Active front-steering control of a sport utility vehicle using a robust linear quadratic regulator method, with emphasis on the roll dynamics

Abstract

One of the well-known methods for improving the lateral stability of a vehicle is to utilize an active steering controller. Common active steering systems use feedback signals from a yaw rate sensor and side-slip angle estimation. However, in some driving conditions, skilled drivers can prevent vehicle rollover using the steering angle of the vehicle. Hence, the effect of an active front-steering controller on the roll angle of the vehicle is studied in this paper. For this study, a three-degree-of-freedom linear model of a vehicle which has the lateral motion, the yaw motion and the roll motion as the degrees of freedom is derived. The effectiveness of the active steering controller on the roll stability of the vehicle is examined by simulations in a wide range of longitudinal velocities of the vehicle using a linear quadratic regulator controller. The results obtained indicate that the active steering controller increases the roll stability of the vehicle only at low vehicle speeds and also that consideration of the roll degree of freedom in the design of the active steering controller is not effective at high vehicle speeds. Therefore a two-degree-of-freedom bicycle model is sufficient for active steering controller design. Another part of this paper is dedicated to designing a practical active steering controller for a vehicle with time-varying and uncertain parameters. In fact, designing a controller which guarantees the stability of the vehicle with simultaneous uncertainties in the cornering stiffnesses of the tyres and in the time-varying velocity is the main goal of this paper. Another important advantage of the proposed controller is its simplicity and static structure. In fact, this controller design is carried out offline and can be implemented for use in a real vehicle. This simple and powerful controller is a robust linear quadratic regulator controller. For designing a robust linear quadratic regulator controller, a polytopic model of the two-degree-of-freedom vehicle is obtained, which considers the uncertainty in the parameters. In addition, a linear matrix inequality is used to design a linear quadratic regulator controller for an uncertain or parameter-varying system. Finally, the performance of the designed robust linear quadratic regulator controller was studied by simulating the vehicle responses in some manoeuvres. A sport utility vehicle model is used for simulation purposes. This non-linear vehicle model has eight degrees of freedom and its tyres are assumed to be both linear and non-linear. The performance of the robust linear quadratic regulator controller was studied for vehicles with both linear and non-linear Pacejka tyres. The proposed controller guarantees robust stability of the closed-loop system in the presence of 50% variation in the vehicle speed and 20% uncertainty in the stiffnesses of the tyres.