Systems and methods for peak-seeking control

• US 8,447,443 B1
• Filed: 02/07/2012
• Issued: 05/21/2013
• Est. Priority Date: 06/21/2011
• Status: Expired due to Fees

• Current Assignee: California State of (State of California)
• Original Assignee: United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration, Regents of the University of California (University of California)
• Inventors: Ryan, John J, Speyer, Jason L
• Primary Examiner(s): Cheung, Mary
• Assistant Examiner(s): Sweeney, Brian P
• Application Number:
  US13/367,990
• Time in Patent Office: 469 Days
• Field of Search: 701/3, 701/480, 701/510, 340/992
• US Class Current: 701/3
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

A computerized system and method for peak-seeking-control that uses a unique Kalman filter design to optimize a control loop, in real time, to either maximize or minimize a performance function of a physical object (“plant”). The system and method achieves more accurate and efficient peak-seeking-control by using a time-varying Kalman filter to estimate both the performance function gradient (slope) and Hessian (curvature) based on direct position measurements of the plant, and does not rely upon modeling the plant response to persistent excitation. The system and method can be naturally applied in various applications in which plant performance functions have multiple independent parameters, and it does not depend upon frequency separation to distinguish between system dimensions.

Claims

1. A system for controlling a plant in order to maximize performance of a user selected dependent parameter of said plant in accordance with an unknown performance function f(x(t), which is a function of an independent parameter x over time t, comprising:

at least a first sensor in operative relation with said plant to sense said independent parameter thereof;

at least a second sensor in operative relation with said plant to sense said dependent parameter thereof;

a programmable controller, said programmable controller in communication with said first sensor for measuring a value of said independent parameter of said plant at discrete time increments k and in communication with said second sensor for measureing a value of said dependent parameter at said time increments, and for controlling said system in accordance therewith, said programmable controller comprising a processor and a modular computer program, said modular computer program including a plurality of software modules for outputting a control signal for controlling said plant as a function of said independent parameter, said plurality of software modules further comprising

a first module for calculating a difference between a current value of said independent parameter of said plant x_k and a previous value of said independent parameter x_k−

,

a second module for calculating a difference in magnitude between a current value of said dependent parameter f(x_k) and a previous value of said independent parameter f(x<sub>k−

1</sub>),

a third module comprising a linear time-varying Kalman filter for inputting said calculated independent parameter difference and dependent parameter difference for estimating a gradient and Hessian of said performance function there from,

a fourth module for estimating a extremum maximum or minimum of said performance function f(x(t)) based on said estimated gradient and Hessian, and for outputting a command to drive the independent parameter of said physical object toward the performance function extremum; and

a modulator in operative communication with said physical object for combining a persistant excitation signal in accordance with said command and for outputting a control signal to said plant.

2. The system for controlling a plant according to claim 1, further comprising a filter in communication with said modulator for smoothing said command.

3. The system for controlling a plant according to claim 1, wherein said plant is an aircraft, said independent parameter is a position of said aircraft and said dependent parameter is aerodynamic drag on said aircraft.

4. A method for generating a control signal for controlling a plant having an associated but unknown performance function f(x(t)), comprising the steps of:

measuring an independent parameter x(t) of said plant at discrete time increments k;

measuring a user selected dependent parameter f(x(t)) of said plant at discrete time increments k;

calculating a difference between a current value of said independent parameter of said plant x_k and a previous value x<sub>k−

1</sub>;

calculating a difference in magnitude between a current value of said dependent parameter f(x_k) and a previous value f(x<sub>k−

1</sub>);

inputting said calculated difference in said independent parameter and difference in said dependent parameter to a linear time-varying Kalman filter and estimating a gradient and Hessian of said performance function,

estimating a extremum maximum or minimum of said performance function f(x(t)) based on said estimated gradient and Hessian;

outputting a command signal based on said estimated extremum to drive the independent parameter of the plant toward the performance function extremum;

combining a persistant excitation signal in accordance with said outputted command signal; and

outputting said modulated persistant excitation signal as a control signal to said plant for control thereof.

5. The method for generating a control signal for controlling a plant according to claim 4, further comprising a step of filtering said command signal to smooth it.

6. The method for generating a control signal for controlling a plant according to claim 4, wherein said plant is an aircraft, said independent parameter is a position of said aircraft and said dependent variable is aerodynamic drag on said aircraft.

7. A computer program stored on computer readable media at a computer for controlling a user defined dependent parameter of a plant as a function of an independent parameter in accordance with the steps of:

measuring the independent parameter of said plant at discrete time increments k;

calculating a difference between a current value of said independent parameter of said plant x_k and a value at a previous time increment x<sub>k−

1</sub>;

calculating a difference in magnitude between a current value of said dependent parameter f(x_k) and a value at a previous time increment f(x<sub>k−

1</sub>);

inputting said calculated difference in independent parameter and difference in dependent parameter to a linear time-varying Kalman filter and estimating a gradient and Hessian of said performance function,

estimating a extremum maximum or minimum of said performance function f(x(t)) based on said estimated gradient and Hessian;

outputting a command signal based on said estimated extremum to drive the plant toward the performance function extremum;

combining a persistant excitation signal in accordance with said outputted command signal; and

outputting said modulated persistant excitation signal as a control signal to said plant for control thereof.

8. The computer program according to claim 7 for controlling a plant as a function of its movement in accordance with the additional step of filtering said command signal to smooth it.

9. The computer program according to claim 7, wherein said plant is an aircraft, said independent parameter is a position of said aircraft and said dependent variable is aerodynamic drag on said aircraft.