LMI-Based Robust Model Predictive Control Architecture for a Quarter Car With Series Active Variable Geometry Suspension

This article proposes a robust model predictive control (RMPC)-based solution for the recently introduced series active variable geometry suspension (SAVGS) to improve the ride comfort and road holding of a quarter car. In order to close the gap between the nonlinear multibody SAVGS model and its linear equivalent, a new uncertain system characterization is proposed that captures unmodeled dynamics, parameter variation, and external disturbances. Based on the newly proposed linear uncertain model for the quarter-car SAVGS system, a constrained optimal control problem (OCP) is presented in the form of a linear matrix inequality (LMI) optimization. More specifically, utilizing semidefinite relaxation techniques, a state-feedback RMPC scheme is presented and integrated with the nonlinear multibody SAVGS model, where state-feedback gain and control perturbation are computed online to optimize performance, while physical and design constraints are preserved. Numerical simulation results with different International Organization for Standardization (ISO)-defined road events demonstrate the robustness and significant performance improvement in terms of ride comfort and road holding of the proposed approach, compared to the conventional passive suspension, as well as, to actively controlled SAVGS by a previously developed conventional $H_{\infty }$ control scheme.