Performance improvement and limitations in extremum seeking control

We propose the inclusion of a dynamic compensator in the extremum seeking algorithm which improves the stability and performance properties of the method. This compensator is added to the integrator used for adaptation to improve the overall relative degree and phase response of the extremum seeking loop. The compensator is potentially more effective in accounting for the plant dynamics than the often used phase shifting of the demodulation signal. We present a detailed analysis of the extremum seeking system based on averaging. This analysis provides two linear models, one for tracking reference changes and the other for sensitivity to noise, which offer insight into how different parameters influence the performance. This analysis is less conservative than in previous cases and allows the use of faster adaptation for improved transients. We extend the extremum seeking method to problems of tracking changes in the set point which are more general than step functions.