Self-perturbing extremum-seeking controller with adaptive gain

Abstract A new extremum-seeking control (ESC) strategy is proposed that can be fully configured from just two macro plant characteristics and that has a negligible oscillation amplitude at steady-state. The strategy is built around a relay with a single gain parameter that affects both the speed of convergence and the amplitude of perturbation. The relay is in a feedback loop that drives the average gradient of a cost function to zero by switching between two states. The strategy is self-perturbing thereby eliminating the need for the traditional ESC dither signal. A second feedback loop adjusts the gain of the relay so that the perturbation amplitude reduces to a small value at steady-state. The ESC strategy was developed with the intent of making it simple to implement and thus viable for use in low cost application areas such as energy systems in buildings. Simulation results using a detailed simulation model of a very common packaged air-conditioning system are presented that demonstrate how the strategy can improve the energy-efficiency compared to current practice.