Extremum-seeking control system for a chilled water plant

1. An extremum-seeking control system for a chilled water plant, the extremum-seeking control system comprising:

a feedback controller for operating equipment of the chilled water plant to achieve a condenser water temperature setpoint, the equipment comprising at least one of a chiller compressor, a condenser water pump, and a cooling tower fan; and

an extremum-seeking controller configured to provide the condenser water temperature setpoint to the feedback controller and to determine an optimal value for the condenser water temperature setpoint by:

perturbing the condenser water temperature setpoint with a stochastic excitation signal;

monitoring a power consumption of the equipment resulting from the perturbed condenser water temperature setpoint;

estimating a normalized correlation coefficient relating the power consumption to the condenser water temperature setpoint;

modulating the condenser water temperature setpoint to drive the normalized correlation coefficient to 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 power consumption, and are applicable to multiple different control loops or plants having multiple different scales.

2. The extremum-seeking control system of claim 1 , wherein the stochastic 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 extremum-seeking control system of claim 1 , wherein the condenser water temperature setpoint comprises:

a stochastic portion defined by the stochastic excitation signal; and

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

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

5. The extremum-seeking control system of claim 1 , wherein the extremum-seeking controller is configured to estimate the normalized correlation coefficient relating the power consumption to the condenser water temperature setpoint by performing a recursive least squares estimation process with exponential forgetting.

6. The extremum-seeking control system of claim 1 , wherein the extremum-seeking controller is configured to estimate a gradient of the power consumption with respect to the condenser water temperature setpoint by performing a regression process.

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

obtaining a linear model for the power consumption, the linear model defining the power consumption as a linear function of the condenser water temperature setpoint and a gradient parameter;

estimating a value for the gradient parameter based on an observed value for the power consumption and an observed value for the condenser water temperature setpoint; and

using the estimated value for the gradient parameter as the gradient of the power consumption with respect to the condenser water temperature setpoint.

8. The extremum-seeking control system of claim 1 , wherein the feedback controller is configured to achieve the condenser water temperature setpoint by adjusting at least one of a speed of the cooling tower fan and a speed of the condenser water pump.

9. An extremum-seeking controller for a chilled water plant, the extremum-seeking controller comprising:

one or more interfaces which provide speed control signals that control equipment of the chilled water plant, the equipment comprising at least one of a chiller compressor, a condenser water pump, and a cooling tower fan; and

a processing circuit configured to determine an optimal value for each of the speed control signals by:

perturbing each of the speed control signals with a different excitation signal;

monitoring a power consumption of the equipment resulting from the perturbed speed control signals;

estimating normalized correlation coefficients relating the power consumption to each of the speed control signals using a recursive estimation process; and

modulating the speed control signals to drive the normalized correlation coefficients to zero using a general set of tuning parameters, wherein the general set of tuning parameters are adapted for use with the normalized correlation coefficients, independent of a scale of the power consumption, and are applicable to different control loops or plants having multiple different scales.

10. The extremum-seeking controller of claim 9 , 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 processing circuit is configured to perform the recursive estimation process for each speed control signal by:

calculating a covariance between the power consumption and the speed control signal;

calculating a variance of the speed control signal; and

using the calculated covariance and the calculated variance to estimate the normalized correlation coefficient relating the power consumption to the speed control signal.

12. The extremum-seeking controller of claim 9 , wherein the processing circuit is configured to perform the recursive estimation process for each speed control signal by:

calculating an exponentially-weighted moving average (EWMA) of a plurality of samples of the speed control signal;

calculating an EWMA of a plurality of samples of the power consumption; and

using the EWMAs to estimate the normalized correlation coefficient relating the power consumption to the speed control signal.

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 processing circuit is configured to perform the regression process by:

obtaining a linear model for the power consumption, the linear model defining the power consumption as a linear function of the speed control signals and a gradient parameter for each of the speed control signals;

estimating a value for each gradient parameter based on observed values for the speed control signals and an observed value for the power consumption; and

using the estimated values for the gradient parameter as the normalized correlation coefficients relating the power consumption to the speed control signals.

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 chilled water plant, the extremum-seeking controller comprising:

one or more interfaces which provide speed control signals that control equipment of the chilled water plant, the equipment comprising at least one of a chiller compressor, a condenser water pump, and a cooling tower fan; and

a processing circuit configured to determine an optimal value for each of the speed control signals by:

perturbing each of the speed control signals with a different excitation signal;

monitoring a power consumption of the equipment resulting from the perturbed speed control signals;

estimating normalized correlation coefficients relating the power consumption to each of the speed control signals; and

modulating the speed control signals to drive the estimated normalized correlation coefficients to zero using a general set of tuning parameters, wherein the general set of tuning parameters are adapted for use with the normalized correlation coefficients, independent of a scale of the power consumption, and are applicable to different control loops or plants having multiple different scales.

17. The extremum-seeking controller of claim 16 , wherein the processing circuit is configured to estimate the normalized correlation coefficient for each speed control signal by:

calculating a covariance between the speed control signal and the power consumption;

calculating a variance of the speed control signal;

calculating a variance of the power consumption; 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 processing circuit is configured to estimate the normalized correlation coefficient for each speed control signal by:

estimating a gradient of the power consumption with respect to the speed control signal;

calculating a standard deviation of the speed control signal;

calculating a standard deviation of the power consumption; 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 processing circuit is configured to estimate the normalized correlation coefficient for each speed control signal by:

calculating an exponentially-weighted moving average (EWMA) of a plurality of samples of the speed control signal;

calculating an EWMA of a plurality of samples of the power consumption; 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.