Design of derivative estimator using adaptive integral variable structure technique

The paper is concerned with designing a first order derivative estimator of a signal based on the concept of variable structure and adaptive control techniques. A PI controller is incorporated in a variable structure scheme so that the upper bound of the steady state derivative estimation error is reduced. The proposed adaptive integral variable structure derivative estimator can be used as a direct differentiator for a smooth signal with bounded derivative. An adaptive algorithm of the switching gain is also incorporated in order to remove the requirement for a priori knowledge about the upper bound of the derivative of observed signal. The upper bound of the derivative estimation error using proposed estimating scheme is computed in order to compare with that of an existing estimator, the adaptive variable structure derivative estimator. An example is demonstrated for showing the advantages of the proposed method