Achievable performances for basic perturbation-based extremum seeking control in Wiener-Hammerstein plants

This paper presents a case study for determining achievable performances in the basic form of extremum seeking control. Despite recent developments on more powerful versions of the algorithm, no detailed study that investigates this aspect thoroughly and provides clear guidelines for the tuning of this simpler, readily-implementable version is yet available. Interest remains for this basic version, for a variety of reasons. A review of extremum seeking fundamentals, with the support of a few simulations, allows to determine better means of selecting the elementary loop components, maximizing the gradient capture information. The choice of the excitation (dither) fundamental frequency is also better addressed under this optimal condition to effectively discuss achievable loop performance aspects. Most results apply to Wiener-Hammerstein classes of systems (strictly proper and stable system dynamics) and still allow other loop improvement modifications to be applied. Extensions to square wave dither signals and a few comparisons with other recently developed loop improvement techniques are also provided.