Approximate Differentiator With Varying Bandwidth for Control Tracking Applications

Approximate Differentiators have been extensively used in the estimation of joint velocity measurements of industrial manipulators. In this letter, we exploit key differences between the continuous-time model of the first-order Approximate Differentiator, commonly known as the Dirty-derivatives Filter (DF), and its discrete-time model. We show that the discrete-time filter shares the characteristics of an exponentially weighted moving average; in particular, the filter smooths the derivative of its input. We numerically and experimentally demonstrate how the filter estimation performance follows a convex trend in function of the filter bandwidth. We further demonstrate how the bandwidth at which the filter achieves “optimal” performance varies with the frequency of the filter's input. Inspired by the latter, we propose an Approximate Differentiator with Varying Bandwidth (ADVB) where the filter bandwidth varies based on the magnitude of the position tracking error. We illustrate the superiority of the proposed ADVB over various differentiation schemes both numerically and experimentally.