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.

Estimating reliable signal component and its derivatives from noisy feedback signal is important in control systems. Toward this problem, this paper presents a new model-free variable gain sliding mode tracking differentiator for derivative estimation of noisy signals by modifying a Levant and Yu's sliding mode tracking differentiator. Specifically, different from Levant and Yu's TD, the new TD employs an additional variable that contributes to overshoot reduction. In addition, the new TD adaptively changes its gains for improving the tracking and filtering performances. Moreover, the new TD only uses previous output values and it does not require input signal model in advance. The advantages of the new TD over previous TDs are confirmed through numerical examples. INDEX TERMS Sliding mode, tracking differentiator, high order, noise attenuation, overshoot, variable gain.

Noise reduction is one of the important issues for feedback control systems. Toward this problem, this paper proposes a new sliding mode filter, which is an improvement of Lv et al.'s parabolic sliding mode filter. The proposed filter employs a first-order derivative feed-forward term for increasing both tracking and noise attenuating performances. Its discrete-time algorithm is derived by applying the implicit-Euler discretization, and it realizes exact convergence without producing chattering in discrete-time implementation. The effectiveness of the proposed filter is evaluated through an open-loop and a closed-loop numerical examples. INDEX TERMS Sliding mode filter, implicit Euler discretization, chattering avoidance, noise reduction, PD control, feedback control.

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