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A Second-order Nonlinear Differentiator (SOND) is presented in this paper. Bycombining both linear and nonlinear terms, this tracking differentiator showsbetter dynamical performances than other conventional differentiators do. Thehyperbolic tangent tanh(.) function is introduced due to two reasons; firstly,the high slope of the continuous tanh(.) function near the origin significantlyaccelerates the convergence of the proposed tracking differentiator and reducesthe chattering phenomenon. Secondly, the saturation feature of the function dueto its nonlinearity increases the robustness against the noise components inthe signal. The stability of the suggested tracking differentiator is provenbased on the Lyapunov analysis. In addition, a frequency-based analysis isapplied to investigate the dynamical performances. The performance of theproposed tracking differentiator has been tested in active disturbancerejection control (ADRC) paradigm, which is a recent robust control technique.The numerical simulations emphasize the expected improvements.

A Novel Second-Order Nonlinear Differentiator With Application to Active Disturbance Rejection Control