Robust Mixed H₂/H State Feedback Controller Development for Uncertain Automobile Suspensions with Input Delay

In order to achieve better dynamics performances of a class of automobile active suspensions with the model uncertainties and input delays, this paper proposes a generalized robust linear H-2/H-infinity state feedback control approach. First, the mathematical model of a half-automobile active suspension is established. In this model, the H-infinity norm of body acceleration is determined as the performance index of the designed controller, and the hard constraints of suspension dynamic deflection, tire dynamic load and actuator saturation are selected as the generalized H-2 performance output index of the designed controller to satisfy the suspension safety requirements. Second, a generalized H-2/H-infinity guaranteed cost state-feedback controller is developed in terms of Lyapunov stability theory. In addition, the Cone Complementarity Linearization (CCL) algorithm is employed to convert the generalized H-2/H-infinity output-feedback control problem into a finite convex optimization problem (COP) in a linear matrix inequality framework. Finally, a numerical simulation case of this half-automobile active suspension is presented to illustrate the effectiveness of the proposed controller in frequency-domain and time-domain.