Design of derivative estimator using adaptive sliding mode technique

Based on Lyapunov stability theorem, a design methodology of a first order adaptive integral variable structure derivative estimator (AIVSDE) is proposed in this paper. The proposed derivative estimator not only can be used to estimate the derivative of a smooth signal but also is an improved version of the existing derivative estimators. A low pass filter is cascaded with AIVSDE so that the effects of noise can be alleviated by adjusting the designing parameters of filter and AIVSDE. An adaptive algorithm is incorporated in the proposed estimator for removing the a priori knowledge of the upper bound of the observed signal. In addition, the stability of the proposed derivative estimator is guaranteed, and the comparison of upper bound of derivative estimation error between recently proposed nonlinear adaptive variable structure derivative estimator (NAVSDE) and AIVSDE is also demonstrated. An example is given for showing the applicability of the proposed AIVSDE