A Second-Order Sliding Mode Controller for Active Suspension Systems

This paper presents a second-order sliding mode controller for active suspension systems. The proposed controller, which occurs a limit cycle as the second-order sliding mode, is designed by the integral sliding mode control theory with the twisting algorithm. With the block diagram algebra, the proposed control system can be converted into a nonlinear feedback system consisting of a linear transfer function and a nonlinear element. For the nonlinear system, the describing function method can approximately lead the existence condition for an ideal limit cycle at desired frequency with desired amplitude. Satisfying the existence condition, the proposed controller could almost occur the desired limit cycle in the vicinity of the switching surface, instead of the perfect sliding mode for the conventional sliding mode control theory. As a result, deterioration of the control efforts due to the chattering in high frequency range, such as the ride comfort or the road holding performance, could be suppressed, since the control input could be smooth. An indicator of the robustness against the perturbation of the plant was led from a view of the existence condition in the Nyquist's plot. Finally, simulation results show the effectiveness of the proposed controller.