Design of sliding mode controller for semi-active suspension systems with magnetorheological dampers

Abstract

This chapter presents two sliding mode controllers of semi-active suspension systems with magnetorheological dampers, which have undesirable nonlinear properties. One sliding mode controller is based on the theory of model-following control. In the model-following controller, a desired semi-active suspension system is chosen as the reference model to be followed, and the control law is determined so that an asymptotically stable sliding mode occurs in the error dynamics between the plant and the reference model states. The advantages of this controller are as follows: (1) measurement of the damping force is not required, (2) the reference model specifies the desired performance considering the passivity constraint of the damper, and (3) it is entirely possible to maintain the sliding mode and achieve high robustness against the nonlinear properties of the damper. The other sliding mode controller is designed by the describing function method so that a switching function is enforced into a desired limit cycle instead of a perfect sliding mode. Although the proposed sliding mode controller cannot generate the limit cycle as desired because of the passivity constraint of controllable dampers, restricting the switching function in the vicinity of the origin can suppress the deterioration due to the passivity constraint, such as increase in jerk of the sprung mass. Moreover, a method for designing an observer is introduced for semi-active suspension systems using variable structure system theory, which provides a highly robust property against modeling errors and disturbances in the context of the matching conditions. The structure of the introduced observer is designed to be robust against road variations, which can be seen as nonstationary system disturbances. Although this structure basically requires the actual damping force to be measured, it is estimated using a model of the damper. Thus, the effect of the estimation errors of the damping force on the state estimation is discussed in detail, and the sufficient conditions for stability of the observer are given using Lyapunov's theory. As a result, both the structure and the design process of the proposed observer are simplified in comparison with existing ones.