Integrated torque-vectoring and anti-roll moment distribution strategies based on optimal control: influence of model complexity and road curvature preview

Abstract

Although the vehicle dynamics effects of variable anti-roll moment distribution actuated through active suspension systems are widely discussed in the literature, their model-based control has only been recently analysed, given the highly nonlinear nature of the involved dynamics. Moreover, the available studies do not discuss the trade-off between internal model complexity and controller performance, nor analyse the opportunities offered by vehicle connectivity, which enables the prediction of the steering angle and reference yaw rate profiles ahead. To address the gap, this paper introduces and assesses three optimal controllers for an electric vehicle with active suspensions, multiple powertrains, and a brake-by-wire system. The formulations are: (a) a gain scheduled output feedback linear quadratic regulator (OFLQR); (b) a nonlinear model predictive controller using a three-degree-of-freedom prediction model, without and with preview of the steering angle and reference yaw rate ahead, respectively referred to as NMPC-3 and NMPC-3-Pre; and (c) a nonlinear model predictive controller based on an eight-degree-of-freedom prediction model, referred to as NMPC-8 and NMPC-8-Pre depending on the absence or presence of preview. The results on an experimentally validated model show that: (i) NMPC-8 provides evident yaw rate tracking benefits with respect to (w.r.t) OFLQR and NMPC-3; and (ii) NMPC-8-Pre can bring ∼20% yaw rate tracking improvement w.r.t. an optimally tuned NMPC-8 configuration.