A gain scheduled robust linear quadratic regulator for vehicle direct yaw moment Control

Direct yaw moment controllers improve vehicle stability and handling in severe manoeuvres. In direct yaw moment control implementations based on Linear Quadratic Regulators (LQRs), the control system performance is limited by the unmodelled dynamics and parameter uncertainties. To guarantee robustness with respect to uncertainties, this paper proposes a gain scheduled Robust Linear Quadratic Regulator (RLQR), in which an extra control term is added to the feedback contribution of a conventional LQR to limit the closed-loop tracking error in a neighbourhood of the origin of its state-space, despite the uncertainties and disturbances acting on the plant. In addition, the intrinsic parameter-varying nature of the vehicle dynamics model with respect to the longitudinal vehicle velocity can compromise the closed-loop performance of fixed-gain controllers in varying driving conditions. Therefore, in this study the control gains optimally vary with velocity to adapt the closed loop system to the variations of this parameter. The effectiveness of the proposed RLQR in improving the robustness of a classical LQR against model uncertainties and parameter variations is proven analytically, numerically and experimentally. The simulation and vehicle test results are consistent with the formal analysis proving that the RLQR reduces the ultimate bound of the error dynamics.