Constraint and limit feasibility handling in a process control system optimizer

• US 7,337,022 B2
• Filed: 06/19/2003
• Issued: 02/26/2008
• Est. Priority Date: 09/11/2002
• Status: Active Grant

• Current Assignee: Fisher-Rosemount Systems Incorporated (Emerson Electric Company)
• Original Assignee: Fisher-Rosemount Systems Incorporated (Emerson Electric Company)
• Inventors: Wojsznis, Wilhelm, Nixon, Mark, Wojsznis, Peter, Blevins, Terrence
• Primary Examiner(s): Hartman, Jr.; Ronald D
• Application Number:
  US10/465,153
• Publication Number:
  US 20040049295A1
• Time in Patent Office: 1,713 Days
• Field of Search: 700 28- 33, 700/36, 700/44, 700/53, 700/51
• US Class Current: 700/36
• CPC Class Codes: G05B 11/32 with inputs from more than one sensing element; with outputs to more than one correcting element
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 13/048 using a predictor

Abstract

An optimization technique for use in driving a process plant controller, such as a model predictive controller, uses an organized, systematic but computationally simple method of relaxing or redefining manipulated, control and/or auxiliary variable constraints when there is no feasible optimal solution within pre-established constraints, to thereby develop an achievable solution for use by the controller. The optimization routine uses penalized slack variables and/or redefines the constraint model in conjunction with the use of penalty variables to develop a new objective function, and then uses the new objective function to determine a control solution that bests meets the original constraint limits.

Claims

1. A method of controlling a process, comprising:

running an optimizer that uses an objective function to develop a solution defining a set of target values;

determining if the solution is feasible with respect to a set of process variable constraints;

if the solution is not feasible;

(1) redefining the process variable constraints for at least one process variable to define a new upper and lower process variable constraint limit for the one process variable;

(2) developing a new objective function by adding a penalty variable to the objective function for the one process variable, wherein the penalty variable penalizes the objective function based on the amount by which the one process variable differs from one of the new process variable constraint limits for the one process variable; and

(3) rerunning the optimizer with the new objective function to develop a new solution defining a new set of target values with the new process variable constraint limits for the one process variable;

providing the target values or the new target values to a controller; and

running the controller using the target values or the new target values to develop a set of control signals for controlling the process.

2. The method of claim 1, further including providing a set of slack variables in the objective function to define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables violates an associated constraint.

3. The method of claim 2, including setting a unit penalty associated with the set of slack variables larger than unit cost variables within the objective function defining one or more economic costs.

4. The method of claim 1, further including providing a set of slack variables in the objective function to define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables differs from an ideal resting value.

5. The method of claim 4, including setting a unit penalty associated with the set of slack variables larger than unit cost variables within the objective function defining one or more economic costs.

6. The method of claim 1, further including providing a set of slack variables in the objective function to define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables differs from a set point.

7. The method of claim 6, including setting a unit penalty associated with the set of slack variables larger than unit cost variables within the objective function defining one or more economic costs.

8. The method of claim 1, including providing a unit penalty for the penalty variable that is larger than one or more unit cost variables defining one or more economic costs within the objective function.

9. The method of claim 1, including providing a unit penalty for the penalty variable that is larger than all unit cost variables defining economic costs within the objective function.

10. The method of claim 1, wherein running the controller includes running a multiple-input, multiple-output controller.

11. The method of claim 10, wherein running the multiple-input, multiple-output controller includes running a model predictive control type controller.

12. A system adapted to be implemented with a processor for use in controlling a process, comprising:

a computer readable medium

an optimizer routine stored on the computer readable medium and executable on the processor to use an objective function to develop a solution defining a set of target values;

a feasibility handling routine stored on the computer readable medium and executable on the processor to determine if the solution is feasible with respect to a set of process variable constraints and if the solution is not feasible;

to redefine the process variable constraints for at least one process variable to define a new upper and lower process variable constraint limit for the one process variable;

to develop a new objective function by adding a penalty variable for the one process variable to the objective function, wherein the penalty variable penalizes the objective function based on the amount by which the one process variable differs from one of the new process variable constraint limits for the one process variable; and

to rerun the optimizer routine with the new objective function to develop a new solution defining a new set of target values with the new process variable constraint limits for the one process variable; and

a controller that receives the target values or the new target values and uses the target values or the new target values to develop a set of control signals to control the process.

13. The system of claim 12, wherein the objective function includes a set of slack variables that define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables violates an associated constraint.

14. The system of claim 13, wherein the objective function includes a unit penalty associated with the set of slack variables that is larger than unit cost variables within the objective function defining one or more economic costs.

15. The system of claim 12, wherein the objective function includes a set of slack variables that define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables differs from an ideal resting value.

16. The system of claim 15, wherein the objective function includes a unit penalty associated with the set of slack variables that is larger than unit cost variables within the objective function defining one or more economic costs.

17. The system of claim 12, wherein the objective function includes a set of slack variables that define a penalty for at least one of the process variables based on the amount by which the at least one of the process variables differs from a set point.

18. The system of claim 17, wherein the objective function includes a unit penalty associated with the set of slack variables that is larger than unit cost variables within the objective function defining one or more economic costs.

19. The system of claim 12, wherein the objective function includes a unit penalty for the penalty variable that is larger than one or more unit cost variables defining one or more economic costs within the objective function.

20. The system of claim 12, wherein the objective function includes a unit penalty for the penalty variable that is larger than all unit cost variables defining an economic cost within the objective function.

21. The system of claim 12, wherein the controller includes a multiple-input, multiple-output controller routine.

22. The system of claim 21, wherein the multiple-input, multiple-output controller routine includes a model predictive control type controller.

23. A method of controlling a process, comprising:

defining at least one constraint associated with each of a set of process variables;

defining an objective function to include one or more economic unit costs associated with the process variables and a penalty variable associated with one of the process variables violating the constraint for the one of the process variables, wherein the penalty variable has a unit penalty that is greater than each of the economic unit costs;

using the objective function to develop a set of process control signals for use in controlling the process; and

using the set of process control signals to control the process.

24. The method of claim 23, wherein defining the at least one constraint includes defining a set of range limits associated with the one of the process variables.

25. The method of claim 23, wherein defining the at least one constraint includes defining a set point associated with the one of the process variables.

26. The method of claim 23, wherein defining the at least one constraint includes defining an ideal resting value associated with the one of the process variables.

27. The method of claim 23, wherein defining the at least one constraint includes defining a first set of range limits associated with the one of the process variables and a second set of range limits associated with the one of the process variables and wherein defining an objective function includes defining a first penalty variable associated with violating the first set of range limits and a second penalty variable associated with violating the second set of range limits, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable.

28. The method of claim 23, wherein defining the at least one constraint includes defining a first value associated with the one of the process variables and a set of range limits associated with the one of the process variables and wherein defining an objective function includes defining a first penalty variable associated with the one of the process variables differing from the first value and a second penalty variable associated with the one of the process variables violating the set of range limits, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable.

29. The method of claim 28, wherein the first value is a set point.

30. The method of claim 28, wherein the first value is an ideal resting value.

31. The method of claim 23, including using the objective function to develop an optimal set of control signals over a time horizon during which one of the process variables is estimated to violate the constraint for that process variable.

32. The method of claim 23, including detecting when the one of the process variables is expected to violate the constraint associated with the one of the process variables and redefining the constraint for the one of the process variables, redefining the objective function and using the redefined objective function to determine the set of process control signals when the one of the process variables is expected to violate the constraint associated with the one of the process variables.

33. The method of claim 32, wherein redefining the objective function includes adding a further penalty variable to the objective function for the one of the process variables, wherein the further penalty variable penalizes the objective function based on the amount by which the one of the process variables differs from the redefined constraint for the one of the process variables.

34. The method of claim 33, wherein adding the further penalty variable includes setting a further unit penalty associated with the further penalty variable larger than the economic unit costs within the objective function defining one or more economic costs.

35. The method of claim 33, wherein adding the further penalty variable includes setting a further unit penalty associated with the further penalty larger than the unit penalty associated with the penalty variable within the objective function.

36. The method of claim 33, wherein adding the further penalty variable includes setting a further unit penalty associated with the further penalty larger than the unit penalty associated with the penalty variable within the objective function.

37. A system for use with a processor to control a process, comprising:

a computer readable medium;

a first routine stored on the computer readable medium and executable on the processor to store at least one constraint associated with each of a set of process variables;

a second routine stored on the computer readable medium and executable on the processor to store an objective function that defines one or more economic unit costs associated with the process variables and a penalty variable associated with at least one of the process variables violating the constraint for the one of the process variables, wherein the penalty variable has a unit penalty that is greater than the economic unit costs; and

a third routine stored on the computer readable medium and executable on the processor to use the objective function to develop a set of process control signals and to use the set of process control signals to control the process.

38. The system of claim 37, wherein the at least one constraint for the one of the process variables includes a set of range limits associated with one of the process variables.

39. The system of claim 37, wherein the at least one constraint for the one of the process variables includes a set point associated with one of the process variables.

40. The system of claim 37, wherein the at least one constraint for the one of the process variables includes an ideal resting value associated with one of the process variables.

41. The system of claim 37, wherein the at least one constraint for the one of the process variables includes a first set of range limits associated with one of the process variables and a second set of range limits associated with the one of the process variables and wherein the objective function includes a first penalty variable associated with the first set of range limits and a second penalty variable associated with the second set of range limits, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable.

42. The system of claim 37, wherein the at least one constraint for the one of the process variables includes a first value associated with the one of the process variables and a set of range limits associated with the one of the process variables and wherein the objective function includes a first penalty variable associated with the one of the process variables differing from the first value and a second penalty variable associated with the one of the process variables violating the set of range limits, wherein a first unit penalty associated with the first penalty variable is less than a second unit penalty associated with the second penalty variable.

43. The system of claim 42, wherein the first value is a set point.

44. The system of claim 42, wherein the first value is an ideal resting value.

45. The system of claim 37, wherein the third routine is executable use the objective function to develop an optimal set of process control signals over a time horizon in which the one of the process variables is estimated to violate the constraint for the one of the process variables.

46. The system of claim 37, including a fourth routine stored on the computer readable medium and executable on the processor to detect when one of the process variables is expected to violate the constraint associated with the one of the process variables and to redefine the constraint for the one of the process variables, to redefine the objective function and to cause the third routine to use the redefined objective function to determine the set of process control signals when the one of the process variables is expected to violate the constraint associated with the one of the process variables.

47. The system of claim 46, wherein the fourth routine is executable to redefine the objective function by adding a further penalty variable to the objective function for the one of the process variables, wherein the further penalty variable penalizes the objective function based on the amount by which the one of the process variables differs from the redefined constraint for the one of the process variables.

48. The system of claim 47, wherein the fourth routine is executable to set a further unit penalty associated with the further penalty variable larger than the economic unit costs within the objective function.

49. The system of claim 47, wherein the fourth routine is executable to set a further unit penalty associated with the further penalty larger than the unit penalty associated with the penalty variable within the objective function.

50. The system of claim 47, wherein the fourth routine is executable to set a further unit penalty associated with the further penalty larger than the unit penalty associated with the penalty variable within the objective function.

51. The system of claim 37, wherein the third routine is an optimizer routine that is executable to develop a set of target values for a controller.

52. The system of claim 37, wherein the third routine is a controller routine.

53. The system of claim 37, wherein the third routine is a model predictive control type controller routine.