Linear time-varying sliding surface design based on co-ordinate transformation for high-order systems

In this study, a sliding mode controller with a linear time-varying sliding surface is proposed for high-order systems by generalizing the co-ordinate transformed sliding surface design algorithm devised by the authors for second-order systems. The sliding mode control law is formulated for the sliding surface that has been defined by using a time-varying function. The equivalent control term of the proposed controller is expressed as a sum of the equivalent control term of the conventional sliding mode controller and an additive signal, which is a linear function of system tracking error vector and a time-dependent monotonous function. Simulations are performed on a third-order non-linear model with external disturbances and parameter variations. The performance of the sliding mode controller with the proposed design methodology is compared both with a conventional sliding mode controller and with another sliding mode controller that also uses an additive term in the control law to minimize the reaching time. The simulation results have shown that the proposed method has improved the robustness and the transient response with respect to related sliding mode controllers.