Error-Dynamics-Based Performance Shaping Methodology for Discrete-time Sliding Mode Control with Disturbance Observer

This paper presents an effective performance shaping methodology of discrete-time sliding mode control (DSMC) with disturbance observer (DOB) based on the analysis of error dynamics. DSMC with DOB exhibits excellent tracking performance and robustness subject to external disturbances and unknowns including uncertain parameters and unmodelled dynamics. In addition, DSMC with DOB can be easily implemented in various control applications attributed to its simple structure and discrete-domain representation. However, the performance cannot be easily predicted by the controller parameters of DSMC with DOB, and much tuning effort is required to achieve the desired performance. This paper derives a relationship between the performance and the controller parameters of DSMC with DOB using a disturbance-to-error transfer function. In addition, a tuning methodology for shaping the performance of DSMC with DOB is also suggested. Finally, the developed analysis is demonstrated experimentally in a commercial linear motor system.