Integral augmented nonlinear differentiator for noisy signals

This paper proposed an arctangent function based integral augmented nonlinear differentiator (IAND) for obtaining of the noise-less derivative signal from a noisy measurement signal. The basic idea of proposed IAND with high noise-attenuation effect is to establish the differentiator by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the IAND is formulated to achieve better noise suppression ability without appreciable delay. Moreover, the convergence characteristic and anti-noise property in the frequency domain are analyzed via singular perturbation theory and describing function method, respectively. The simulation comparison results with other differentiators show the superiority of IAND in noise suppression.