Method and apparatus for approximating gains in dynamic and steady-state processes for prediction, control, and optimization

• US 20060241786A1
• Filed: 02/21/2006
• Published: 10/26/2006
• Est. Priority Date: 05/06/1996
• Status: Active Grant

• Current Assignee: Rockwell Automation Technologies Incorporated (Rockwell Automation, Inc.)
• Original Assignee: Rockwell Automation, Inc.
• Inventors: Piche, Stephen, Martin, Gregory D., Boe, Eugene
• Granted Patent: US 7,418,301 B2
• Time in Patent Office: Days
• US Class Current: 700/29
• 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

A method and apparatus for controlling a non-linear mill. A linear controller is provided having a linear gain k that is operable to receive inputs representing measured variables of the plant and predict on an output of the linear controller predicted control values for manipulatible variables that control the plant. A non-linear model of the plant is provided for storing a representation of the plant over a trained region of the operating input space and having a steady-state gain K associated therewith. The gain k of the linear model is adjusted with the gain K of the non-linear model in accordance with a predetermined relationship as the measured variables change the operating region of the input space at which the linear controller is predicting the values for the manipulatible variables. The predicted manipulatible variables are then output after the step of adjusting the gain k.

Claims

1. A method for controlling a nonlinear system, comprising:

a linear controller receiving inputs representing measured variables of the system, wherein values of the measured variables of the system are in a first operating region, wherein the linear controller is operable to determine predicted control values for manipulable variables that control the system, and wherein the linear controller has a linear gain k;

executing a nonlinear steady-state model of the system, wherein the nonlinear steady-state model has been trained to represent operation of the system over a specified region of the system'"'"'s operating space, and wherein the nonlinear steady state model has a steady-state gain K;

initiating a change in operation of the system, wherein the change operates to move the values of the measured variables of the system from a first operating point to a second operating point, wherein said initiating comprises modifying the nonlinear model in accordance with the change in operation of the system;

determining values of the steady-state gain K at the first and second operating points;

adjusting the linear gain k of the linear controller as a function of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points;

the linear controller determining predicted control values for the manipulable variables in response to said adjusting; and

outputting the predicted control values for the manipulable variables, wherein the predicted control values are useable to control the system.

2. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to a simple average of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points.

3. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to a larger absolute value of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points.

4. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to a weighted average of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points.

5. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to one or more values between the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points inclusively.

6. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to a linear interpolation between the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points inclusively.

7. The method of claim 1, wherein the linear gain k of the linear controller is adjusted according to a nonlinear interpolation between the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points inclusively.

8. The method of claim 1, the method further comprising:

modifying one or more additional parameters of the linear controller as a function of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points, wherein said linear controller determining predicted control variables is further based on said modifying.

9. The method of claim 1, further comprising:

providing the predicted control values as input to the system to control the system.

10. The method of claim 1, further comprising:

adjusting one or more additional parameters of the linear controller based on an associated one or more parameters of the nonlinear model as the values of the measured variables move.

11. The method of claim 10, wherein said adjusting one or more parameters of the linear controller based on an associated one or more parameters of the nonlinear model as the values of the measured variables move comprises:

adjusting allowed changes in the predicted control values for the manipulable variables.

12. The method of claim 1, wherein the change in operation of the system comprises one or more of:

startup of the system; and

changing an objective of the system.

13. The method of claim 12, wherein said changing an objective of the system comprises one or more of:

changing a product; and

changing a product grade.

14. The method of claim 1, further comprising:

controlling the system using the predicted control values for the manipulable variables.

15. The method of claim 14, further comprising:

performing said receiving, said executing, said initiating, said adjusting, said determining, said outputting, and said controlling in an iterative manner to operate the system.

16. The method of claim 1, wherein the linear controller is operable to model the dynamics of the system.

17. The method of claim 1, wherein the specified region of the system'"'"'s operating space over which the nonlinear model has been trained to represent the system is greater than that over which the linear controller is valid.

18. A system for controlling a nonlinear system, comprising:

means for a linear controller receiving inputs representing measured variables of a nonlinear system, wherein values of the measured variables of the nonlinear system are in a first operating region, wherein the linear controller is operable to determine predicted control values for manipulable variables that control the nonlinear system, and wherein the linear controller has a linear gain k;

means for executing a nonlinear steady-state model of the nonlinear system, wherein the nonlinear steady-state model has been trained to represent operation of the nonlinear system over a specified region of the nonlinear system'"'"'s operating space, and wherein the nonlinear steady state model has a steady-state gain K;

means for initiating a change in operation of the nonlinear system, wherein the change operates to move the values of the measured variables of the nonlinear system from a first operating point to a second operating point, wherein said initiating comprises modifying the nonlinear model in accordance with the change in operation of the nonlinear system;

means for determining values of the steady-state gain K at the first and second operating points;

means for adjusting the linear gain k of the linear controller as a function of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points;

means for the linear controller determining predicted control values for the manipulable variables in response to said adjusting; and

means for outputting the predicted control values for the manipulable variables, wherein the predicted control values are useable to control the nonlinear system.

19. A system for operating a nonlinear system, the system comprising:

a linear controller, operable to;

receive inputs representing measured variables of a nonlinear system, wherein values of the measured variables of the nonlinear system are in a first operating region; and

determine predicted control values for manipulable variables that control the nonlinear system, and wherein the linear controller has a linear gain k; and

a nonlinear steady-state model of the nonlinear system, coupled to the linear controller, wherein the nonlinear steady-state model has been trained to represent operation of the nonlinear system over a specified region of the nonlinear system'"'"'s operating space, and wherein the nonlinear steady state model has a steady-state gain K;

wherein, in response to an initiated change in operation of the nonlinear system from a first operating point to a second operating point, including a modification to the nonlinear model in accordance with the change in operation of the nonlinear system, the linear controller is further operable to;

adjust the linear gain k as a function of values of the steady-state gain K of the nonlinear steady-state model at first and second operating points;

output predicted control values for the manipulable variables based on the adjusted linear gain k, wherein the predicted control values are useable to control the nonlinear system.

20. A computer-accessible memory medium that stores program instructions for operating a nonlinear system, wherein the program instructions implement:

a linear controller, operable to;

receive inputs representing measured variables of a nonlinear system, wherein values of the measured variables of the nonlinear system are in a first operating region; and

determine predicted control values for manipulable variables that control the nonlinear system, and wherein the linear controller has a linear gain k; and

a nonlinear steady-state model of the nonlinear system, wherein the nonlinear steady-state model has been trained to represent operation of the nonlinear system over a specified region of the nonlinear system'"'"'s operating space, and wherein the nonlinear steady state model has a steady-state gain K, wherein the program instructions are executable by a processor to perform;

executing the nonlinear steady-state model of the system;

initiating a change in operation of the system, wherein the change operates to move the values of the measured variables of the system from a first operating point to a second operating point, wherein said initiating comprises modifying the nonlinear model in accordance with the change in operation of the system;

determining values of the steady-state gain K at the first and second operating points;

adjusting the linear gain k of the linear controller as a function of the values of the steady-state gain K of the nonlinear steady-state model at the first and second operating points;

the linear controller determining predicted control values for the manipulable variables in response to said adjusting; and

outputting the predicted control values for the manipulable variables, wherein the predicted control values are useable to control the system.