Discrete-time extremum-seeking for Wiener–Hammerstein plants

This paper presents a new formulation of extremum-seeking control for discrete-time Wiener–Hammerstein plants. A novel method of analysis using Linear Parameter-Varying (LPV) system theory demonstrates semi-global stability of the control scheme. Assuming only limited plant knowledge, the stability result ensures convergence of the plant output in steady state to a point in an arbitrarily small neighbourhood of the extremum, for appropriately chosen controller parameters. The behaviour of the control scheme is analysed on a simple simulated system, prior to being implemented on an internal combustion engine. Experiments demonstrate how the scheme is able to maximise engine output torque in the presence of an uncertain fuel composition by modifying the spark timing.