Experimental Evaluation of Homogeneous Differentiators Applied to Hydraulic Stroke with Measurement Noise and Acceleration Disturbance

The design and experimental evaluation of continuous homogeneous differentiators are considered. The differentiator gains follow the high-gain setup with variable gain-scaling parameter L. This parameter results from a minimization of the effect of measurement noise and disturbance on the differentiation estimation error in terms of the homogeneous <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L₂</tex> -gain. We consider and compare various homogeneity degrees including the linear (high-gain) case. It turns out that an optimum exists not only w.r.t. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> but also w.r.t. homogeneity degree d. For experimental evaluation, a hydraulic cylinder controlled by a servo-valve is excited over a frequency range and the noisy cylinder stroke measurements are differentiated. Via classical metrics (root-mean-square and maximum absolute error) and a precise full-order simulation model, we evaluate the velocity estimation accuracy. Applying a second differentiation to the stroke measurements, an acceleration disturbance can be detected from a comparison of its measurement and estimate.