|
US (1) | US8436283B1 (en) |
Cited By (58)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20120259579A1 (en) * | 2011-04-07 | 2012-10-11 | Icefield Tools Corporation | Method and apparatus for determining orientation using a plurality of angular rate sensors and accelerometers |
US20140207361A1 (en) * | 2011-08-09 | 2014-07-24 | Toyota Jidosha Kabushiki Kaisha | Sliding mode controller and internal combustion engine system control device |
US20140360157A1 (en) * | 2013-06-07 | 2014-12-11 | Raytheon Company | Rocket vehicle with integrated attitude control and thrust vectoring |
CN104266546A (en) * | 2014-09-22 | 2015-01-07 | 哈尔滨工业大学 | Sight line based finite time convergence active defense guidance control method |
WO2015069366A1 (en) * | 2013-11-05 | 2015-05-14 | Raytheon Company | Nadir/zenith inertial pointing assistance for two-axis gimbals |
CN104778376A (en) * | 2015-05-04 | 2015-07-15 | 哈尔滨工业大学 | Method for predicting skipping trajectory of hypersonic glide warhead in near space |
US20160097621A1 (en) * | 2014-10-06 | 2016-04-07 | The Charles Stark Draper Laboratory, Inc. | Multi-hypothesis fire control and guidance |
CN106774385A (en) * | 2016-12-05 | 2017-05-31 | 烟台南山学院 | A kind of dirigible spot hover control method of use adaptive variable structure |
CN106909165A (en) * | 2017-02-23 | 2017-06-30 | 上海航天控制技术研究所 | Rotary missile body attitude information extracting method based on target seeker multisensor |
CN107766967A (en) * | 2017-09-21 | 2018-03-06 | 北京航空航天大学 | A kind of interceptor Predictor-corrector guidance method based on polynomial fitting method |
CN108362174A (en) * | 2018-02-09 | 2018-08-03 | 中国人民解放军火箭军工程大学 | Multiple blocker collaboration detections and the integrated hold-up interception method of guidance and system |
CN109085848A (en) * | 2018-08-02 | 2018-12-25 | 西北工业大学 | Air-to-air missile direct force/aerodynamic force finite time anti-saturation control method |
CN109696090A (en) * | 2019-01-16 | 2019-04-30 | 哈尔滨工业大学 | It is a kind of for carrier rocket guided missile online single-shot thrust discrimination method |
CN109885074A (en) * | 2019-02-28 | 2019-06-14 | 天津大学 | Quadrotor drone finite time convergence control attitude control method |
CN110045609A (en) * | 2019-04-17 | 2019-07-23 | 北京理工大学 | It is a kind of that perpendicular apparatus control system is played based on PID- sliding-mode variable structure algorithm |
CN110471439A (en) * | 2018-09-25 | 2019-11-19 | 浙江工业大学 | A kind of calm method of rigid aircraft set time posture based on neural network estimation |
CN110488854A (en) * | 2018-09-25 | 2019-11-22 | 浙江工业大学 | A kind of rigid aircraft set time Attitude tracking control method based on neural network estimation |
CN110618608A (en) * | 2018-06-20 | 2019-12-27 | 河南科技大学 | Composite guidance tracking control method and device |
CN110764523A (en) * | 2019-11-13 | 2020-02-07 | 中国人民解放军海军航空大学 | Proportional-integral pre-guiding attack target method based on anti-saturation smooth transformation |
CN110793405A (en) * | 2019-09-16 | 2020-02-14 | 上海航天控制技术研究所 | Self-adaptive control method for preventing instantaneous impact of unfolding of folding rudder of electric steering engine |
CN111026139A (en) * | 2019-09-25 | 2020-04-17 | 中国人民解放军63850部队 | Three-dimensional model attitude adjustment control method based on flight trajectory |
CN111027206A (en) * | 2019-12-05 | 2020-04-17 | 哈尔滨工业大学 | Adaptive sliding mode control method for interceptor maneuvering target with specified performance |
CN111174643A (en) * | 2020-01-16 | 2020-05-19 | 中国人民解放军火箭军工程大学 | Aircraft interception method and system under condition of bait interference |
CN111324142A (en) * | 2020-01-07 | 2020-06-23 | 湖北航天技术研究院总体设计所 | Missile navigator disturbance compensation control method |
CN111342086A (en) * | 2020-02-29 | 2020-06-26 | 同济大学 | Fuel cell air oxygen ratio and flow pressure cooperative control method and system |
CN111591472A (en) * | 2020-05-15 | 2020-08-28 | 北京世冠金洋科技发展有限公司 | Method and related device for adjusting satellite attitude |
CN111752158A (en) * | 2020-07-17 | 2020-10-09 | 哈尔滨工业大学 | Second-order sliding mode control method for finite time convergence |
CN112001120A (en) * | 2020-08-24 | 2020-11-27 | 哈尔滨工业大学 | Spacecraft-to-multi-interceptor autonomous avoidance maneuvering method based on reinforcement learning |
US10852412B2 (en) * | 2018-10-18 | 2020-12-01 | Bae Systems Information And Electronic Systems Integration Inc. | Bullet state estimator using observer based dynamic system |
CN112066943A (en) * | 2020-07-28 | 2020-12-11 | 中国空间技术研究院 | Calculation method and device for rotation angle of vector adjustment rotating mechanism |
CN112084571A (en) * | 2020-07-16 | 2020-12-15 | 北京航空航天大学 | Method for modeling and decoupling movement of air-drop cruise aircraft with speed reducer |
CN112099348A (en) * | 2020-08-19 | 2020-12-18 | 南京理工大学 | Collision angle control guidance method based on observer and global sliding mode |
CN112130578A (en) * | 2020-09-22 | 2020-12-25 | 中国人民解放军海军航空大学 | Method for tracking attack angle of aircraft by sliding mode and switching control |
CN112344795A (en) * | 2020-11-08 | 2021-02-09 | 西北工业大学 | Terminal guidance method for predetermined time convergence |
CN112558631A (en) * | 2020-12-04 | 2021-03-26 | 北京理工大学 | Variable parameter guidance method with large falling angle constraint based on measurement information |
CN112577489A (en) * | 2020-12-08 | 2021-03-30 | 北京电子工程总体研究所 | Seeker sight rotation rate extraction method based on interactive multi-model filtering |
CN112597619A (en) * | 2020-09-14 | 2021-04-02 | 湖南航天机电设备与特种材料研究所 | Stability simulation design method for primary guidance process of cruise missile |
US20210116216A1 (en) * | 2017-04-10 | 2021-04-22 | Bae Systems Information And Electronic Systems Integration Inc. | Dynamic autopilot |
CN112799429A (en) * | 2021-01-05 | 2021-05-14 | 北京航空航天大学 | Multi-missile cooperative attack guidance law design method based on reinforcement learning |
CN112815787A (en) * | 2020-11-27 | 2021-05-18 | 南京理工大学 | Missile guidance law for multiple missiles to attack maneuvering target simultaneously |
EP3822733A1 (en) * | 2019-11-15 | 2021-05-19 | MBDA UK Limited | Methods of controlling self-propelled flying devices |
WO2021094711A1 (en) * | 2019-11-15 | 2021-05-20 | Mbda Uk Limited | Method of controlling self-propelled flying devices |
CN112965371A (en) * | 2021-01-29 | 2021-06-15 | 哈尔滨工程大学 | Water surface unmanned ship track rapid tracking control method based on fixed time observer |
CN113009824A (en) * | 2021-02-03 | 2021-06-22 | 武汉理工大学 | Self-adaptive strain stability control method and system for stability-variable ship and storage medium |
CN113110554A (en) * | 2021-04-30 | 2021-07-13 | 南京航空航天大学 | Four-rotor unmanned aerial vehicle composite continuous rapid terminal sliding mode attitude control method |
CN113110048A (en) * | 2021-04-13 | 2021-07-13 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Nonlinear system output feedback adaptive control system and method adopting HOSM observer |
CN113255234A (en) * | 2021-06-28 | 2021-08-13 | 北京航空航天大学 | Method for carrying out online target distribution on missile groups |
CN113639594A (en) * | 2021-05-27 | 2021-11-12 | 西北工业大学 | Fuzzy association fusion method of multi-missile cooperative system |
CN113656887A (en) * | 2021-07-28 | 2021-11-16 | 上海机电工程研究所 | Coordinate bias optimization-based extension method and system for bullet motion simulation capability |
US11175115B2 (en) * | 2017-01-05 | 2021-11-16 | Bae Systems Information And Electronic Systems Integration Inc. | Determination of guided-munition roll orientation |
CN113759954A (en) * | 2020-06-03 | 2021-12-07 | 北京理工大学 | Composite guidance method for maneuvering target |
CN113959462A (en) * | 2021-10-21 | 2022-01-21 | 北京机电工程研究所 | Quaternion-based inertial navigation system self-alignment method |
CN114034215A (en) * | 2021-11-23 | 2022-02-11 | 航天科工火箭技术有限公司 | Rocket guiding method and device |
CN114280937A (en) * | 2021-12-27 | 2022-04-05 | 南京工业大学 | Bridge crane control method based on finite time compounding |
CN114459479A (en) * | 2022-02-21 | 2022-05-10 | 北京航天嘉诚精密科技发展有限公司 | Device and method for measuring attitude and position of rotating carrier |
CN115200916A (en) * | 2022-09-16 | 2022-10-18 | 中国电力科学研究院有限公司 | Load decoupling loading device, method and system for wind turbine generator and control system |
CN115289908A (en) * | 2022-06-07 | 2022-11-04 | 西北工业大学 | Method and device for guiding air defense missile introduction section through remote control instruction |
CN116839429A (en) * | 2023-09-01 | 2023-10-03 | 北京航空航天大学 | Guidance control integrated method considering view field angle constraint of seeker |
Families Citing this family (26)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
AU2011294891B2 (en) * | 2010-08-23 | 2015-01-29 | Mbda Uk Limited | Guidance method and apparatus |
US11313650B2 (en) | 2012-03-02 | 2022-04-26 | Northrop Grumman Systems Corporation | Methods and apparatuses for aerial interception of aerial threats |
US9551552B2 (en) | 2012-03-02 | 2017-01-24 | Orbital Atk, Inc. | Methods and apparatuses for aerial interception of aerial threats |
US9170070B2 (en) | 2012-03-02 | 2015-10-27 | Orbital Atk, Inc. | Methods and apparatuses for active protection from aerial threats |
US11947349B2 (en) | 2012-03-02 | 2024-04-02 | Northrop Grumman Systems Corporation | Methods and apparatuses for engagement management of aerial threats |
US9501055B2 (en) | 2012-03-02 | 2016-11-22 | Orbital Atk, Inc. | Methods and apparatuses for engagement management of aerial threats |
US9606214B2 (en) * | 2014-09-30 | 2017-03-28 | The Boeing Company | Aero-wave instrument for the measurement of the optical wave-front disturbances in the airflow around airborne systems |
CN106059413B (en) * | 2016-05-30 | 2018-07-10 | 中国人民解放军国防科学技术大学 | A kind of fly wheel system method for controlling number of revolution of direct current generator driving |
US10295973B1 (en) * | 2016-07-12 | 2019-05-21 | Lockheed Martin Corporation | System and method for control and guidance of an object |
US10323907B1 (en) * | 2016-08-26 | 2019-06-18 | Cummings Aerospace, Inc. | Proportional velocity-deficit guidance for ballistic targeting accuracy |
CN106370059B (en) * | 2016-08-26 | 2018-08-31 | 方洋旺 | A kind of random quickly smooth Second Order Sliding Mode terminal guidance method |
CN106406337B (en) * | 2016-12-16 | 2019-12-17 | 北京理工大学 | Method and system for optimizing robustness of spacecraft attitude control system |
CA2972498C (en) * | 2017-06-28 | 2024-01-23 | Bombardier Inc. | Takeoff pitch guidance system and method |
CN107703952B (en) * | 2017-08-29 | 2020-10-30 | 浙江工业大学 | Nonsingular fixed time self-adaptive attitude control method for rigid aircraft |
CN108490773A (en) * | 2018-03-16 | 2018-09-04 | 北京理工大学 | A kind of bionical segmentation combined terminal guidance method of view-based access control model sensing |
CN108880369B (en) * | 2018-06-12 | 2021-01-15 | 广州市香港科大霍英东研究院 | Motor anti-interference control method, system and device based on fractional order sliding mode control |
CN109543135B (en) * | 2018-11-09 | 2021-01-05 | 西北工业大学 | Multi-AUV (autonomous Underwater vehicle) cooperative simultaneous guidance method based on information maximization |
CN109739088B (en) * | 2019-01-07 | 2021-08-27 | 大连海事大学 | Unmanned ship finite time convergence state observer and design method thereof |
CN109634307B (en) * | 2019-01-15 | 2021-08-03 | 大连海事大学 | Unmanned underwater vehicle composite track tracking control method |
CN109850015B (en) * | 2019-02-21 | 2021-08-03 | 江苏大学 | Electric vehicle active front wheel steering control method with automatically adjustable control parameters |
CN110220416B (en) * | 2019-05-15 | 2021-12-10 | 南京理工大学 | Self-adaptive rapid trajectory tracking guidance method |
US11353301B2 (en) * | 2020-01-22 | 2022-06-07 | Raytheon Company | Kinetic energy vehicle with attitude control system having paired thrusters |
US11473884B2 (en) * | 2020-01-22 | 2022-10-18 | Raytheon Company | Kinetic energy vehicle with three-thruster divert control system |
CN111397449B (en) * | 2020-04-03 | 2021-07-20 | 中国北方工业有限公司 | Data chain end guidance method aiming at seeker failure mode |
CN112193236A (en) * | 2020-09-11 | 2021-01-08 | 江苏大学 | Second-order sliding mode anti-collision control method based on active steering and yaw moment control |
US11913757B2 (en) * | 2022-01-18 | 2024-02-27 | Rosemount Aerospace Inc. | Constraining navigational drift in a munition |
Citations (32)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3323757A (en) * | 1961-07-06 | 1967-06-06 | Gen Dynamics Corp | Missile autopilot |
US3946968A (en) * | 1974-08-02 | 1976-03-30 | Raytheon Company | Apparatus and method for aerodynamic cross-coupling reduction |
US4033525A (en) * | 1975-12-08 | 1977-07-05 | The United States Of America As Represented By The Secretary Of The Army | Feedback PDM encoder and method for actuating a pneumatic actuator with a digital autopilot |
US4044237A (en) * | 1976-03-16 | 1977-08-23 | The United States Of America As Represented By The Secretary Of The Army | Missile maneuver concept |
US4054254A (en) * | 1975-12-04 | 1977-10-18 | General Dynamics Corporation | Rolling airframe autopilot |
US4142695A (en) * | 1971-10-27 | 1979-03-06 | Raytheon Company | Vehicle guidance system |
US4198015A (en) * | 1978-05-30 | 1980-04-15 | The United States Of America As Represented By The Secretary Of The Army | Ideal trajectory shaping for anti-armor missiles via time optimal controller autopilot |
US4277038A (en) * | 1979-04-27 | 1981-07-07 | The United States Of America As Represented By The Secretary Of The Army | Trajectory shaping of anti-armor missiles via tri-mode guidance |
US4383662A (en) * | 1978-03-13 | 1983-05-17 | The United States Of America As Represented By The Secretary Of The Army | Ideal trajectory shaping for anti-armor missiles via gimbal angle controller autopilot |
US4470562A (en) * | 1965-10-22 | 1984-09-11 | The United States Of America As Represented By The Secretary Of The Navy | Polaris guidance system |
US4530476A (en) * | 1981-08-12 | 1985-07-23 | E-Systems, Inc. | Ordnance delivery system and method including remotely piloted or programmable aircraft with yaw-to-turn guidance system |
US4589610A (en) * | 1983-11-08 | 1986-05-20 | Westinghouse Electric Corp. | Guided missile subsystem |
US4643373A (en) * | 1984-12-24 | 1987-02-17 | Honeywell Inc. | Missile system for naval use |
US4883239A (en) * | 1987-11-13 | 1989-11-28 | Diehl Gmbh & Co. | Guided artillery projectile with trajectory regulator |
US5058836A (en) * | 1989-12-27 | 1991-10-22 | General Electric Company | Adaptive autopilot |
US5062583A (en) * | 1990-02-16 | 1991-11-05 | Martin Marietta Corporation | High accuracy bank-to-turn autopilot |
US5064141A (en) * | 1990-02-16 | 1991-11-12 | Raytheon Company | Combined sensor guidance system |
US5094406A (en) * | 1991-01-07 | 1992-03-10 | The Boeing Company | Missile control system using virtual autopilot |
US5102072A (en) * | 1990-11-19 | 1992-04-07 | General Dynamics Corporation, Convair Division | Adaptive gain and phase controller for autopilot for a hypersonic vehicle |
US5248114A (en) * | 1974-06-20 | 1993-09-28 | Ankeney Dewey P | Adaptive autopilot |
US5435503A (en) * | 1993-08-27 | 1995-07-25 | Loral Vought Systems Corp. | Real time missile guidance system |
US5544843A (en) * | 1991-08-01 | 1996-08-13 | The Charles Stark Draper Laboratory, Inc. | Ballistic missile remote targeting system and method |
US5590850A (en) * | 1995-06-05 | 1997-01-07 | Hughes Missile Systems Company | Blended missile autopilot |
US5647015A (en) * | 1991-12-11 | 1997-07-08 | Texas Instruments Incorporated | Method of inferring sensor attitude through multi-feature tracking |
US5785281A (en) * | 1994-11-01 | 1998-07-28 | Honeywell Inc. | Learning autopilot |
US5975460A (en) * | 1997-11-10 | 1999-11-02 | Raytheon Company | Nonlinear guidance gain factor for guided missiles |
US6064332A (en) * | 1994-04-26 | 2000-05-16 | The United States Of America As Represented By The Secretary Of The Air Force | Proportional Guidance (PROGUIDE) and Augmented Proportional Guidance (Augmented PROGUIDE) |
US6142412A (en) * | 1999-02-22 | 2000-11-07 | De Sa; Erwin M. | Highly accurate long range optically-aided inertially guided type missile |
US6244536B1 (en) * | 1997-11-26 | 2001-06-12 | The United States Of America As Represented By The Secretary Of The Air Force | Air to air homing missile guidance |
US6254030B1 (en) * | 1983-11-17 | 2001-07-03 | Lockheed Martin Corporation | Vehicle guidance system for guided missiles having adaptive trajectory bias |
US7185844B2 (en) * | 2004-04-30 | 2007-03-06 | Technology Service Corporation | Methods and systems for guiding an object to a target using an improved guidance law |
US7487933B1 (en) * | 2005-07-05 | 2009-02-10 | Chen Robert H | Homing missile guidance and estimation algorithms against advanced maneuvering targets |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5631830A (en) | 1995-02-03 | 1997-05-20 | Loral Vought Systems Corporation | Dual-control scheme for improved missle maneuverability |
US6532454B1 (en) | 1998-09-24 | 2003-03-11 | Paul J. Werbos | Stable adaptive control using critic designs |
US6341249B1 (en) | 1999-02-11 | 2002-01-22 | Guang Qian Xing | Autonomous unified on-board orbit and attitude control system for satellites |
US6611823B1 (en) | 2000-04-20 | 2003-08-26 | Board Of Regents, The University Of Texas System | Backlash compensation using neural network |
US7080055B2 (en) | 2000-10-03 | 2006-07-18 | Board Of Regents, The University Of Texas System | Backlash compensation with filtered prediction in discrete time nonlinear systems by dynamic inversion using neural networks |
US7043345B2 (en) | 2003-10-10 | 2006-05-09 | Raytheon Company | System and method with adaptive angle-of-attack autopilot |
-
2009
- 2009-07-10 US US12/501,395 patent/US8436283B1/en active Active
Patent Citations (33)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US3323757A (en) * | 1961-07-06 | 1967-06-06 | Gen Dynamics Corp | Missile autopilot |
US4470562A (en) * | 1965-10-22 | 1984-09-11 | The United States Of America As Represented By The Secretary Of The Navy | Polaris guidance system |
US4142695A (en) * | 1971-10-27 | 1979-03-06 | Raytheon Company | Vehicle guidance system |
US5248114A (en) * | 1974-06-20 | 1993-09-28 | Ankeney Dewey P | Adaptive autopilot |
US3946968A (en) * | 1974-08-02 | 1976-03-30 | Raytheon Company | Apparatus and method for aerodynamic cross-coupling reduction |
US4054254A (en) * | 1975-12-04 | 1977-10-18 | General Dynamics Corporation | Rolling airframe autopilot |
US4033525A (en) * | 1975-12-08 | 1977-07-05 | The United States Of America As Represented By The Secretary Of The Army | Feedback PDM encoder and method for actuating a pneumatic actuator with a digital autopilot |
US4044237A (en) * | 1976-03-16 | 1977-08-23 | The United States Of America As Represented By The Secretary Of The Army | Missile maneuver concept |
US4383662A (en) * | 1978-03-13 | 1983-05-17 | The United States Of America As Represented By The Secretary Of The Army | Ideal trajectory shaping for anti-armor missiles via gimbal angle controller autopilot |
US4198015A (en) * | 1978-05-30 | 1980-04-15 | The United States Of America As Represented By The Secretary Of The Army | Ideal trajectory shaping for anti-armor missiles via time optimal controller autopilot |
US4277038A (en) * | 1979-04-27 | 1981-07-07 | The United States Of America As Represented By The Secretary Of The Army | Trajectory shaping of anti-armor missiles via tri-mode guidance |
US4530476A (en) * | 1981-08-12 | 1985-07-23 | E-Systems, Inc. | Ordnance delivery system and method including remotely piloted or programmable aircraft with yaw-to-turn guidance system |
US4589610A (en) * | 1983-11-08 | 1986-05-20 | Westinghouse Electric Corp. | Guided missile subsystem |
US6254030B1 (en) * | 1983-11-17 | 2001-07-03 | Lockheed Martin Corporation | Vehicle guidance system for guided missiles having adaptive trajectory bias |
US4643373A (en) * | 1984-12-24 | 1987-02-17 | Honeywell Inc. | Missile system for naval use |
US4883239A (en) * | 1987-11-13 | 1989-11-28 | Diehl Gmbh & Co. | Guided artillery projectile with trajectory regulator |
US5058836A (en) * | 1989-12-27 | 1991-10-22 | General Electric Company | Adaptive autopilot |
US5064141A (en) * | 1990-02-16 | 1991-11-12 | Raytheon Company | Combined sensor guidance system |
US5062583A (en) * | 1990-02-16 | 1991-11-05 | Martin Marietta Corporation | High accuracy bank-to-turn autopilot |
US5102072A (en) * | 1990-11-19 | 1992-04-07 | General Dynamics Corporation, Convair Division | Adaptive gain and phase controller for autopilot for a hypersonic vehicle |
US5094406A (en) * | 1991-01-07 | 1992-03-10 | The Boeing Company | Missile control system using virtual autopilot |
US5544843A (en) * | 1991-08-01 | 1996-08-13 | The Charles Stark Draper Laboratory, Inc. | Ballistic missile remote targeting system and method |
US5870486A (en) * | 1991-12-11 | 1999-02-09 | Texas Instruments Incorporated | Method of inferring sensor attitude through multi-feature tracking |
US5647015A (en) * | 1991-12-11 | 1997-07-08 | Texas Instruments Incorporated | Method of inferring sensor attitude through multi-feature tracking |
US5435503A (en) * | 1993-08-27 | 1995-07-25 | Loral Vought Systems Corp. | Real time missile guidance system |
US6064332A (en) * | 1994-04-26 | 2000-05-16 | The United States Of America As Represented By The Secretary Of The Air Force | Proportional Guidance (PROGUIDE) and Augmented Proportional Guidance (Augmented PROGUIDE) |
US5785281A (en) * | 1994-11-01 | 1998-07-28 | Honeywell Inc. | Learning autopilot |
US5590850A (en) * | 1995-06-05 | 1997-01-07 | Hughes Missile Systems Company | Blended missile autopilot |
US5975460A (en) * | 1997-11-10 | 1999-11-02 | Raytheon Company | Nonlinear guidance gain factor for guided missiles |
US6244536B1 (en) * | 1997-11-26 | 2001-06-12 | The United States Of America As Represented By The Secretary Of The Air Force | Air to air homing missile guidance |
US6142412A (en) * | 1999-02-22 | 2000-11-07 | De Sa; Erwin M. | Highly accurate long range optically-aided inertially guided type missile |
US7185844B2 (en) * | 2004-04-30 | 2007-03-06 | Technology Service Corporation | Methods and systems for guiding an object to a target using an improved guidance law |
US7487933B1 (en) * | 2005-07-05 | 2009-02-10 | Chen Robert H | Homing missile guidance and estimation algorithms against advanced maneuvering targets |
Cited By (66)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20120259579A1 (en) * | 2011-04-07 | 2012-10-11 | Icefield Tools Corporation | Method and apparatus for determining orientation using a plurality of angular rate sensors and accelerometers |
US9134131B2 (en) * | 2011-04-07 | 2015-09-15 | Icefield Tools Corporation | Method and apparatus for determining orientation using a plurality of angular rate sensors and accelerometers |
US20140207361A1 (en) * | 2011-08-09 | 2014-07-24 | Toyota Jidosha Kabushiki Kaisha | Sliding mode controller and internal combustion engine system control device |
US9518515B2 (en) * | 2011-08-09 | 2016-12-13 | Toyota Jidosha Kabushiki Kaisha | Sliding mode controller and internal combustion engine system control device |
US20140360157A1 (en) * | 2013-06-07 | 2014-12-11 | Raytheon Company | Rocket vehicle with integrated attitude control and thrust vectoring |
US9429105B2 (en) * | 2013-06-07 | 2016-08-30 | Raytheon Company | Rocket vehicle with integrated attitude control and thrust vectoring |
US9482530B2 (en) | 2013-11-05 | 2016-11-01 | Raytheon Company | Nadir/zenith inertial pointing assistance for two-axis gimbals |
WO2015069366A1 (en) * | 2013-11-05 | 2015-05-14 | Raytheon Company | Nadir/zenith inertial pointing assistance for two-axis gimbals |
CN104266546A (en) * | 2014-09-22 | 2015-01-07 | 哈尔滨工业大学 | Sight line based finite time convergence active defense guidance control method |
US10041774B2 (en) * | 2014-10-06 | 2018-08-07 | The Charles Stark Draper Laboratory, Inc. | Multi-hypothesis fire control and guidance |
US20160097621A1 (en) * | 2014-10-06 | 2016-04-07 | The Charles Stark Draper Laboratory, Inc. | Multi-hypothesis fire control and guidance |
CN104778376A (en) * | 2015-05-04 | 2015-07-15 | 哈尔滨工业大学 | Method for predicting skipping trajectory of hypersonic glide warhead in near space |
CN106774385A (en) * | 2016-12-05 | 2017-05-31 | 烟台南山学院 | A kind of dirigible spot hover control method of use adaptive variable structure |
US11175115B2 (en) * | 2017-01-05 | 2021-11-16 | Bae Systems Information And Electronic Systems Integration Inc. | Determination of guided-munition roll orientation |
AU2017390611B2 (en) * | 2017-01-05 | 2023-08-17 | Bae Systems Information And Electronic Systems Integration, Inc. | Determination of guided-munition roll orientation |
CN106909165A (en) * | 2017-02-23 | 2017-06-30 | 上海航天控制技术研究所 | Rotary missile body attitude information extracting method based on target seeker multisensor |
US11480413B2 (en) * | 2017-04-10 | 2022-10-25 | Bae Systems Information And Electronic Systems Integration Inc. | Dynamic autopilot |
US20210116216A1 (en) * | 2017-04-10 | 2021-04-22 | Bae Systems Information And Electronic Systems Integration Inc. | Dynamic autopilot |
CN107766967A (en) * | 2017-09-21 | 2018-03-06 | 北京航空航天大学 | A kind of interceptor Predictor-corrector guidance method based on polynomial fitting method |
CN108362174A (en) * | 2018-02-09 | 2018-08-03 | 中国人民解放军火箭军工程大学 | Multiple blocker collaboration detections and the integrated hold-up interception method of guidance and system |
CN110618608A (en) * | 2018-06-20 | 2019-12-27 | 河南科技大学 | Composite guidance tracking control method and device |
CN109085848A (en) * | 2018-08-02 | 2018-12-25 | 西北工业大学 | Air-to-air missile direct force/aerodynamic force finite time anti-saturation control method |
CN110471439A (en) * | 2018-09-25 | 2019-11-19 | 浙江工业大学 | A kind of calm method of rigid aircraft set time posture based on neural network estimation |
CN110488854A (en) * | 2018-09-25 | 2019-11-22 | 浙江工业大学 | A kind of rigid aircraft set time Attitude tracking control method based on neural network estimation |
US10852412B2 (en) * | 2018-10-18 | 2020-12-01 | Bae Systems Information And Electronic Systems Integration Inc. | Bullet state estimator using observer based dynamic system |
CN109696090A (en) * | 2019-01-16 | 2019-04-30 | 哈尔滨工业大学 | It is a kind of for carrier rocket guided missile online single-shot thrust discrimination method |
CN109885074A (en) * | 2019-02-28 | 2019-06-14 | 天津大学 | Quadrotor drone finite time convergence control attitude control method |
CN110045609A (en) * | 2019-04-17 | 2019-07-23 | 北京理工大学 | It is a kind of that perpendicular apparatus control system is played based on PID- sliding-mode variable structure algorithm |
CN110793405A (en) * | 2019-09-16 | 2020-02-14 | 上海航天控制技术研究所 | Self-adaptive control method for preventing instantaneous impact of unfolding of folding rudder of electric steering engine |
CN111026139A (en) * | 2019-09-25 | 2020-04-17 | 中国人民解放军63850部队 | Three-dimensional model attitude adjustment control method based on flight trajectory |
CN110764523A (en) * | 2019-11-13 | 2020-02-07 | 中国人民解放军海军航空大学 | Proportional-integral pre-guiding attack target method based on anti-saturation smooth transformation |
EP3822733A1 (en) * | 2019-11-15 | 2021-05-19 | MBDA UK Limited | Methods of controlling self-propelled flying devices |
WO2021094711A1 (en) * | 2019-11-15 | 2021-05-20 | Mbda Uk Limited | Method of controlling self-propelled flying devices |
US20220404122A1 (en) * | 2019-11-15 | 2022-12-22 | Mbda Uk Limited | Method of controlling self-propelled flying devices |
CN111027206A (en) * | 2019-12-05 | 2020-04-17 | 哈尔滨工业大学 | Adaptive sliding mode control method for interceptor maneuvering target with specified performance |
CN111324142A (en) * | 2020-01-07 | 2020-06-23 | 湖北航天技术研究院总体设计所 | Missile navigator disturbance compensation control method |
CN111174643A (en) * | 2020-01-16 | 2020-05-19 | 中国人民解放军火箭军工程大学 | Aircraft interception method and system under condition of bait interference |
CN111342086A (en) * | 2020-02-29 | 2020-06-26 | 同济大学 | Fuel cell air oxygen ratio and flow pressure cooperative control method and system |
CN111591472A (en) * | 2020-05-15 | 2020-08-28 | 北京世冠金洋科技发展有限公司 | Method and related device for adjusting satellite attitude |
CN113759954A (en) * | 2020-06-03 | 2021-12-07 | 北京理工大学 | Composite guidance method for maneuvering target |
CN112084571A (en) * | 2020-07-16 | 2020-12-15 | 北京航空航天大学 | Method for modeling and decoupling movement of air-drop cruise aircraft with speed reducer |
CN111752158A (en) * | 2020-07-17 | 2020-10-09 | 哈尔滨工业大学 | Second-order sliding mode control method for finite time convergence |
CN112066943A (en) * | 2020-07-28 | 2020-12-11 | 中国空间技术研究院 | Calculation method and device for rotation angle of vector adjustment rotating mechanism |
CN112099348A (en) * | 2020-08-19 | 2020-12-18 | 南京理工大学 | Collision angle control guidance method based on observer and global sliding mode |
CN112001120A (en) * | 2020-08-24 | 2020-11-27 | 哈尔滨工业大学 | Spacecraft-to-multi-interceptor autonomous avoidance maneuvering method based on reinforcement learning |
CN112597619A (en) * | 2020-09-14 | 2021-04-02 | 湖南航天机电设备与特种材料研究所 | Stability simulation design method for primary guidance process of cruise missile |
CN112130578A (en) * | 2020-09-22 | 2020-12-25 | 中国人民解放军海军航空大学 | Method for tracking attack angle of aircraft by sliding mode and switching control |
CN112344795A (en) * | 2020-11-08 | 2021-02-09 | 西北工业大学 | Terminal guidance method for predetermined time convergence |
CN112815787A (en) * | 2020-11-27 | 2021-05-18 | 南京理工大学 | Missile guidance law for multiple missiles to attack maneuvering target simultaneously |
CN112558631A (en) * | 2020-12-04 | 2021-03-26 | 北京理工大学 | Variable parameter guidance method with large falling angle constraint based on measurement information |
CN112577489A (en) * | 2020-12-08 | 2021-03-30 | 北京电子工程总体研究所 | Seeker sight rotation rate extraction method based on interactive multi-model filtering |
CN112799429A (en) * | 2021-01-05 | 2021-05-14 | 北京航空航天大学 | Multi-missile cooperative attack guidance law design method based on reinforcement learning |
CN112965371A (en) * | 2021-01-29 | 2021-06-15 | 哈尔滨工程大学 | Water surface unmanned ship track rapid tracking control method based on fixed time observer |
CN113009824A (en) * | 2021-02-03 | 2021-06-22 | 武汉理工大学 | Self-adaptive strain stability control method and system for stability-variable ship and storage medium |
CN113110048A (en) * | 2021-04-13 | 2021-07-13 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Nonlinear system output feedback adaptive control system and method adopting HOSM observer |
CN113110554A (en) * | 2021-04-30 | 2021-07-13 | 南京航空航天大学 | Four-rotor unmanned aerial vehicle composite continuous rapid terminal sliding mode attitude control method |
CN113639594A (en) * | 2021-05-27 | 2021-11-12 | 西北工业大学 | Fuzzy association fusion method of multi-missile cooperative system |
CN113255234A (en) * | 2021-06-28 | 2021-08-13 | 北京航空航天大学 | Method for carrying out online target distribution on missile groups |
CN113656887A (en) * | 2021-07-28 | 2021-11-16 | 上海机电工程研究所 | Coordinate bias optimization-based extension method and system for bullet motion simulation capability |
CN113959462A (en) * | 2021-10-21 | 2022-01-21 | 北京机电工程研究所 | Quaternion-based inertial navigation system self-alignment method |
CN114034215A (en) * | 2021-11-23 | 2022-02-11 | 航天科工火箭技术有限公司 | Rocket guiding method and device |
CN114280937A (en) * | 2021-12-27 | 2022-04-05 | 南京工业大学 | Bridge crane control method based on finite time compounding |
CN114459479A (en) * | 2022-02-21 | 2022-05-10 | 北京航天嘉诚精密科技发展有限公司 | Device and method for measuring attitude and position of rotating carrier |
CN115289908A (en) * | 2022-06-07 | 2022-11-04 | 西北工业大学 | Method and device for guiding air defense missile introduction section through remote control instruction |
CN115200916A (en) * | 2022-09-16 | 2022-10-18 | 中国电力科学研究院有限公司 | Load decoupling loading device, method and system for wind turbine generator and control system |
CN116839429A (en) * | 2023-09-01 | 2023-10-03 | 北京航空航天大学 | Guidance control integrated method considering view field angle constraint of seeker |
Also Published As
Publication number | Publication date |
---|---|
US8436283B1 (en) | 2013-05-07 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US8436283B1 (en) | System and method for guiding and controlling a missile using high order sliding mode control | |
Bayat | Model predictive sliding control for finite-time three-axis spacecraft attitude tracking | |
Shtessel et al. | Integrated higher-order sliding mode guidance and autopilot for dual control missiles | |
Xin et al. | Indirect robust control of spacecraft via optimal control solution | |
Padhi et al. | Partial integrated guidance and control of interceptors for high-speed ballistic targets | |
US4725024A (en) | Method for spinning up a three-axis controlled spacecraft | |
Burchett et al. | Model predictive lateral pulse jet control of an atmospheric rocket | |
Fresconi et al. | High maneuverability projectile flight using low cost components | |
Zhao et al. | Integrated guidance and control with L2 disturbance attenuation for hypersonic vehicles | |
Zhao et al. | Acceleration autopilot for a guided spinning rocket via adaptive output feedback | |
Creagh et al. | Attitude guidance for spinning vehicles with independent pitch and yaw control | |
Gao et al. | Immersion and invariance-based control of novel moving-mass flight vehicles | |
Orr et al. | Lunar spacecraft powered descent control using higher-order sliding mode techniques | |
Talole et al. | Proportional navigation through predictive control | |
Yeh et al. | Variable structure-based nonlinear missile guidance/autopilot design with highly maneuverable actuators | |
Yeh | Design of nonlinear terminal guidance/autopilot controller for missiles with pulse type input devices | |
Barman et al. | Singularity avoidance controller design for spacecraft attitude control using double-gimbal variable-speed control moment gyro | |
US5875993A (en) | Flight control of an airborne vehicle at low velocity | |
Wong et al. | An attitude control design for the Cassini spacecraft | |
Tournes et al. | Integrated guidance and autopilot for dual controlled missiles using higher order sliding mode controllers and observers | |
Hodžić et al. | Simulation of short range missile guidance using proportional navigation | |
Das et al. | Robust partial integrated guidance and control of interceptors in terminal phase | |
Taur et al. | A composite guidance strategy for SAAMM with side jet controls | |
Krzysztofik et al. | Application of an optimal control algorithm for a gyroscope system of a homing air-to-air missile | |
Thurman et al. | New pulse-modulation technique for guidance and control of automated spacecraft |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AS | Assignment |
Owner name: DAVIDSON TECHNOLOGIES, INC., ALABAMA Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:TOURNES, CHRISTIAN H.;SHTESSEL, YURI B.;REEL/FRAME:023210/0581 Effective date: 20090824 |
|
STCF | Information on status: patent grant |
Free format text: PATENTED CASE |
|
REMI | Maintenance fee reminder mailed | ||
FPAY | Fee payment |
Year of fee payment: 4 |
|
SULP | Surcharge for late payment | ||
FEPP | Fee payment procedure |
Free format text: MAINTENANCE FEE REMINDER MAILED (ORIGINAL EVENT CODE: REM.); ENTITY STATUS OF PATENT OWNER: SMALL ENTITY |
|
FEPP | Fee payment procedure |
Free format text: 7.5 YR SURCHARGE - LATE PMT W/IN 6 MO, SMALL ENTITY (ORIGINAL EVENT CODE: M2555); ENTITY STATUS OF PATENT OWNER: SMALL ENTITY |
|
MAFP | Maintenance fee payment |
Free format text: PAYMENT OF MAINTENANCE FEE, 8TH YR, SMALL ENTITY (ORIGINAL EVENT CODE: M2552); ENTITY STATUS OF PATENT OWNER: SMALL ENTITY Year of fee payment: 8 |