Robust dynamic surface control of vehicle lateral dynamics using disturbance estimation

Abstract

This paper reports a disturbance estimation-based dynamic surface control method for stabilizing vehicle lateral dynamics through yaw moment control. Based on the single track vehicle model, an uncertain model of the vehicle lateral dynamics is developed which represents the effect of parametric uncertainty and lateral tire force nonlinearity by mismatched, lumped total disturbances. In this model, the longitudinal velocity of the vehicle is considered as a time-varying parameter. Using the developed mathematical vehicle model, an extended state observer is proposed to estimate the total disturbance signals. Next, a dynamic surface controller is designed with the objective of tracking the desired lateral velocity generated by a linear two-degrees-of-freedom vehicle dynamics. The dynamic surface controller uses the estimated disturbances of the extended state observer as feedforward inputs to compensate for the effects of the total disturbances. To achieve an improved robust performance against disturbance estimation errors, the ${\mathcal{H}}_{\infty }$ control technique is incorporated into the DSC design. To this end, using a norm-bounded representation of the longitudinal velocity, the control design is formulated as the feasibility of a finite number of linear matrix inequalities. The stability and robustness of the extended state observer and the dynamic surface control systems are analyzed in a Lyapunov framework and the required mathematical proofs are presented. Considering a lane change and a J-turn maneuver, extensive numerical simulations are performed to show the effectiveness of the proposed control system. The results confirm the improved performance of the closed-loop system compared to the open-loop one, in various driving and road conditions.