Extremum seeking controller tuning for heat pump optimization using failure-robust Bayesian optimization

Abstract

Extremum seeking controllers have been investigated for multivariable data-driven energy optimization in heat pumps. In particular, proportional–integral extremum seeking control (PI-ESC) has demonstrated potential for significant acceleration compared to other ESC variants for nonlinear closed-loop control systems. A barrier to PI-ESC’s utilization in self-optimizing control is the fact that the PI-ESC algorithm is fragile. That is, unless the PI-ESC gains (e.g., controller gains, estimator gains) are carefully tuned, small perturbations to these gains can render the closed-loop unstable. Since arbitrary combinations of PI-ESC gains can result in instabilities, we propose a failure-robust Bayesian optimization (FRBO) algorithm that computes PI-ESC gains that ensure the closed-loop system can be driven rapidly to the optimum, while identifying and avoiding regions in the space of PI-ESC gains that are likely to result in instabilities (i.e., failures). The FRBO-tuned PI-ESC is shown to result in rapid closed-loop convergence to optimal values both on benchmark examples and a production-level model of an air conditioning system.