Koopman-based H_∞/GH₂ control for in-wheel motor driven semi-active suspensions with magnetorheological dampers

To comprehensively improve the vertical dynamics of in-wheel motor driven electric vehicles (IWM-EVs), the optimal control of semi-active suspension systems equipped with magnetorheological (MR) dampers is investigated in this paper. The conflicting objectives of ride comfort, driving safety, and suspension stroke are addressed, along with the control challenges introduced by the nonlinear behavior of the MR damper. To accommodate the strong nonlinear coupling between the MR damper and suspension system states, an integrated modeling and control framework is proposed. This framework overcomes the approximation limitations of conventional hierarchical control in handling nonlinear dissipation constraints and eliminates the discontinuities associated with fixed switching logic in segmented control architectures. However, the nonlinear coupled dynamics significantly increase the complexity of controller design and computation. In response to this issue, the Koopman operator theory is employed to derive a globally linear representation of the MR damper dynamics, upon which an integrated linear equivalent model is constructed. Furthermore, an output-feedback H_∞/Generalized H₂ (H_∞/GH₂) control strategy is developed on this basis to optimize the overall vertical performance of the vehicle. Simulation comparisons show that, relative to hierarchical control methods and the conventional Sky-hook control, the proposed integrated strategy better exploits the real-time adjustability of the MR damper, leading to notable improvements in vehicle vertical dynamics under various road excitations.