Extremum-seeking control system for on/off systems

1. An extremum-seeking control system comprising:

an on/off system operable to affect a variable state or condition of a building by switching between an on state and an off state;

a controller configured to operate the on/off system by providing a pulse width modulated (PWM) control signal having a duty cycle to the on/off system, the PWM control signal causing the on/off system to operate to affect the variable state or condition of the building;

wherein the controller is configured to generate the PWM control signal by:

receiving a performance variable as feedback from the on/off system;

extracting a gradient of the performance variable with respect to the duty cycle;

modulating the duty cycle using an extremum-seeking control technique to determine an optimal value of the duty cycle that drives the gradient toward zero; and

generating the PWM control signal such that each period of the PWM control signal has a pulse width proportional to the duty cycle.

2. The extremum-seeking control system of claim 1 , the controller comprising one or more filters configured to process the performance variable feedback from the on/off system before the controller extracts the gradient of the performance variable with respect to the duty cycle.

3. The extremum-seeking control system of claim 1 , wherein the period of the PWM control signal is defined by a user.

4. The extremum-seeking control system of claim 1 wherein the PWM control signal generated is a pulse train, with each pulse of the pulse train having a constant amplitude.

5. The extremum-seeking control system of claim 1 , wherein the pulse width of a pulse train is determined by an input signal such that a value of the duty cycle will be equal to a percentage of a cycle period occupied by a pulse.

6. The extremum-seeking control system of claim 1 , wherein the controller is configured to:

identify a change in the duty cycle resulting from modulating the duty cycle to drive the gradient toward zero; and

update the pulse width such that the pulse width is maintained proportional to the duty cycle after the change in the duty cycle.

7. The extremum-seeking control system of claim 1 , wherein the controller is configured to:

determine a steady-state value of the duty cycle that drives the performance gradient toward zero; and

perturb the steady-state value of the duty cycle with a dither signal to determine the duty cycle of the PWM control signal.

8. The extremum-seeking control system of claim 1 , wherein the controller is configured to drive the performance variable toward an extremum by driving the gradient toward zero, the extremum comprising a maximum or minimum of the performance variable.

9. The extremum-seeking control system of claim 1 , wherein one or more filters receive and process the performance variable from the on/off system prior to a calculation of the duty cycle.

10. The extremum-seeking control system of claim 1 , wherein the PWM control signal is continuously adjusted and outputted to the on/off system for a period equal to that for which the performance variable is received as feedback.

11. A method for system control comprising:

affecting a variable state or condition of a building by switching between an on state and an off state using an on/off system;

operating a controller to provide a pulse width modulated (PWM) control signal having a duty cycle to the on/off system, the PWM control signal causing the on/off system to operate to affect the variable state or condition of the building;

wherein operating the controller comprises:

receiving a performance variable as feedback from the on/off system;

extracting a gradient of the performance variable with respect to the duty cycle;

modulating the duty cycle using an extremum-seeking control technique to determine an optimal value of the duty cycle that drives the gradient toward zero; and

generating the PWM control signal such that each period of the PWM control signal has a pulse width proportional to the duty cycle.

12. The method of claim 11 , wherein the performance variable received from the on/off system is processed by one or more filters prior to extraction of the gradient of the performance variable with respect to the duty cycle.

13. The method of claim 11 , the generating of the PWM control signal is determined by an input signal such that a value of the duty cycle will be equal to a percentage of a cycle period occupied by a pulse.

14. The method of claim 11 , wherein a cycle period of the PWM control signal is user-defined.

15. The method of claim 11 , wherein widths of pulses of the generated PWM control signal are determined such that a value of the duty cycle will be equal to the pulse width as a percentage of a cycle period.

16. The method of claim 11 , wherein operating the controller includes:

identifying a change in the duty cycle resulting from modulating the duty cycle to drive the gradient toward zero; and

updating the pulse width such that the pulse width is maintained proportional to the duty cycle after the change in the duty cycle.

17. The method of claim 11 , wherein the PWM control signal generated has a constant amplitude.

18. The method of claim 11 , wherein extracting the gradient of the performance variable with respect to the duty cycle includes perturbation using a dither signal.

19. The method of claim 11 , wherein determining the optimal value of the duty cycle corresponds to a PWM control signal configured to drive the performance variable to a desired extremum.

20. The method of claim 11 , wherein generating the PWM control signal is continuous, the PWM control signal being adjusted and outputted to the on/off system for a period equal to that for which the performance variable is received as feedback.