Finite Frequency Fuzzy Static Output Feedback $H_{\infty}$ Control for Diesel Engine Air-Path : Descriptor Approach

This paper is concerned with the finite frequency (FF) fuzzy static output feedback (FSOF) $H_{\infty}$ control design for a four-cylinder diesel engine air-path using descriptor approach. The objective is to regulate the intake and exhaust manifold pressures to desired reference pressures by controlling the Geometry Turbine (VGT) and exhaust gas recirculation (EGR) valves (mass flow rates). For this, the nonlinear average value model based descriptor approach is used to design a FSOF controller to ensure a good tracking of the reference pressures in large operating domain in spite of the fuel flow variation. By using the extended generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions and Finsler's lemma, sufficient conditions are established to ensure both the tracking of reference pressures and the prescribed $H_{\infty}$ performance over a FF interval of the fuel flow variation. Simulation results for constant and variable fuel flow are given to demonstrate the effectiveness of the proposed FSOF fuzzy controller.