  This article presents a quasistatic model of a hydraulic actuator driven by a
four-valve independent metering circuit. The presented model describes the
quasistatic balance between the velocity and force and that between the
flowrate and the pressure. In such balanced states, the pressure difference
across each valve determines the oil flowrate through the valve, the oil
flowrate into the actuator determines the velocity of the actuator, and the
pressures in the actuator chambers are algebraically related to the external
force acting on the actuator. Based on these relations, we derive a set of
quasistatic representations, which analytically relates the control valve
openings, the actuator velocity, and the external force. This analytical
expression is written with nonsmooth functions, of which the return values are
set-valued instead of single-valued. We also show a method of incorporating the
obtained nonsmooth quasistatic model into multibody simulators, in which a
virtual viscoelastic element is used to mimic transient responses. In addition,
the proposed model is extended to include a regeneration pipeline and to deal
with a collection of actuators driven by a single pump.
