Backstepping designed sliding mode control for a two-axis tracking system

This paper develops backstepping-sliding mode control method for multi-input and multi-out nonlinear system. In order to solve the chattering problem, three continuous functions are introduced and the error function is employed as the sliding surface function finally after detailed comparison. Certain kind of two-axis tracking system is taken as an example. And dynamic model of the system is established based on Lagrange-Maxwell electromechanical equations, and controller designing based on the above developed control method is presented in detail. The simulation using Matlab are presented, which obtained controllers on the basis of backstepping method and backstepping-sliding mode control method, respectively. Comparison between them indicates that it is proper and effective for the two-axis tracking system to employ the controller designed based to backstepping-sliding mode control method. Simulation results based on improved sliding surface function are also presented which prove it is applicable to use error function in backstepping-sliding mode control method. Based on simulation results presented, the position tracking accuracy of the two-axis system can meet the project´s need.