Section 4–4 / Hydraulic Systems 123The transfer function of this controller is
By defining
and noting that under normal operation
and we obtain
(4–24)
where
Equation (4–24) indicates that the controller shown in Figure 4–16(a) is a proportional-
plus-integral-plus-derivative controller or a PID controller.
4–4 Hydraulic Systems
Except for low-pressure pneumatic controllers, compressed air has seldom been used for
the continuous control of the motion of devices having significant mass under external
load forces. For such a case, hydraulic controllers are generally preferred.
Hydraulic Systems. The widespread use of hydraulic circuitry in machine tool
applications, aircraft control systems, and similar operations occurs because of such fac-
tors as positiveness, accuracy, flexibility, high horsepower-to-weight ratio, fast starting,
stopping, and reversal with smoothness and precision, and simplicity of operations.
The operating pressure in hydraulic systems is somewhere between 145 and 5000 lbfin.^2
(between 1 and 35 MPa). In some special applications, the operating pressure may go up
to 10,000 lbfin.^2 (70 MPa). For the same power requirement, the weight and size of
the hydraulic unit can be made smaller by increasing the supply pressure. With high-
pressure hydraulic systems, very large force can be obtained. Rapid-acting, accurate
positioning of heavy loads is possible with hydraulic systems. A combination of elec-
tronic and hydraulic systems is widely used because it combines the advantages of both
electronic control and hydraulic power.
Kp=
bks
aA
=Kpa 1 +
1
Ti s
+Td sb
bks
aA
Td Ti s^2 +Ti s+ 1
Ti s
Pc(s)
E(s)
bks
aA
ATd s+ 1 BATi s+ 1 B
ATi-TdBs
TiTd ,
@KaAATi-TdBsC(a+b)ksATd s+ 1 BATi s+ 1 BD@ 1
Ti=Ri C, Td=Rd C