Automatic tuning of motion controllers using search techniques

• US 7,035,694 B2
• Filed: 05/13/2003
• Issued: 04/25/2006
• Est. Priority Date: 05/13/2003
• Status: Active Grant

• Current Assignee: National Instruments Corporation (Emerson Electric Company)
• Original Assignee: National Instruments Corporation (Emerson Electric Company)
• Inventors: Ramamoorthy, Subramanian, Falcon, Jeanne S.
• Primary Examiner(s): Knight, Anthony
• Assistant Examiner(s): Pham, Thomas
• Application Number:
  US10/436,839
• Publication Number:
  US 20040230325A1
• Time in Patent Office: 1,078 Days
• Field of Search: 700/18, 700/63, 700/61, 700/188, 700/28, 700/159, 700/169, 700/13, 700/86, 700/181
• US Class Current: 700/18
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 19/414 Structure of the control system, e.g. common controller or multiprocessor systems, interface to servo, programmable interface controller
• CPC Class Codes: G05B 2219/34208 Motion controller
• CPC Class Codes: G05B 2219/42152 Learn, self, auto tuning, calibrating, environment adaptation, repetition

Abstract

System and method for user configuration of an autotuning algorithm for a controller in a motion control system. A desired trajectory in one or more dimensions for the motion control system is received. Values of one or more gains for a controller are initialized. A response trajectory of the controller and motion control system in response to the desired trajectory is received, and an error determined between the response trajectory and the desired trajectory. A gain space is then experimentally searched to determine final values of the one or more gains for the controller that minimize the error (e.g., Euclidean norm) between the response trajectory and the desired trajectory, e.g., via simulated annealing, or other stochastic, quasi-random, and/or deterministic approaches. After experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined values of the one or more gains.

Claims

1. A carrier medium which stores program instructions for automatically tuning a motion control system, wherein the program instructions are executable by a processor to perform:

receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions, wherein each dimension corresponds to an axis of the motion controller;

initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space;

receiving a response trajectory of the controller and motion control system in response to the desired trajectory;

determining an error between the response trajectory and the desired trajectory; and

experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory;

wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

2. The carrier medium of claim 1, wherein said determining the error between the response trajectory and the desired trajectory comprises:

computing a norm of a difference between the response trajectory and the desired trajectory.

3. The carrier medium of claim 2, wherein the norm comprises a Euclidean norm.

4. The carrier medium of claim 3, wherein the Euclidean norm, L₂, comprises:

${<br><br>d<br><br>}_2={\left(\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>{\left(y<br><br>\left(i\right)-x<br><br>\left(i\right)\right)}^2\right)}^{\frac{1}{2}},$

wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

5. The carrier medium of claim 2, wherein the norm comprises a finite norm.

6. The carrier medium of claim 2, wherein the norm comprises an L₁ norm, comprising:

${<br><br>d<br><br>}_1=\left(\underset{i=0}{\overset{N}{\sum <br><br>}}<br><br>\left(y<br><br>\left(i\right)-x<br><br>\left(i\right)\right)\right),$

wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

7. The carrier medium of claim 2, wherein the norm comprises an L_p norm, comprising:

${<br><br>d<br><br>}_p={\left(\underset{i=0}{\overset{n}{\sum <br><br>}}<br><br>{\left(y<br><br>\left(n\right)-x<br><br>\left(n\right)\right)}^p\right)}^{\frac{1}{p}},$

wherein x comprises the desired trajectory, and wherein y comprises the response trajectory.

8. The carrier medium of claim 7, wherein p is greater than 2.

9. The carrier medium of claim 7, wherein p is greater than 3.

10. The carrier medium of claim 7, wherein p is less than 1.

11. The carrier medium of claim 7, wherein p is infinite.

12. The carrier medium of claim 7, wherein p is equal to a maximum deviation between the desired trajectory and the response trajectory.

13. The carrier medium of claim 1, wherein the controller comprises a PID controller, and wherein the one or more gains comprise:

a proportional gain, an integral gain, and a derivative gain for each respective dimension of the one or more dimensions.

14. The carrier medium of claim 1, wherein the controller operates in accordance with the relation:

u(t)=ƒ

(e(t))

e(t)=y(t)−

x(t)

wherein y(t) and x(t) represent observed and desired values, respectively, of a variable, and wherein the one or more gains comprise a corresponding one or more coefficients or parameters of ƒ

(e(t)).

15. The carrier medium of claim 14, wherein y(t), x(t), and ƒ

(e(t)) are multivariable functions, and wherein the one or more gains comprise coefficients or parameters for each respective dimension of the one or more dimensions.

16. The carrier medium of claim 1, wherein said initializing values of the one or more gains comprises:

selecting a point in the gain space.

17. The carrier medium of claim 16, wherein selecting a point in the gain space comprises:

selecting a random, pseudo-random, or quasi-random point in the gain space.

18. The carrier medium of claim 1, wherein said experimentally searching the gain space comprises:

experimentally searching the gain space using stochastic means.

19. The carrier medium of claim 18, wherein said experimentally searching the gain space using stochastic means comprises:

performing simulated annealing to search the gain space.

20. The carrier medium of claim 19, wherein said performing simulated annealing comprises:

a) evaluating a current response trajectory of the system and controller using current values of the one or more gains, thereby computing a current error of the current response trajectory with respect to the desired trajectory;

b) stochastically determining new values of the one or more gains, wherein the new values are in a specified neighborhood of the current values;

c) evaluating a new response trajectory of the system and controller using the new values of the one or more gains, thereby computing a new error of the new response trajectory with respect to the desired trajectory;

d) if the new error is less than the current error,

setting the current values of the one or more gains to the new values; and

setting the current error to the new error;

e) iteratively performing b) through d) until a stopping condition occurs;

wherein, after said iteratively performing, the controller is operable to control the motion control system.

21. The carrier medium of claim 20, wherein d) further comprises:

if the new error is not less than the current error,

stochastically determining whether to set the current values of the one or more gains to the new values based on a temperature schedule; and

if the determination is made to set the current values of the one or more gains to the new values based on a temperature schedule, setting the current values of the one or more gains to the new values.

22. The carrier medium of claim 21, wherein the program instructions are further executable to perform:

f) if the stopping condition occurs, updating the temperature in accordance with the temperature schedule; and

iteratively performing b) through f) until a halting condition occurs.

23. The carrier medium of claim 1, wherein said experimentally searching the gain space comprises:

experimentally searching the gain space using pseudo-random means.

24. The carrier medium of claim 1, wherein said experimentally searching the gain space comprises:

experimentally searching the gain space using quasi-random means.

25. The carrier medium of claim 24, wherein said experimentally searching the gain space using quasi-random means is performed using a Halton sequence.

26. The carrier medium of claim 1, wherein said experimentally searching the gain space comprises:

experimentally searching the gain space using deterministic means.

27. The carrier medium of claim 1, wherein said experimentally searching the gain space comprises:

experimentally searching the gain space using a hill-climbing technique.

28. The carrier medium of claim 1, wherein said one or more dimensions comprises two or more dimensions.

29. The carrier medium of claim 1, wherein said one or more dimensions comprises three or more dimensions.

30. The carrier medium of claim 1, wherein said one or more dimensions comprises four or more dimensions.

31. The carrier medium of claim 1, wherein the program instructions are further executable to perform:

operating the controller and motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

32. The carrier medium of claim 31, wherein the program instructions are further executable to perform:

performing adaptive automatic tuning of the controller and motion control system by iteratively performing said experimentally searching the gain space to determine successive final values of the one or more gains for the controller during said operating the controller and motion control system.

33. The carrier medium of claim 1, wherein said experimentally searching the gain space to determine final values of the one or more gains for the controller comprises:

a) evaluating a current response trajectory of the system and controller using current values of the one or more gains, thereby computing a current error of the current response trajectory with respect to the desired trajectory;

b) determining new values of the one or more gains;

c) evaluating a new response trajectory of the system and controller using the new values of the one or more gains, thereby computing a new error of the new response trajectory with respect to the desired trajectory;

d) if the new error is less than the current error,

setting the current values of the one or more gains to the new values; and

setting the current error to the new error;

e) iteratively performing b) through d) until a stopping condition occurs;

wherein, after said iteratively performing, the controller is operable to control the motion control system.

34. A computer-based system for automatically tuning a motion control system, the computer system comprising:

a processor;

a memory medium coupled to the processor, wherein the memory medium stores program instructions executable by the processor to;

receive a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions;

initialize values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space;

receive a response trajectory of the controller and motion control system in response to the desired trajectory;

determine an error between the response trajectory and the desired trajectory; and

experimentally search the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory;

wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

35. The computer system of claim 34, further comprising:

a display device coupled to the processor, wherein the display device is operable to display the desired trajectory and the response trajectory.

36. The computer system of claim 34, wherein the display device is further operable to display the error between the desired trajectory and the response trajectory.

37. A memory medium comprising program instructions for automatically tuning a motion control system, wherein the program instructions are computer-executable to perform:

receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions;

initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space;

receiving a response trajectory of the controller and motion control system in response to the desired trajectory;

determining an error between the response trajectory and the desired trajectory; and

experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory;

wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.

38. A computer-implemented method for automatically tuning a controller coupled to a motion control system, the method comprising:

a) initializing current values of one or more gains for the controller;

b) providing an input signal to the controller and system, wherein the input signal specifies a position trajectory/motion profile for the motion control system in one or more dimensions;

c) evaluating a current response of the system and controller to the input signal using the current values of the one or more gains, thereby computing a current value of a metric quantifying an error of the current response with respect to the input signal;

d) determining new values of the one or more gains, wherein the new values are in a specified neighborhood of the current values;

e) evaluating a new response of the system and controller to the input signal using the new values of the one or more gains, thereby generating a new value of the metric quantifying an error of the new response with respect to the input signal;

f) if the new value of the metric and the current value of the metric indicate that the error of the new response is less than the error of the current response,

setting the current values of the one or more gains to the new values; and

setting the current value of the metric to the new value of the metric; and

g) iteratively performing d) through f) until a stopping condition occurs;

wherein, after said iteratively performing, the controller is operable to control the motion control system.

39. A system for automatically tuning a motion control system, the system comprising:

means for receiving a desired trajectory for the motion control system, wherein the desired trajectory is in one or more dimensions, wherein each dimension corresponds to an axis of the motion controller;

means for initializing values of one or more gains for a controller, wherein the one or more gains are comprised in a gain space;

means for receiving a response trajectory of the controller and motion control system in response to the desired trajectory;

means for determining an error between the response trajectory and the desired trajectory; and

means for experimentally searching the gain space to determine final values of the one or more gains for the controller, wherein the final values minimize the error between the response trajectory and the desired trajectory;

wherein after said experimentally searching, the controller is operable to control the motion control system substantially in accordance with the desired trajectory using the determined final values of the one or more gains.