Design and implementation of a gain scheduled robust linear quadratic regulator for vehicle direct yaw moment control

Abstract

Modern vehicle safety control systems are critical to the enhancement of lateral vehicle stability and the reduction of fatal accidents. Safety control systems based on direct yaw moment control (DYC) enhance vehicle stability during cornering. In such systems, the yaw moment adjustment is obtained from the difference of the traction/braking forces between the left and right wheels. A DYC can be actuated through the friction brakes, mechanical devices, or individually controlled electric motors. The implementation of the DYC through the friction brakes is not desirable, as it reduces vehicle velocity and consequently degrades driving comfort. On the other hand, electrical differentials and DYC actuation through individually controlled motors are more effective and less intrusive. The major contribution of this project is to propose novel high-level control algorithms for DYC systems that aim to improve vehicle lateral stability using individually controlled electric motors and a novel electrical differential system known as Twinster. The novelty is in the formulation of a control algorithm that improves vehicle stability and handling in severe driving manoeuvres while ensuring robustness against system uncertainties. To guarantee robustness of the control system against system uncertainties and disturbances, this thesis proposes a gain scheduled robust linear quadratic regulator (RLQR), in which an extra control term is added to the feedback term of a conventional LQR to limit the closed-loop tracking error in the neighbourhood of the origin of its state space. In addition, the gains of the proposed regulator optimally vary based on the actual longitudinal vehicle velocity to adapt the closed-loop system to the variations of this parameter. It is noted that the intrinsic parameter-varying nature of the vehicle dynamics model with respect to the longitudinal vehicle velocity can jeopardise the closed-loop performance of fixed-gain control algorithms in different driving conditions. Both numerical and experimental results show the superior performance of the proposed control system compared to conventional LQR control systems in terms of vehicle stability and handling improvement. In addition, the experimental results indicate that the controller is robust against unmodelled dynamics and uncertainties on both individually wheel-controlled and rear-wheel torque-vectoring axle vehicles. This thesis is organised as follows. Chapter 1 introduces the motivation and scope for this thesis, while Chapter 2 includes the literature survey on DYC, the control algorithms, and torque differential devices. Chapter 3 is devoted to the vehicle model for control system design and to the formulation of the control algorithm. Chapter 4 represents the numerical and experimental results of the proposed controller on an electric vehicle with individually controlled wheels. Chapter 5 explains the design process of retrofitting a torque-vectoring device (GKN Twinster) on an electric Formula Student car, whereas Chapter 6 discusses the implementation of the controller on the retrofitted electric Formula Student car. Finally, the discussion and final remarks are included in Chapter 7.