A Novel Second-Order Nonlinear Differentiator With Application to Active Disturbance Rejection Control
For control engineers, this provides an improved differentiator for robust control techniques like ADRC, but the improvements are incremental over existing methods.
The paper proposes a Second-order Nonlinear Differentiator (SOND) combining linear and nonlinear terms to improve convergence and reduce chattering, with stability proven via Lyapunov analysis. Simulations in active disturbance rejection control demonstrate better dynamical performance than conventional differentiators.
A Second-order Nonlinear Differentiator (SOND) is presented in this paper. By combining both linear and nonlinear terms, this tracking differentiator shows better dynamical performances than other conventional differentiators do. The hyperbolic tangent tanh(.) function is introduced due to two reasons; firstly, the high slope of the continuous tanh(.) function near the origin significantly accelerates the convergence of the proposed tracking differentiator and reduces the chattering phenomenon. Secondly, the saturation feature of the function due to its nonlinearity increases the robustness against the noise components in the signal. The stability of the suggested tracking differentiator is proven based on the Lyapunov analysis. In addition, a frequency-based analysis is applied to investigate the dynamical performances. The performance of the proposed tracking differentiator has been tested in active disturbance rejection control (ADRC) paradigm, which is a recent robust control technique. The numerical simulations emphasize the expected improvements.