In this paper, we design an adaptive controller to compensate the nonlinear friction model when the output is the position. First, we present an adaptive differential filter to estimate the velocity. Secondly, the dynamic friction force is compensated by a fuzzy adaptive controller with position measurements. Finally, a simulation result for the proposed controller is demonstrated.

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The design of an ideal differentiator is a difficult and a challenging task. In this paper, we propose two adaptive observers for a scalar first-order plant with a time-varying parameter. The update law consist of the gradient-type one and a signurn function. Based on the proposed adaptive observers, three time-derivative trackers are given to estimate the derivative of an output signal. The MATLAB simulations are done to demonstrate their performances.

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