Time-Varying Gain Differentiator: A Mobile Hydraulic System Case Study.

In mobile hydraulic systems, velocities are typically not measured. However, using their reliable estimates for feedback is known to allow designing better control laws. We are going to present a specialized technique to compute such estimates using measurements of positions and pressures in the chambers of hydraulic cylinders. With a rough estimate for an upper bound of the second derivative, computed online from pressures, the goal is to find the first derivative of the position signal in the presence of noise. We propose a differentiator with a continuous time-varying gain, constructed from pressure measurements, achieving chattering attenuation without compromising the performance of estimation. The gain is constructively tuned using analysis based on a time-varying Lyapunov function. In addition, the obtained ultimate bounds on differentiation errors provide a criterion for the enhancement of the precision of the proposed algorithm with a constructive design of its parameters. The experimental results over a forestry-standard mobile hydraulic crane confirm the advantages of the methodology.