Systematic comparison of numerical differentiators and an application to model-free control

Abstract

Recent tuning guidelines for algebraic differentiators based on the analysis of the Fourier transform of the kernels are reviewed. A region of validity for the previous analyses carried out for high frequencies is proposed and the results are related to those based on the analysis of the L2-norm of the Fourier transform of the differentiators. These results are then used for a systematic comparison with established approaches from the literature (homogeneous, high-gain and sliding mode differentiators) for the estimation of the second derivative of a known signal corrupted by a known disturbance. It is shown that properly tuned and discretized algebraic differentiators outperform the other analyzed approaches in terms of robustness, convergence time, and tuning simplicity. The tuning guidelines are then used in the context of control of a partially known system, thus bridging the gap to the tuning of recent model-free control approaches.