Continuous homogeneous differentiators with optimal gains applied to noisy measurements of hydromechanic drives

Whenever time-derivatives of measurements are necessary for observation, fault detection or control, these signals need to be estimated, e.g. using differentiators. In general, large differentiator gains increase the effect of measurement noise on the differentiation estimation error whereas small gains yield insufficient attenuation of higher-order derivatives (of the base signal to be differentiated). This work deals with the optimal gain design for the family of continuous weighted homogeneous differentiators. That is, we design, apply and evaluate homogeneous differentiators (with negative homogeneity degree) based on a theoretical framework developed recently. The design follows a high-gain setup, meaning that stabilizing differentiator parameters are fixed and the only variable tuning parameter is a gain-scaling. This is chosen to minimize the estimated effect of noise and higher-order derivative on the differentiation estimation error in terms of the homogeneous L p -gain for p = 3 and p = ∞ . Due to their practical relevance, hydromechanic drives are considered where the differentiator is applied to the noisy position measurements in order to estimate the cylinder piston’s acceleration. The experimental setup includes an accelerometer rendering the differentiation estimation error available for evaluation. Several harmonic excitation signals are considered (sinusoidal, chirp, multi-sine) and the performance is evaluated via standard metrics (root-mean-squared error), the transient response and frequency-domain characteristics. The differentiators are compared to a high-gain differentiator with optimal gains and a straight-forward approach. The evaluation underlines the promising theoretical results that it is based on.