Tracking differentiator based on inverse hyperbolic sine function

The inverse hyperbolic sine function is a smooth and continuous function, which is swift and can eliminate velocity high frequency oscillations. An acceleration function is constructed by using the inverse hyperbolic sine function, so as to design a second-order tracking differentiator. The convergence of the tracking differentiator is proved, and the magnitude-frequency characteristic and phase-frequency characteristic are analyzed. Finally, the simulation experiments demonstrate the tracking differentiator can perform lowpass filtering of input signals, and it has the higher tracking precision and the swifter response velocity. Moreover, the tracking differentiator can inhibit the noise amplification effect and output ideal differential signals of the input function.