An Output-Tracking-Based Discrete PID-Sliding Mode Control for MIMO Systems

Due to its ability to reject disturbance, sliding mode control (SMC) has been widely employed in various control applications with the presence of uncertainty and/or disturbance. However, chattering, caused by the switching function used in SMC, can greatly deteriorate its performance, and thus, limit its applications. In addition to chattering, the application of SMC to a multi-input–multi-output (MIMO) system becomes more challenging due to the coupling effects between the control variables. This paper presents the development of an output-tracking-based discrete proportional-integral-derivative SMC (PID-SMC) for MIMO systems, in which the problem of output tracking is defined to the one of state tracking by using the model reference approach. The developed control scheme allows for both achieving the zero steady-state error and eliminating the chattering problem. For validation, experiments were performed on a commercially available three degrees-of-freedom nanopositioning stage with the developed control scheme, as compared to a traditional PID controller. Experimental results illustrate that with the developed control scheme, the positioning performance of the stage can be significantly improved, including the zero steady-state error and eliminated chattering.