Input–Output Decoupling Control by Measurement Feedback in Four-Wheel-Steering Vehicles

Abstract

The well-known single-track linearized model for four-wheel-steering vehicle dynamics is used to design a second-order dynamic decoupling controller. Yaw rate and lateral speed are the outputs to be decoupled, while the rear steering angle and an additive steering angle with respect to the driver command are the control inputs. It is shown that the lateral speed dynamics and the yaw rate dynamics can be decoupled by feeding back longitudinal speed, yaw rate, and lateral acceleration measurements, while the effect of sensor disturbances on yaw rate is attenuated. Lateral speed measurements or observers are not required. The yaw rate controlled dynamics are independent from lateral speed and are described by a third-order input-output model, depending on the driver steering wheel command and sensor disturbances; the lateral speed dynamics are autonomous and tend exponentially to zero with a vehicle-dependent time constant while the lateral acceleration tends to be proportional to the yaw rate. The nonlinear analysis on a single-track model shows the suppression of the unstable equilibrium points of the uncontrolled system, the generation of new stable equilibrium points as the critical driver step input increases, and the enlargement of the stability regions. Simulations of typical maneuvers and disturbances on a nonlinear third-order single-track model and on a higher order model provided by CarSim show robustness with respect to unmodeled dynamics, vehicle parameter uncertainty, and sensor disturbances; moreover, significant dynamic decoupling, larger bandwidth, overshoot suppression, and improved maneuverability even at high speed are confirmed.