Proportional-Integral Extremum Seeking for Vapor Compression Systems

In this paper, we optimize vapor compression system (VCS) power consumption through the application of a novel proportional-integral extremum-seeking controller (PI-ESC) that converges at the same timescale as the process. This extremum-seeking method uses time-varying parameter estimation to determine the local gradient in the map from manipulated inputs to performance output. Additionally, the extremum-seeking control law includes terms proportional to the estimated gradient, which requires subsequent modification of the estimation routine in order to avoid bias. The PI-ESC algorithm is derived and compared to other methods on a benchmark example that demonstrates the improved convergence rate of PI-ESC. PI-ESC is applied to the problem of compressor discharge temperature setpoint selection for a VCS such that power consumption is driven to a minimum. A physics-based simulation model of the VCS is used to demonstrate that with PI-ESC, convergence to the optimal operating point occurs faster than the bandwidth of typical disturbances-enabling application of extremum-seeking control to VCSs in environments under realistic operating conditions. Finally, experiments on a production room air conditioner installed in an adiabatic test facility validate the approach in the presence of significant noise and actuator and sensor quantization.