Abstract

This paper presents an LMI-based discrete PI–P cascade control method for active quarter-car suspension systems. The quarter-car dynamics are reformulated into a modified cascade sampled-data model that retains the body–wheel coupling between the sprung-mass and unsprung-mass dynamics. Based on this structure, a finite-memory discrete PI–P controller is developed, where the primary PI loop regulates the body-side response and the secondary proportional loop shapes the wheel–actuator-side dynamics. A Lyapunov stability condition and a tractable LMI synthesis method are derived for controller gain co-design. Numerical simulations show that the proposed controller improves sprung-mass acceleration attenuation while keeping the suspension deflection, tire-load-related response, and actuator effort bounded. The study is positioned for vertical ride comfort control rather than full-vehicle handling evaluation.

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