Stability Study of a Pump-Controlled Circuit for Single Rod Cylinders via the Concept of Lyapunov Exponents

Pump-controlled hydraulic actuators of single rod cylinders, while efficient, often exhibit undesirable performances during pump mode of operation switching. Although the oscillatory performances have been found in both simulations and experiments, a rigorous proof of such undesirable dynamics has rarely been reported due to lack of proper theoretical tools. In many previous works, traditional stability analysis of pump-controlled single rod hydraulic actuator systems was carried out by studying eigenvalues of the linearized models in each of various regions, separately. This may lead to a conservative conclusion. In this paper, such mode switching instability is analyzed using the concept of Lyapunov exponents. More specifically, the impact of the cracking pressures of the pilot operated check valves on system dynamics of a commonly used pump-controlled circuit is investigated. The numerical results are in agreement with the experimental findings, indicating the efficacy of the proposed method. The paper thus contributes to the systematic stability analysis for non-smooth hydraulic actuator systems, which can subsequently facilitate the controller design.