Dual objective nonlinear PD sliding mode control based on a reference model for an active suspension system

For an active suspension system based on a reference model, tracking errors always exist due to nonlinearity and unmodeled dynamics. This results in the difficulty of effectively achieving the reference trajectory's acceleration in practical situations, meaning that ride comfort cannot be effectively improved. To solve this problem, the paper explores a tracking controller with dual objectives. This includes a nonlinear PD controller for tracking the desired trajectory and a sliding mode controller concerning body velocity and acceleration. This approach ensures that the body displacement approximately tracks the desired trajectory while significantly improving ride comfort. Additionally, this control method has the advantages of structural simplicity and insensitivity to tracking errors, implying that control parameters can be easily tuned, and control inputs can be effectively reduced. The stability of the controlled system is demonstrated through the Lyapunov stability theory, and a range for the body displacement tracking error is derived. Finally, the controller's performance is tested on an experimental platform and simulation model. The experimental results indicated a substantial reduction of 69.22% and 54.66% in the root mean square values of body acceleration under bump and random excitation, respectively.