Method for optimal selection of deadbands in on/off controllers
An on-off control system includes on-off equipment configured to operate in either an on state or an off state, an on-off controller configured to cause the equipment to transition between the on state and the off state based on a setpoint value and a deadband value to drive a control variable toward the setpoint value, and a deadband controller, according to some embodiments. In some embodiments, the deadband controller is configured to generate the deadband value used by the on-off controller. In some embodiments, the deadband controller is configured to generate the deadband value by obtaining a cost function that defines a cost based on at least a set of control values and the deadband value and selecting the deadband value that results in an optimal value of the cost function over a range of possible deadband values, the selected deadband value defining an optimal deadband value.
1. An on-off control system comprising:
on-off equipment configured to operate in either an on state or an off state;
an on-off controller configured to cause the on-off equipment to transition between the on state and the off state based on a setpoint value and a deadband value to drive a control variable toward the setpoint value; and
a deadband controller configured to generate the deadband value used by the on-off controller that cause the on-off equipment to transition between the on state and the off state by:
obtaining a cost function that defines a cost based on at least a set of control values and a variable representing the deadband value:
selecting a value of the variable representing the deadband value that results in an optimal value of the cost function from a range of possible deadband values; and
providing the selected value of the variable representing the deadband value for use as the deadband value to the on-off controller.
2. The system of claim 1 , wherein the deadband controller is configured to minimize the cost function using extremum seeking control to select the value of the variable representing the deadband value that results in the optimal value of the cost function.
3. The system of claim 1 , wherein the cost function comprises at least one of:
a determined difference between a peak and a trough of a collected set of control variable values;
an absolute error of the collected set of control variable values relative to the setpoint value;
a mean squared error of the collected set of control variable values relative to the setpoint value; and
an exponentially weighted average of the mean squared error of the collected set of control variable values.
4. The system of claim 3 , wherein the deadband controller is further configured to generate the deadband value based on an empirical relationship between the determined difference and the selected value of the variable representing the deadband value.
5. The system of claim 3 , wherein the deadband controller is configured to cause the on-off controller to operate with a negligible deadband value and collect the set of control variable values over a predetermined time horizon.
6. The system of claim 3 , wherein the deadband controller is configured to generate the deadband value by generating a dither signal for a signal associated with adjusting the deadband value used by the on-off controller, and wherein the deadband controller is further configured to select the value of the variable representing the deadband value that results in an optimal value of the cost function by filtering the mean squared error of the collected set of control variable values.
7. The system of claim wherein the deadband controller is further configured to generate the deadband value by modulating the variable representing the deadband value.
8. The system of claim 1 , wherein the cost function further comprises one or more terms that account for at least one of equipment wear, cycle frequency, and control performance.