Modular modelling and predictive control for vehicles with anti-roll bar and semi-active electronic dampers

Active chassis systems play a crucial role in enhancing vehicle stability and safety, complementing technologies like Electronic Stability Control (ESC). Among these, active anti-roll bars and semi-active electronic dampers have gained attention for their ability to improve handling and ride comfort while operating on relatively simple principles. In this context, this paper extends the Modular Modelling Methodology (MMM) to incorporate these components into a multibody vehicle model, enabling advanced control strategies for improved dynamic performance. A half-car system, conceived as a multibody system, is used as a case study, considering different configurations for the anti-roll bar (passive and active) and semi-active electronic dampers. The modelling of the passive anti-roll bar is performed using the Finite Element Method (FEM), while the nonlinear dynamics of the semi-active electronic dampers are derived using the continuity equation and the flow-through-orifice equation. The results obtained from the model derived through the MMM are compared to those of commercial multibody system analysis software. A new Reduced Order Model (ROM) is proposed for the half-car system to synthesize control algorithms for vertical nonlinear dynamics. This ROM accounts for important effects generally neglected, such as spring and tire pretension and the variation of the damping coefficients of the semi-active electronic dampers. A time-varying Model Predictive Control (MPC) is designed based on the proposed ROM. The MPC is tested through numerical simulations, considering the multibody model derived through the MMM and coupled with the anti-roll bar and semi-active electronic dampers as the real plant in two scenarios: (1) a roll test and (2) a fishhook maneuver. The performance is compared with different controllers, such as PD, LQR, and LQG. The comparisons reveal the superior performance of the MPC in attenuating the roll angle (up to 61.4%), increasing energy dissipation through the dampers (up to 23.1%), and reducing the energy consumption of the active anti-roll bar (by more than 51.7%). Additionally, interesting insights are gained into how the MPC optimally varies the damping coefficient of the semi-active electronic dampers.