Page 185 - Servo Motors and Industrial Control Theory

Appendix A 181

L3 L2 L1

F
m

X
K c

55. An electrohydraulic device as shown below is used to control the position of a
mass of 100 kg against the spring with stiffness of 100 N/m. The flow rate and
its direction are controlled by an electrohydraulic servo valve. The servo valve
is of spool with internal feedback (not shown in the diagram) form. The spool
displacement is a maximum of 10 mm and with supply pressure of 150 bars it
can control a maximum flow rate of 9 lit/min. Note that at high pressure large
volume of fluid can be displaced by a small opening.
xi
+
Ps v K -
x
m
K

P1 P2

There is an internal feedback in the servo valve so that the spool displacement
(x) is proportional to the applied voltage at steady state and the transient behav-
ior can be approximated by the following transfer function.

x := K s
V τ s1+
where τ = 0.01 s.
Note that the servo valve is quite fast. The actual time constant for a particular
application must be obtained from manufacturers. Determine the gain of servo
valve when 10 V of applied voltage produces 10 mm of spool displacement.
Note that the unit of all parameters must be consistent.
Write the nonlinear equation of the flow rate through the servo valve. Linear-
ize the two variables flow equation and find the parameters assuming that with
valve opening of 0.5 mm and with zero back pressure, the flow rate is 9 lit/min.