Time-Variant Discrete-Time Sliding Mode Control

Time-variant sliding planes have been successfully applied in continuous-time sliding mode control for decades. Their main advantage is the elimination of the reaching phase, which results in the system’s insensitivity to external disturbances and modelling uncertainties in the whole regulation process. In this paper, the properties of time-variant sliding planes are transferred to the discrete-time domain. The study presents a new time-variant sliding mode control for sampled data systems. The strategy assumes generating a reference sliding variable profile in advance and treating it as a time-variant sliding plane. Therefore, the sliding variable of the real system is defined as the distance between the system’s representative point and its reference position in each step. This approach eliminates the reaching phase, provides all the properties of the switching-type quasi-sliding mode, as defined by Gao et al., and ensures a reduction of the quasi-sliding mode band width compared to reaching law based approach in the entire regulation process.