Performance Improvement in Fast Extremum Seeking With Adaptive Phase Compensator and High-Gain Optimizer

In this article, an adaptive phase compensator and a high-gain optimizer are proposed for the fast extremum-seeking (ES) scheme acting on a Hammerstein plant. Unlike the widely applied three-time scale tuning, a time scale-independent tuning is achieved by restricting the plant to have a Hammerstein structure and elevating the adaptation of the control input which makes it as fast as the dither signal. Albeit the existed fast ES schemes utilize a high-frequency sinusoidal dither in order to achieve fast minimization of the plant's static nonlinearity, the phase shift of the plant could not be neglected as the frequency is high and the ES may fail to reach the extreme values if the shift is large enough. Thus, an effective adaptive frequency varying phase compensation method is introduced to deal with the phase shift under the assumptions in this article. Moreover, a high-gain optimizer is presented to remove the restriction that the adaptation gain has to be small and could still guarantee the stability properties, which makes the proposed scheme more practical. The effectiveness of the proposed scheme is illustrated by numerical simulations.