A new design method for sliding mode controllers using a linear time-varying sliding surface

The main objective of this study is to present a time-varying sliding surface using a new design method to improve the performance of a classical sliding mode controller that has a constant linear sliding surface. In the proposed method, the sliding surface is defined on new coordinate axes: one of the coordinates is the original sliding surface and the other one is naturally chosen as perpendicular to this axis. An important property of the proposed method is that it has a simple geometric interpretation and provides continuous movement of the sliding surface. A comparison of the proposed method against both the classical sliding mode controller and sliding mode controller with a discretely rotating sliding surface is made through simulations. Simulations are first performed on a typical second-order linear system without any disturbances and parameter variations. Next, bounded external disturbance and parameter variations are inserted into the system simulations. Results have shown that the proposed method improved the system performance, providing decreases in the reaching and settling times, and the proposed method has demonstrated more robustness to disturbances and parameter variations compared to its counterparts.