Robust gain-scheduling energy-to-peak control of vehicle lateral dynamics stabilisation

In this paper, we investigate the vehicle lateral dynamics stabilisation problem to enhance vehicle handling by considering time-varying longitudinal velocity. The longitudinal velocity is described by a polytope with finite vertices and a novel technique is proposed to reduce the number of vertices. Since the tyre dynamics is nonlinear, the cornering stiffness is represented via the norm-bounded uncertainty. Concerning the time-varying velocity and the nonlinear tyre model, a linear parameter-varying vehicle model is obtained. As the velocity and the states are measurable, a gain-scheduling state-feedback controller is introduced. In the lateral control, the sideslip angle is required to be as small as possible and the yaw rate is constrained to a certain level. Thus, the control objective is to minimise the sideslip angle while the yaw rate is under a prescribed level or constrain both the sideslip angle and the yaw rate to prescribed levels. To consider the transient response of the closed-loop system, the -stability is also employed in the energy-to-peak control. The optimal controller can be obtained by solving a set of linear matrix inequalities. A nonlinear vehicle model is utilised to illustrate the design procedure and the effectiveness of the proposed design method. Finally, simulations and comparisons are carried out to show the significant advantage of the designed controller. Compared to the open-loop system, the closed-loop system with the designed controller can achieve much smaller sideslip angle and the yaw rate is closer to the desired yaw rate from a reference model. Therefore, the vehicle safety and the handling are both improved in our simulation cases.