Multi-Objective Finite-Frequency H _∞/GH ₂ Static Output-Feedback Control Synthesis for Full-Vehicle Active Suspension Systems: A Metaheuristic Optimization Approach

Abstract

In this paper, the problem of multi-objective control for active suspension systems with polytopic uncertainty is addressed via H ∞ /GH 2 static output feedback with a limited-frequency characteristic. For the overall analysis of the performance demanding both vehicle-ride comfort related to vertical-and transversal-directional dynamics and the time-domain constraints related to the driving maneuverability, a seven-degree-of-freedom full-vehicle model with an active suspension system is investigated. The robust static output-feedback control strategy is adopted because some state variables may not be directly measured in a realistic implementation. In designing this control, the finite-frequency H ∞ performance using the generalized Kalman-Yakubovich-Popov lemma is optimized to improve the passenger's ride comfort, while the GH 2 performance is optimized to guarantee the constraints concerning the suspension deflection limitation, road-holding ability, and actuator saturation problem. This control synthesis problem is formulated as nonconvex bilinear matrix inequalities and requires simultaneous consideration of different finite-frequency domain ranges for vertical and transversal motions for evaluating the H ∞ performance. These design difficulties are overcome by the proposed multi-objective quantum-behaved particle swarm optimizer, which efficiently explores the relevant trade-offs between the considered multiple performance objectives and eventually provides the desired Pareto-optimal control set. Further, the numerical simulation cases of a full-vehicle active suspension system are presented to illustrate the effectiveness of the proposed control synthesis methodology in frequency and time domains.INDEX TERMS Active suspension system, static output feedback, finite frequency, generalized Kalman-Yakubovich-Popov lemma, bilinear matrix inequalities, multi-objective metaheuristic algorithm.