Scaling and parameterizing a controller

• US 8,406,905 B2
• Filed: 08/18/2011
• Issued: 03/26/2013
• Est. Priority Date: 04/18/2002
• Status: Active Grant

• Current Assignee: Cleveland State University
• Original Assignee: Cleveland State University
• Inventors: Gao, Zhiqiang
• Primary Examiner(s): Gami, Tejal
• Assistant Examiner(s): Norton, Jennifer L
• Application Number:
  US13/212,274
• Publication Number:
  US 20120035747A1
• Time in Patent Office: 586 Days
• Field of Search: 700/28, 700/32, 700/33, 700/37, 700/42, 700/44, 700/45, 318/561, 318/638
• US Class Current: 700/37
• CPC Class Codes: G05B 11/42 for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
• CPC Class Codes: G05B 13/024 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 15/02 electric
• CPC Class Codes: G05B 19/416 characterised by control of velocity, acceleration or deceleration G05B19/19 takes precedence
• CPC Class Codes: G05B 2219/33347 Master sends servo address, speed, kind of interpolation to slave
• CPC Class Codes: G05B 5/01 electric

Abstract

Controller scaling and parameterization are described. Techniques that can be improved by employing the scaling and parameterization include, but are not limited to, controller design, tuning and optimization. The scaling and parameterization methods described here apply to transfer function based controllers, including PID controllers. The parameterization methods also applies to state feedback and state observer based controllers, as well as linear active disturbance rejection controllers. It is emphasized that this abstract is provided to comply with the rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the application. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

Claims

1. A system for controlling a process of an Nth order closed-loop system, comprising:

a controller having two or more identified gains that are functions of a single control tuning parameter, wherein the controller is embodied on at least one of an integrated circuit, a microprocessor, or a programmable logic device, and wherein

the two or more gains are represented by respective two or more mathematically related functions, wherein an only variable of the respective two or more functions is the single control tuning parameter to yield a parameterized controller,

the single control tuning parameter is a control system bandwidth ω

_c of the controller that defines a common location of N poles of the Nth order closed-loop system, the Nth order closed-loop system comprising the controller and a plant, where N is an integer; and

wherein the parameterized controller is used to control the plant.

2. The system of claim 1, wherein the controller is at least one of a proportional/integral/derivative controller, a state feedback controller, a linear active disturbance rejection controller, or a transfer function based controller.

3. The system of claim 1, wherein the controller is related to the plant in terms of the control system bandwidth ω

_c, a Laplace Transform variable s, and a coefficient ξ

according to;

4. The system of claim 1, further comprising a state observer having an observer gain that is a function of a single tuning parameter ω

_o, wherein ω

_o is an observer bandwidth.

10. The system of claim 1, wherein the controller is a proportional/integral/derivative (PID) controller having parameters that include one or more of proportional gain k_p, integral gain k_i, or derivative gain k_d.

11. The system of claim 1, wherein the controller has a form of:

12. The system of claim 1, wherein the closed-loop system includes a linear extended state observer.

13. The system of claim 1, wherein the linear extended state observer is parameterized to be a function of a single tuning parameter ω

_o, wherein ω

_o is an observer bandwidth.

14. The system of claim 1, wherein M observer poles are placed at −

ω

₀ for an Mth order plant, where M is an integer.

15. The system of claim 1, wherein the controller comprises a transfer function based controller.

16. The system of claim 1, wherein the controller is a state feedback controller.

17. The system of claim 1, wherein the state feedback controller has a form of:

u=r+K{circumflex over (X)}

where u is a control input, r is a reference, K is a state feedback matrix, and {circumflex over (X)} is an estimated state vector.

18. The system of claim 1, wherein the closed-loop system includes a state observer having a form:

=A{circumflex over (X)}+Bu+L(y−

ŷ

)

where is a derivative of the estimated state vector, A is a state matrix, B is an input matrix, L is an observer gain, y is an output, and ŷ

is an observed output.

5. A non-transitory computer-readable medium having stored thereon computer-executable instructions that, in response to execution, cause a processor to perform operations, the operations comprising:

implementing a controller comprising two or more identified gains that are functions of a single tuning parameter, the two or more gains defined by respective two or more mathematically related functions for which an only variable is the single tuning parameter to yield a parameterized controller,

wherein the single tuning parameter is a control system bandwidth ω

_c of the controller that defines a common location of N poles of an Nth order closed-loop system comprising the controller and a plant, where N is an integer; and

controlling the plant using the parameterized controller.

6. The non-transitory computer-readable medium of claim 5, wherein the controller is at least one of a proportional/integral/derivative controller, a state feedback controller, a linear active disturbance rejection controller, or a transfer function based controller.

7. The non-transitory computer-readable medium of claim 6, the operations further comprising tuning the controller for control of the plant by adjusting the control system bandwidth ω

_c.

8. The non-transitory computer-readable medium of claim 5, wherein the controller is related to the plant in terms of the control system bandwidth ω

_c, a Laplace Transform variable s, and a coefficient ξ

according to;

9. The non-transitory computer-readable medium of claim 5, the operations further comprising implementing a state observer having an observer gain that is a function of a single tuning parameter ω

_o, wherein ω

_o is an observer bandwidth.