Nonsmooth funnel transformation function-based discrete-time sliding-mode control with deterministic performance margin for servo systems

This paper proposes a nonsmooth funnel transformation function-based discrete-time sliding-mode control strategy for the discrete-time servo systems with unknown frictions and disturbances. For obtaining a more accurate discrete-time system model, a filter-based adaptive identification algorithm (FAIA) is introduced, where the unknown measurement noises are considered. Based on the identified system model and a novel discrete-time nonsmooth funnel transformation function (improving the tracking performances), a discrete-time sliding-mode surface is designed to confine the tracking error to a smaller funnel region compared with the predefined one, which has a deterministic performance margin related to the upper bound of the lumped disturbance. Furthermore, selections of steady-state funnel boundary and sliding-mode surface parameter can be guided theoretically according to the upper bound of the lumped disturbance. Experimental results show that the tracking error is guaranteed in the predefined funnel with a deterministic performance margin by using the proposed control strategy.