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ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 457
the pump dynamics is very critical in closed-center EH systems (closed center valve and
variable displacement pump EH systems). The reason is the fact that the bandwidth of the
main flow control valve is much faster than the bandwidth of the pump control. During
any kind of valve closure, if the valve reaches the null position (hence almost zero flow
demand) much faster than the pump can de-stroke, the pump flow will have no place to
go and result in very large pressure spikes. This will most likely blow the pressure relief
valves and result in low performance operation.
A mathematical model of a pump can be derived based on
1. the physical principles of fluid and inertial motion, or
2. based on the input–output (I/O) relationship using empirical data and modeled as a
static gain (possibly nonlinear) plus dynamic filter effects.

Input variables of the pump are:
1. swash plate angle (or equivalent control element variable), and
2. input shaft speed.
And output variables of interest are:
1. outlet pressure,
2. outlet flow rate.
Some of the non-ideal characteristics of hydraulic pump (and motors) are:

1. Variation of displacement as a function of rotor position within one revolution. Since
there is a finite number of fluid cavities (cylinder-piston pairs in a piston pump), the
displacement has ripple as a function of the rotor position and number of piston–
cylinder pairs (this is in principle the same as the commutation ripple in a brush-type
DC motor).
2. Every hydraulic pump, valve, motor, and cylinder has leakage and it increases with
the pressure.

7.4 HYDRAULIC ACTUATORS: HYDRAULIC CYLINDER
AND ROTARY MOTOR

The translational cylinder and rotary hydraulic motor are the power delivering actuators in
translational and rotary motion systems, respectively. The basic functionality of the actuator
is to convert the hydraulic fluid power to mechanical power, which is the opposite of the
pump function (Figure 7.41). Unidirectional pumps and motors are optimized to work in one
direction in terms of reduced noise and increased efficiency. Bidirectional hydraulic pumps
and motors have symmetric performance in either direction. In general, a pump can operate
both in pumping or motoring mode. Similarly, a hydraulic motor can operate in motoring
or pumping mode. However, there are exceptions. Some pump designs incorporate check

FIGURE 7.41: Hydraulic actuator
functionality: convert hydraulic
power to mechanical power. The
hydraulic cylinder converts hydraulic
Hydraulic Motor/ Mechanical power to translational motion power,
power cylinder power the hydraulic motor converts it to
rotational motion power.