A New Quick-Response Sliding Mode Tracking Differentiator With its Chattering-Free Discrete-Time Implementation

This paper presents a new quick-response sliding mode tracking differentiator (new TD) for feedback control of mechatronic systems. The new TD is an extension of Jin et al.’s sliding mode tracking differentiator (TD-J) by employing an exponential reaching term for balancing the trade-off between noise attenuating efficiency and convergence speed. The discrete-time algorithm of the new TD is derived by using the implicit-Euler discretization and an equivalent between a set-valued signum function and a saturation function, and it does not produce chattering, which has been one major challenge of implementing sliding mode technique in discrete-time. Simulations and experiments are conducted for validating the effectiveness of the new TD.