A Nonsmooth Quasi-Static Modeling Approach for Hydraulic Actuators

Abstract

This paper presents an analytical approach for modeling the quasi-static characteristics of hydraulic actuators driven by four-valve independent metering circuits. The presented model is described as a nonsmooth, set-valued function from the velocity to the set of forces with which the equilibrium is achieved at the velocity. It is derived from algebraic relations among the velocity of the actuator, the steady-state force generated by the actuator, and the flowrate and the steady-state pressure at all valves in the circuit. This approach is also applied to more involving circuits including a regeneration pipeline and those with multiple actuators. The contribution of the paper can be seen as an example case study of the fact that these complicated circuit structures are analytically tractable through an extension of the conventional hydraulic–electric analogy. The obtained analytical expressions of the steady-state velocity–force relations allow for concise visualization of the actuators' characteristics.