Page 129 - Servo Motors and Industrial Control Theory -

124 7 Electrohydraulic Servo Motors

Hence, the total flow rate at high pressure may be written as
V d
q : = C · ω m +λ m o p (7.18)
· p +
m
m
B dt
By analogy of q to voltage (V) and p to current (I), Eq. (7.17) is similar to the volt-
m
age equation of electrical motors. Allowing for mechanical losses between the rotor
and the supplied power, the torque equation of the motor may be written as

T : η= m ·C · p (7.19)
m
m
where η is the efficiency of the motor and for mathematical modeling purposes,
m
it can be taken as one. Equation (7.19) is also similar to the torque equation of DC
motors.
The above analysis shows that the mathematical model obtained for electrical
motors may be used for hydraulic motors. Although the above analysis is done on
a hydraulic axial type motor, similar results may also be obtained for other types of
hydraulic motors and actuators.
The complexity of mathematical model usually depends on applications. In the
above case, the compressibility of oil was also considered. In some applications,
this effect like the inductance of electrical motors may be neglected. It all depends
on the engineer’s judgment as what effect is dominant in the system behavior. For
example, the compressibility of oil may be considered for the linear actuator dis-
cussed in previous section. This raises the order of the transfer function by one. In
this case, the roots of characteristic equations must be obtained numerically. The
parameters of the controller must be adjusted so that all roots are located in desired
location on the s plane.
For velocity control, a velocity feedback such as a tachometer must be used. For
position control, a variable resistance or a digital encoder must be used. A control-
ler of proportional and integral may be used to control the system. For complex
model state space approach is a better model to study the behavior of the system.
For mechanical systems, the use of derivative term in the controller must be avoided
because of the noise in the system.

7.5 A Numerical Investigation of the Transient Behavior
of an Electrohydraulic Servo Motor Under Different
Conditions

It has been shown by other research workers that the linearized model obtained in
the previous sections provide a satisfactory model for the dynamic characteristic of
electrohydraulic servo motors. In this section, the performance of a hydraulic axial
piston motor type pm60, from Lucas Fluid Power is investigated. The specifications
of the motor is as follows: