Adaptive-predictive control system

• US 4,358,822 A
• Filed: 03/30/1981
• Issued: 11/09/1982
• Est. Priority Date: 08/04/1976
• Status: Expired due to Term

• Current Assignee: KERR Controls Limited A Body Corporate of Nova Scotia
• Original Assignee: KERR Controls Limited A Body Corporate of Nova Scotia
• Inventors: Sanchez, Juan M.
• Primary Examiner(s): Ruggiero, Joseph F.
• Application Number:
  US06/249,230
• Time in Patent Office: 589 Days
• Field of Search: 364/105, 364/106, 364/116, 364/118, 364/108, 364/121, 364/501, 364/500, 364/502, 364/148-159, 364/164-165, 364/172, 364/178, 364/179, 364/194
• US Class Current: 700/31
• CPC Class Codes: B01D 3/425 Head-, bottom- and feed stream
• CPC Class Codes: G05B 13/048 using a predictor

Abstract

An adaptive-predictive control system for controlling single-input, single-output or multivariable time-variant processes with known or unknown parameters and with or without time delay, is disclosed. The adaptive-predictive control system of the present invention uses an adaptive-predictive model to determine what control vector should be applied to the processs being controlled to cause the process output to be at some desired value at a future time instant. The parameters of the adaptive-predictive model are updated on a real time basis in a manner which will cause the output vector predicted by the model to approach the actual process output vector.

Claims

1. A method for generating a control vector during each of a plurality of sampling instants k, said control vector to be applied to an apparatus which carries out a process having at least one input variable and at least one output variable, at least one of said input variables defining a process input vector, said apparatus varying said process input vector in accordance with the value of said control vector, said method comprising the steps of:

(A) storing a model which is capable of predicting the trajectory of a dynamic process output vector, which vector is composed of at least one of said process output variables, between future sampling instants k+r+1 and k+r+1+λ

, λ

being a positive integer, as a function of a future sequence of said control vectors between sampling instants k and k+λ

;

(B) selecting, at each of said sampling instants k, a desired dynamic process output trajectory between sampling instants k+r+1 and k+r+1+λ

, said desired dynamic process output trajectory being equal to that specific process output trajectory between sampling instants k+r+1 and k+r+1+λ

, which said model predicts would be caused by a specific future sequence of control vectors between sampling instants k and k+λ

, and such that said specific process output trajectory and said specific future control sequence optimize a chosen performance criterion defined by an index which includes a first set of weighting matrices corresponding to the set of dynamic process output vectors included in the process output trajectory predicted by said model and a second set of weighting matrices corresponding to the set of the control vectors included in the sequence of control vectors that said model predicts will cause said process output trajectory, said weighting matrices being selected such that said index may be minimized without requiring the solution of a Ricatti equation; and

(C) generating, at each of said sampling instants k, that control vector which said model predicts will cause said dynamic process output vector at sampling instant k+r+1 to be equal to the value of said desired dynamic process output trajectory at said sampling instant k+r+1, such that said control vector is equal to the value at sampling instant k of said specific control vector sequence and thereby optimizes said chosen performance criterion.

2. The method of claim 1, further comprising the step of periodically updating the parameters of said model in such a manner that the difference between the actual dynamic process output vector at sampling instant k+r+1 and the dynamic process output vector which said model predicts would result at said sampling instant k+r+1 is reduced towards 0, said step of periodically updating the parameters of said model including the steps of:

(A) periodically generating, in accordance with said adaptive-predictive model as updated at a prior sampling instant, an estimation vector d(k) representative of either an output vector, a control vector or a measurable disturbance vector of said process being controlled at a given sampling instant;

(B) periodically generating an estimated error vector representative of the difference between said estimation vector at said given sampling instant and the actual value of the vector estimated by said estimation vector at said given sampling instant; and

(C) periodically modifying the parameters of said model as a function of said estimated error vector.

3. The method of claim 2, wherein optimization of said chosen performance criterion is obtained by minimizing the value of said index, said index varying as a function of at least one of a reference trajectory of process output vectors, a setpoint of said process, previously measured process output and control vectors, constraints on the permissible value of said control vectors and any other parameter or variables that influence the control performance of said process.

4. The method of claim 3, wherein said index varies as a function of the difference between the values of the process output vector trajectory predicted by said adaptive-predictive model and the values of said reference trajectory and also as a function of the incremental values of the control vector sequence that said model predicts will generate said values of said process output vector trajectory.

5. The method of claim 4, wherein the minimization of said index is obtained when said future specific control sequence is assumed constant from instant k to instant k+λ

.

6. The method of claims 2, 3, 4 or 5, further including the step of generating an incremental vector indicative of the difference between the actual value of said one of said control, output or measurable disturbance vectors at said given sampling instant and the actual value of said one of said control, output or measurable disturbance vectors at an earlier sampling instant;

wherein said estimation vector is the value of said incremental vector estimated by said model as updated at said prior sampling instant; and

wherein said step of generating an estimated error vector comprises the step of determining the difference between the value of said incremental vector and the value of said estimation vector.

7. The method of claim 6, wherein said step of generating said control vector includes the step of generating an incremental control vector, representative of the incremental variation in the input vector of said process, which said model predicts will cause an incremental variation in said dynamic process output vector such that said dynamic process output vector at said sampling instant k+r+1 will be equal to the value of said desired dynamic process output trajectory at said sampling instant k+r+1.

15. The method of claim 3, wherein said reference trajectory is periodically redefined as a function of the previously measured process outputs and evolves according to desired dynamics to the setpoint.

17. The method of claim 1, wherein optimization of said chosen performance criterion is obtained by minimizing the value of said index, said index varying at the function of at least one of a reference trajectory of process output vectors, a setpoint of said process, previously measured process and control vectors, constraints on the permissible value of said control vectors and any other parameter or variables that influence the control performance of said process.

18. The method of claim 17, wherein said index varies as a function of the difference between the values of the process output vector trajectory predicted by said adaptive-predictive model and the values of said reference trajectory and also as a function of the incremental values of the control vector sequence that said adaptive-predictive model predicts will generate said values of said process output vector trajectory.

19. The method of claim 18, wherein the minimization of said index is obtained when said future specific control sequence is assumed constant from instant k to instant k+λ

.

20. The method of claim 1, wherein at least one weighting matrix of said second set of weighting matrices is different than a second weighting matrix of said second set of weighting matrices.

8. A system for generating a control vector during each of a plurality of sampling instants k, said control vector to be applied to an apparatus which carries out a process having at least one input variable and at least one output variable, at least one of said input variables defining a process input vector, said apparatus varying said process input vector in accordance with the value of said control vector, said system comprising:

(A) means for storing a model which is capable of predicting the trajectory of a dynamic process output vector, which vector is composed of at least one of said process output variables, between future sampling instants k+r+1 and k+r+1+λ

, λ

being a positive integer, as a function of a future sequence of said control vector between sampling instants k and k+λ

;

(B) means for selecting, at each of said sampling instants k, a desired dynamic process output trajectory between sampling instants k+r+1 and k+r+1+λ

, said desired dynamic process output trajectory being equal to a specific process output trajectory between sampling instants k+r+1 and k+r+1+λ

, that said model predicts would be caused by a specific future sequence of control vectors between sampling instants k and k+λ

, and such that said specific process output trajectory and said specific future control sequence optimize a chosen performance criterion defined by an index which includes a first set of weighting matrices corresponding to the set of dynamic process output vectors included in the process output trajectory predicted by said model and a second set of weighting matrices corresponding to the set of the control vector included in the sequence of control vectors that said model predicts will cause said process output trajectory, said weighting matrices being selected such that said index may be minimized without requiring the solution of a Ricatti equation; and

(C) means for generating, at each of said sampling instants k, that control vector which said model predicts will cause said dynamic process output vector at sampling instant k+r+1 to be equal to the value of said desired dynamic process output trajectory at said sampling instant k+r+1, such that said control vector is equal to the value at sampling instant k of said specific control vector sequence and thereby optimizes said chosen performance criterion.

9. The system of claim 8, further comprising:

means for periodically updating the parameters of said model in such a manner that the difference between the actual dynamic process output vector at sampling instant k+r+1 and the dynamic process output vector which said model predicts would result at said sampling instant k+r+1 is reduced toward zero, said updating means updating the parameters of said model by;

(A) periodically generating, in accordance with said adaptive-predictive model as updated at a prior sampling instant, an estimation vector d(k) representative of either an output vector, a control vector, or a measurable disturbance vector of said process being controlled at a given sampling instant;

(B) periodically generating an estimated error vector representative of the difference between said estimation vector at said given sampling instant and the actual value of said vector estimated by said estimation vector at said given sampling instant; and

(C) periodically modifying the parameters of said model as a function of said estimated error vector.

10. The system of claim 9, wherein optimization of said chosen performance criterion is obtained by minimizing the value of said index, said index varying as a function of at least one of a reference trajectory of process output vectors, a setpoint of said process, previously measured process output and control vector sequences, constraints on the permissible value of said control vector and any other parameter or variables that influence the control performance of said process.

11. The system of claim 10, wherein said index varies as a function of the difference between the values of the process output vector trajectory predicted by said adaptive-predictive model and the values of said reference trajectory and is also a function of the incremental values of the control vector sequence that said adaptive-predictive model predicts will generate said values of said process output vector trajectory.

12. The system of claim 11, wherein the minimization of said index is obtained when said future specific control sequence is assumed constant from instant k to instant k+λ

.

13. The system of claim 8, 9, 10, 11 or 12, further including means for generating an incremental vector indicative of the difference between the actual value of said one of said control, output or measurable disturbance vectors at said given sampling instant and the actual value of said one of said control, output or measurable disturbance vectors at an earlier sampling instant;

and wherein;

said estimation vector is the value estimated by said model, as updated at said prior sampling instant, of said incremental vector; and

said means for periodically updating the parameters of said model generates said estimated error vector by determining the difference between the value of said incremental vector and the value of said estimation vector.

14. The system of claim 13, wherein said means for generating said control vector includes means for generating an incremental control vector representative of the incremental variation in the input vector of said process, which said model predicts will cause an incremental variation in said dynamic process output vector such that said dynamic process output vector at said sampling instant k+r+1 will be equal to the value of said desired dynamic process output trajectory at said sampling instant k+r+1.

16. The system of claim 10, wherein said reference trajectory is periodically redefined as a function of the previously measured process outputs and evolves according to desired dynamics to the setpoint.