Fast proportional integral phasor extremum seeking control for a class of nonlinear system * *Funding received from the Horizon 2020 Research Programme of the European Commission under the grant number 649796 (www.opti2020.eu) and the Swedish Governmental Agency for Innovation Systems SIP-PiiA (VIN-NOVA) - PI-SKALP Project (K.A.) and the Natural Sciences and Engineering Research Council of Canada. (M.G.) is hereby gratefully

Abstract

Abstract In this paper, we present a modification of the phasor extremum-seeking control for the fast optimization of a class of Wiener-Hammerstein nonlinear dynamical systems with a general strict unimodal nonlinearity. Based on the prior knowledge of the system’s relative order and number of non-minimum phase zeros, the proposed approach uses a high frequency perturbation signal and the phasor of the plant output to enable fast convergence of the overall system without the need for filters of the plant’s input and output. The extremum-seeking controller has two modes. In addition to the integral term, a proportional term is used to enable the application to very slow and integrating systems. Semi-global practical asymptotic stability analysis of the overall system to the unknown optimum is achieved. The effectiveness of the proposed approach is illustrated using numerical examples for different types of Wiener-Hammerstein systems.