Proportional--Integral Extremum Seeking for Vapor Compression Systems

In this paper, we optimize vapor compression system power consumption through the application of a newlydeveloped proportional--integral extremum seeking controller (PI-ESC) that converges at the same timescale as the process. This method modifies the control law to include terms proportional to the estimated gradient, but this modification of the control law requires a more sophisticated gradient estimator in order to avoid bias. We develop a PI-ESC for which this bias is eliminated. PI-ESC is applied to the problem of compressor discharge temperature setpoint selection for a vapor compression system where setpoints are automatically determined so that power consumption is minimized. The vapor compression system operates with a regulating feedback controller configured to drive the compressor discharge temperature to setpoints selected by the PI-ESC, and we use a physics-based simulation model to demonstrate that power consumption is minimized dramatically faster than by traditional perturbation-based methods.