Characterization and tracking control of a nonlinear electrohydraulic valve-cylinder system

It is well known that simple proportional, integral, and derivative control yields poor tracking performance due to the friction- and flow-related nonlinearities in electrohydraulic servo-systems. Nonlinear effects are more significant in proportional valve having deadband and non-matched ports with potential application in systems with complex ground friction in off-road vehicles or complex inertia loads in simulators meant for pilot training. A feedforward-based controller has been designed here by performing a number of characterization experiments for achieving good tracking performance overcoming severe nonlinearities. An algebraic model of friction has been developed for including hysteresis beyond the static friction zone in a double-rod piston-cylinder arrangement. A proportional valve with non-matched ports and large deadband has been characterized in terms of command signal to flow gains for each metered port and a leakage coefficient. Also, a dynamic model for the valve with embedded control has been constructed. All these models have been integrated together to predict the piston-motion dynamics. A simple theoretical analysis with a fixed command excitation revealed that following the initial transients a sustained oscillation over a constant mean piston velocity could exist for low pump pressure and valve damping due to the flow-motion coupling. The bandwidth and damping coefficient of the valve flow have been estimated through a comparison between the predicted and experimentally measured piston displacement variation with time. Besides evaluating the feedforward using the algebraic friction model along with assuming incompressible flow and negligible valve leakage, the predictions of the complete model were used to ascertain the proportional, integral, and derivative gains to be implemented in real-time control. Up to 0.5 Hz sinusoidal excitation, the proposed control revealed excellent tracking performance. Controls with only proportional, integral, and derivative and proportional, integral, and derivative together with feedforward exhibited noticeable phase shifts, respectively, from frequencies 0.0625 Hz and 0.6 Hz. Hence, the proposed controller can be useful in low-cost, low-power, precision applications up to 0.5 Hz input excitations.