Extremum-seeking control system with saturation constraints

An extremum-seeking controller comprising a processing circuit configured to:

• modulate a manipulated variable provided as an input to a plant using an extremum- seeking control technique to drive a gradient of an objective function with respect to the manipulated variable toward an extremum;
• wherein the objective function comprises a performance variable characterizing a performance of the plant responsive to the manipulated variable and a saturation adjustment term based on both:
• a value of a saturation variable capable of becoming saturated at a subset of values of the manipulated variable, wherein the performance variable remains substantially constant responsive to changes in the manipulated variable when the saturation variable becomes saturated;
• and
• a value of the manipulated variable at which the gradient is calculated relative to a value of the manipulated variable at which the saturation variable is non-saturated.

A real-time optimization controller comprising a processing circuit configured to:

• provide a value of manipulated variable as an input to a plant;
• obtain (1) a value of a performance variable characterizing a performance of the plant responsive to the manipulated variable and (2) a value of a saturation variable affected by the manipulated variable and capable of becoming saturated at a subset of values of the manipulated variable, wherein the performance variable remains substantially constant responsive to changes in the manipulated variable when the saturation variable becomes saturated;
• evaluate an objective function comprising a performance variable term and a saturation adjustment term, the performance variable term comprising the performance variable, and the saturation adjustment term comprising (1) a function of the saturation variable and (2) a function of the value of manipulated variable provided as the input to the plant relative to a value of the manipulated variable at which the saturation variable is non-saturated;
• and
• adjust the value of the manipulated variable provided as the input to the plant using a real-time optimization technique to drive a gradient of the objective function with respect to the manipulated variable toward an extremum.