Extremum-seeking control system for a plant

1. A control system for a plant, the control system comprising:

a feedback controller for operating the plant to achieve a value of a manipulated variable; and

an extremum-seeking controller configured to provide the value of the manipulated variable to the feedback controller and to determine a value for the manipulated variable by:

perturbing the manipulated variable with an excitation signal;

monitoring a performance variable of the plant resulting from the perturbed manipulated variable;

estimating a normalized correlation coefficient relating the performance variable to the manipulated variable;

modulating the manipulated variable to drive the normalized correlation coefficient toward zero using a general set of tuning parameters, wherein the general set of tuning parameters are adapted for use with the normalized correlation coefficient, independent of a scale of the performance variable.

2. The control system of claim 1 , wherein the excitation signal is a non periodic signal comprising at least one of a random walk signal, a non deterministic signal, and a non-repeating signal.

3. The control system of claim 1 , wherein the value of the manipulated variable comprises:

a stochastic portion defined by a stochastic excitation signal; and

a non-stochastic portion determined by driving the normalized correlation coefficient to zero.

4. The control system of claim 1 , wherein the extremum-seeking controller comprises an integrator configured to generate the excitation signal by integrating a random noise signal.

5. The control system of claim 1 , wherein the extremum-seeking controller is configured to estimate the normalized correlation coefficient relating the performance variable to the manipulated variable by performing a recursive least squares estimation process with exponential forgetting.

6. The control system of claim 1 , wherein the extremum-seeking controller is configured to estimate a gradient of the performance variable with respect to the manipulated variable by performing a regression process.

7. The control system of claim 6 , wherein the regression process comprises:

obtaining a linear model for the performance variable, the linear model defining the performance variable as a linear function of the manipulated variable, an offset parameter, and a gradient parameter;

estimating a value for the gradient parameter based on an observed value for the performance variable and an observed value for the manipulated variable; and

using the estimated value for the gradient parameter as the gradient of the performance variable with respect to the manipulated variable.

8. The control system of claim 1 , wherein the feedback controller is configured to achieve the manipulated variable by adjusting operation of equipment of the plant.

9. An extremum-seeking controller for a plant comprising:

one or more processors; and

one or more non-transitory computer-readable media storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

perturbing a manipulated variable with an excitation signal and providing the perturbed manipulated variable as an input to a plant;

monitoring a performance variable of the plant resulting from the perturbed manipulated variable;

estimating a normalized correlation coefficient relating the performance variable to the manipulated variable; and

modulating the manipulated variable to drive the normalized correlation coefficient toward zero using a general set of tuning parameters, wherein the general set of tuning parameters are adapted for use with the normalized correlation coefficient, independent of a scale of the performance variable.

10. The extremum-seeking controller of claim 9 , wherein the normalized correlation coefficient is estimated with a recursive estimation process, wherein the recursive estimation process is a recursive least squares estimation process with exponential forgetting.

11. The extremum-seeking controller of claim 9 , wherein the one or more processors are configured to perform the recursive estimation process for the manipulated variable by:

calculating a covariance between the performance variable and the manipulated variable;

calculating a variance of the manipulated variable; and

using the calculated covariance and the calculated variance to estimate the normalized correlation coefficient relating the performance variable to the manipulated variable.

12. The extremum-seeking controller of claim 9 , wherein the one or more processors are configured to perform the recursive estimation process for the manipulated variable by:

calculating an exponentially-weighted moving average (EWMA) of a plurality of samples of the manipulated variable;

calculating an EWMA of a plurality of samples of the performance variable; and

using the EWMAs to estimate the normalized correlation coefficient relating the performance variable to the manipulated variable.

13. The extremum-seeking controller of claim 9 , wherein the recursive estimation process is a regression process.

14. The extremum-seeking controller of claim 13 , wherein the one or more processors are configured to perform the regression process by:

obtaining a linear model for the performance variable, the linear model defining the performance variable as a linear function of the manipulated variable and a gradient parameter for the manipulated variable;

estimating a value for the gradient parameter based on observed value for the manipulated variable and an observed value for the performance variable; and

using the estimated values for the gradient parameter as the normalized correlation coefficients relating the performance variable to the manipulated variable.

15. The extremum-seeking controller of claim 9 , wherein the excitation signal is a non periodic signal comprising at least one of a random walk signal, a non deterministic signal, and a non-repeating signal.

16. An extremum-seeking controller for a plant, the extremum-seeking controller comprising:

one or more processors; and

one or more non-transitory computer-readable media storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

perturbing each of a plurality of manipulated variables with a different excitation signal;

monitoring a performance variable of the plant resulting from each of the perturbed manipulated variables;

estimating normalized correlation coefficients relating the performance variable to each of the perturbed manipulated variables; and

modulating the manipulated variables to drive the estimated normalized correlation coefficients toward zero using a general set of tuning parameters, wherein the general set of tuning parameters are adapted for use with the normalized correlation coefficient, independent of a scale of the performance variable.

17. The extremum-seeking controller of claim 16 , wherein the one or more processors are configured to estimate the normalized correlation coefficient for each manipulated variable by:

calculating a covariance between each of the manipulated variables and the performance variable;

calculating a variance of each of the manipulated variables;

calculating a variance of the performance variable; and

using the calculated covariance and the calculated variances to estimate the normalized correlation coefficient.

18. The extremum-seeking controller of claim 16 , wherein the one or more processors are configured to estimate the normalized correlation coefficient for each of the manipulated variables by:

estimating a gradient of the performance variable with respect to each of the manipulated variables;

calculating a standard deviation of each of the manipulated variables;

calculating a standard deviation of the performance variable; and

using the estimated gradient and the calculated standard deviations to estimate the normalized correlation coefficient.

19. The extremum-seeking controller of claim 16 , wherein the one or more processors are configured to estimate the normalized correlation coefficient for each of the manipulated variables by:

calculating an exponentially-weighted moving average (EWMA) of a plurality of samples of each of the manipulated variables;

calculating an EWMA of a plurality of samples of the performance variable; and

using the EWMAs to estimate the normalized correlation coefficient.

20. The extremum-seeking controller of claim 16 , wherein the excitation signal is a non periodic signal comprising at least one of a random walk signal, a non deterministic signal, and a non-repeating signal.