A noise attenuating sliding mode filter with improved sliding surface

In this paper, a noise removing sliding mode filter is proposed. The proposed filter increases the second-order derivative of the output for rapid response for a large error. On the other hand, when the error is small, the filter has the same value of the second-order derivative of the output to that of a previous filter for smooth output. The discrete-time algorithm of the new filter is derived through the application of the implicit-Euler method, and there is chattering in the output. The advantages of the proposed method are validated through numerical examples.