WO1996031811A1

WO1996031811A1 - A method of optimal scaling of variables in a multivariable predictive controller utilizing range control

Info

Publication number: WO1996031811A1
Application number: PCT/US1996/004486
Authority: WO
Inventors: Zhuxin J. Lu
Original assignee: Honeywell Inc.
Priority date: 1995-04-03
Filing date: 1996-04-01
Publication date: 1996-10-10
Also published as: CN1138191C; JP3910212B2; US5574638A; JPH11509344A; DE69608887T2; EP0819271A1; CN1179839A; EP0819271B1; DE69608887D1

Abstract

A process control system which includes at least one manipulated variable and at least one controlled variable, provides a method for robust control of a process. Predetermined constraints of the manipulated variables and the controlled variables, and the present values of the manipulated variables are obtained. A set of scale factors for the manipulated variables and the process variables are calculated. The controller (10) is initialized with the set of scale factors, the scale factors determining the relative importance of the manipulated variables and the process variables to the process. New values are calculated for the controlled variables for a predetermined number of points in the future, such that the values of the controlled variables are within the predetermined range thereby obtaining an optimal robustness of the resultant controller. The manipulated variables are also calculated to be within predetermined constraints, and the controlled variables to fall within a predetermined range when controllable. From a plurality of solutions, a most robust solution is selected. Then the manipulated variables are adjusted to cause the process control system to drive the values of the controlled variables to the calculated values.

Description

A METHOD OF OPTIMAL SCALING OF

VARIABLES IN A MULTIVARIABLE PREDICTIVE

CONTROLLER UTILIZING RANGE CONTROL

BACKGROUND OF THE INVENTION

The present invention relates to control systems, and more particularly, to a

method of determining the weight of the controlled and manipulated variables of a

robust multivariable predictive controller (RMPC) utilizing range control.

In current systems, the controller (RMPC) has no idea of the importance of the

controlled variables and manipulated variables, thus requiring the operator (or engineer)

to "tell" the controller which is the most important variable, the second most important

variable,... or if the variables are of equal importance. The user inputs the importance

(or weight) of the variables as part of the initialization procedure of a robust

multivariable predictive controller. The importance of the controlled variables (cv) or

manipulated variables (mv) is a function of several factors, including the units utilized

for the cvs and mvs. Engineers currently account for the units for the cvs and mvs and

attach an importance to the high-low weights of the cvs and mvs.

Assume for example there are three controlled variables, cvl , cv2, and cv3,

where cvl is a temperature, cv2 is a pressure, and cv3 is a concentration variable of the

process, all of course in different engineering units. In this instance one controlled

variable can be more important to the controller than another controlled variable. If the

pressure is in small engineering units (PSI) which can have a range up to 25,000 PSI,

each unit of pressure change may not be as important as 1 ° of temperature change for the process. If the pressure, however, is in atmospheres, then one atmosphere change in

pressure may be more significant then 1° of temperature change.

In the present invention, there is provided an optimal solution for an RJMPC in

the off-line that will determine in a relative sense how important each cv and mv is to

the process. Thus, the operator does not have to be concerned with making the

determination. The user can still override or fine-tune the solution output (i.e., the

weight for the individual variables can be made more or less), however, the present

invention provides the user with an excellent starting point for initializing the controller.

Thus by attaching a weight to the variables of the process, the impact to the

system is reduced and results in a more robust controller.

SUMMARY OF THE INVENTION

Therefore, there is provided by the present invention a method of determining

the weight of the controlled and manipulated variables of a robust multivariable

predictive controller utilizing range control. There is provided by the present invention,

a controller which controls each controlled variable of a process to be within a

corresponding predetermined range. A process control system includes at least one

manipulated variable and at least one controlled variable. A method which provides

robust control of a process, comprises the steps of calculating a set of scale factors for

the manipulated variables and the process variables. The controller is initialized with

the set of scale factors, the scale factors determining the relative importance to the

process of the manipulated variables and the process variables. The robust control is

initialized to have predetermined constraints of the manipulated variables and the controlled variables. The present values of the manipulated variables and the controlled

variables are then obtained. New values are calculated for the controlled variables for a

predetermined number of points in the future, such that the values of the controlled

variables are within the predetermined range thereby obtaining an optimal robustness of

the resultant controller. The manipulated variables are also calculated to be within

predetermined constraints, and the controlled variables to fall within a predetermined

range when controllable; otherwise, to keep the controlled variable constraint violations

to a minimum. From a plurality of solutions, a most robust solution is selected. Then

the manipulated variables are adjusted to cause the process control system to drive the

values of the controlled variables to the calculated values.

Accordingly, it is an object of the present invention to provide a method for

determining the weight of the controlled and manipulated variable of a robust

multivariable predictive controller utilizing range control.

This and other objects of the present invention will become more apparent when

taken in conjunction with the following description and attached drawings, wherein like

characters indicate like parts, and which drawings form a part of the present application.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows a functional block diagram of the process control system in

which the present invention may be utilized; and

Figure 2 shows a flow diagram of determining a minimum condition number of

the resulting diagonal matrix. DETAILED DESCRIPTION

In a robust multiv arible predictive controller (RMPC) utilizing range control of

the present invention, there is devised an optimal solution in an off-line mode that will

determine in the relative sense how important each controlled variable (cv) and each

manipulated variable (mv) is for the process. A detailed description of the RMPC

utilizing range control can be had by reference to U.S. Patent 5,351,184, assigned to the

same assignee as the present application, and is incorporated by reference herein to the

extent necessary for an understanding of the present invention.

Referring to Figure 1 , there is shown a functional block diagram of a process

control system in which the present invention may be utilized. A controller 10 has

multiple outputs, which are coupled as input variables u to a process 20. The process 20

can include, for example, a plurality of elements which can be controlled such as valves,

heaters,.... Process variables y of process 20 include temperature, pressure,

concentration,... which govern product quality. The input variables u (or manipulated

variables mv), are defined as:

and the output variables y (process variables pn or controlled variables cv), are defined

as:

Thus, in this example, the process 20 is a dynamic process P(s) having three (3)

manipulated variables and three (3) controlled variables.

The process 20 is defined by G, where G (original model matrix) is:

Thus, if cvj is pressure, cv2 is temperature and CV3 is concentration

carrying forth the example mentioned previously,

(pressure) cv\ = g\ \ • mvj + g γ - v2 + g_j3- mv3

(temperature) cv2 = g2l ^■ mvj + g22' rnv2 + g23' πιv3

(concentration) CV3 = g3i ^• mvj + g32- mv2 + g33- mv3

As can be seen, pressure is affected by the three respective mvs (^mvl . ^v2- mv3),....

The values of gi \, g 2, gl3.— will vary as a function of the engineering units

(or more simply units) selected for the controlled variables.

If cv2 is a linear measure in inches, and if for example purposes g2i, g22_> ^an^

g23 are 10, 12, 24, respectively, then :

cv2 (inch) = 10 ^• mv\ + 12 ^• mv2 + 24 ^• mv3

such that for every one unit (i.e., one inch) mvj changes cv2 changes 10 inches, for

every inch that mv2 changes cv2 changes 12 inches, and for every inch that mv3

changes cv2 changes 24 inches. If the units are in feet rather than inches then g21 , g22

and g23 are changed to .8, 1.0, and 2.0, respectively. But, the significance of cv2 has increased because for every unit change in cv2 corresponds to a one infect rather than

inches change in cv2- Thus in the overall control process it is undesirable to have CV2

deviating from the set point by one unit, as compared to when CV2 was expressed in

inches.

Since the controller is not sensitized to units, the controller will try to correct a

cv having a higher deviation from its desired position first. Thus, for example, if cv_x

has a deviation of 2 and cvy has a deviation of 1 from their respective desired positions,

the controller will try to move cv_x to its desired position first since it has a higher

number; the controller has no knowledge of units. However, a 2 unit deviation in cv_x

can be less significant than a 1 unit deviation in cvy. (For example, if cv_x is in

millimeters and cv_γ is in feet, cvχ is 2 millimeters apart versus cv_v which is 1 foot

apart. In this case cv_v should be the parameter of concern.) Thus, there must exist a

higher cv weight on cv_y. Similarly, the selection of units for mv must also be

determined. The present invention determines a scaling factor which includes the units

of cvs and mvs.

The method of finding "scaling factors" in accordance with the method of the

present invention will now be described. A diagonal matrix is defined such that:

(Row (Column

Scaling) Scaling) DR determines the importance of each cv, and DC determines the importance of

each mv. Then (using matrix algebra operations well known to those skilled in the art:

DR, • g„ • DC, DR, • g₁₂ • DC₂ DR, • g,₃ • DC₃

G(s) DR₂ • g_2I • DC, DR, • g₂₂ • DC₂ DR, • g₂₃ • DC₃

DR₃ • g₃, • DC, DR₃ • g₃₂ • DC₂ DR₃ • g₃₃ • DC₃

(Scaled)

Next, find a pre scale factor (row scale factor) and a post scale factor (column scale

factor) such that the condition number of the resulting matrix [G(s) scaled matrix] is

minimized. The minimized condition number always gives optimal importance

selecting (i.e., optimal scaling or optimal weighting).

The optimal scaling factors, DR and DC, are is determined in accordance with

the flow diagram of Figure 2. In order to find a minimum condition number an iterative

process is performed.

The process starts with tø = ∞ (where t₀ = condition number of (G) = cond(G))

where G is:

DR is calculated (block 101) where:

DR„

DC is then calculated (block 105) where:

DC,

DC =

DC.

The values of DR and DC are saved for each iteration.

Cond (G) is calculated (block 110) where:

G = (DR)^{r ■} G ^• (DC)^r

The condition number of G is checked against the condition number of G of the

previous iteration (block 115), and if it is less than a predetermined number, the process

exits. If the difference is greater than the predetermined number ε, (tolerance level), the

process repeats at block 101, and the condition number of the iteration just completed is saved (block 120). Note that the first time through the loop, the answer to block 115 is

always NO. In a typical case, the number of iterations is about ten (10).

At the rώ iteration, when the process is exited

DR = DR(1) ^• DR.²) ^• ... -DR(^r).

DC = DCO) ^• DC(²) ^• ... -DC ^").

and

G(s) = DR ^• G ^• DC

The solutions obtained above off-line are then applied to the controller, and

specifically to the RMPC controller of the predetermined embodiment. The scaled

model data is loaded in the RMPC controller (i.e., G(s)). G(s) is essentially a new gain

matrix with different cv units and mv units. Also loaded are the pre and post scale

factors determined above, yielding a controller 10 configuration as shown in Figure 1.

Although the above has been described in conjunction with the RMPC, it will be

understood by those skilled in the art the technique of optimal scaling can be applied to

any process controller.

While there has been shown what is considered the preferred embodiment of the

present invention, it will be manifest that many changes and modifications can be made

therein without departing from the essential spirit and scope of the invention. It is

intended, therefore, in the annexed claims to cover all such changes and modifications

which fall within the true scope of the invention.

Claims

CLAIMS Claim 1. In a process control system having a controller for providing robust

control to a process, the process further having at least one manipulated variable and at

least one process variable, a method for providing the robust control of a process,

comprising the steps of:

a) calculating a set of scale factors for the manipulated

variables and the process variables;

b) initializing the controller with the set of scale factors, the set

of scale factors determining a relative importance to the

process of the manipulated variables and the process

variables;

c) initializing the robust control to have predetermined

constraints of the manipulated variables and the controlled

variables;

d) obtaining present values of the manipulated variables and the process

variables said process variables corresponding to measurement parameters of the

process;

e) calculating new values of the process variables for a predetermined

number of points in the future in order to have the values of the process variables

within the predetermined range to obtain an optimal robustness of the resultant

controller, the manipulated variables being within predetermined constraints,

and the process variables falling within a predetermined range when controllable; otherwise, keeping process variable constraint violations to a

minimum;

f) from a plurality of solutions, selecting a most robust

solution; and

g) controlling the process in accordance with the most robust solution.

Claim 2. A method according to Claim 1 wherein the step of calculating a set of

scale factors includes the steps of:

a) defining a diagonal matrix including row scaling matrix, a gain matrix of

the controller, and a column scaling matrix;

b) from the row scaling matrix, determining a pre scaling factor;

c) from the column scaling matrix, determining a post scaling factor;

d) from the pre scaling factor and the post scaling factor, determining a

condition number;

e) determining if the condition number is less than a predetermined

tolerance level;

f) if the condition number is greater than the predetermined tolerance level,

repeating step (b) thru step (e), otherwise continuing;

g) calculating the set of scale factors from the pre scale factors and the post

scale factors calculated from each iteration for loading into the controller.

Claim 3. In a process control system, a method for providing robust control of a process according to Claim 2, wherein the step of controlling comprises the steps

of: a) outputting the manipulated variables of the most robust solution of step

(f) of Claim 1 to the process; and

b) adjusting the process in response to the manipulated variables to cause the process control system to drive the values of the process variables to the

calculated values of step (f) of Claim 1, thereby providing the control of the

process.

Claim 4. In a process control system, a method for providing robust control of a process according to Claim 3, wherein the step of selecting comprises the step

of: a) determining a set of controlled variables which correspond to minimum

controller magnitude.