Robust weighted gain-scheduling H∞ vehicle lateral dynamics control in the presence of steering system backlash-type hysteresis

A robust weighted gain-scheduling H
_∞
controller for lateral motion control of in-wheel-motor-driven electric vehicles is presented in this paper. The main control objective is to track the reference yaw rate and regulate the vehicle lateral velocity, with the steering angle and the external yaw moment as two inputs. Two major challenges are dealt with. First, the backlash-type hysteresis embedded in the steering system of a ground vehicle adds a disturbance term to the system. Second, the vehicle longitudinal velocity and the tire cornering stiffness are considered variable, thus making the vehicle lateral dynamics model a linear time-varying uncertain system. The state feedback gain matrix of the controller is designed in the envelope of the weighted H
_∞
performance, and solved using a linear matrix inequality tool. The relative importance of the tracking error and the steering hysteresis can be tuned by a weighting factor; and the uncertainties in the system matrices are resolved by a gain-scheduling design. In addition, the physical limitations of the actuators are treated by an eigenvalue placement technique. Simulation studies conducted in CarSim
^®
show that the proposed controller is capable of attenuating the effects of both the steering system nonlinearities and the time-varying parameters.