A case study of performance improvement in extremum seeking control

The authors previously (1999) proposed 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. A detailed analysis based on averaging was presented there, an extension of the extremum seeking method was given for problems of tracking not just set points but general reference signals, and numerical results for LTI approximations of the scheme were performed. In this paper we move on to an extensive simulation study of the fully nonlinear time-varying scheme and present the key results of this study. These results confirm the theory-based design guidelines that we offered in the previous paper