Digital Signal Processing Reference
In-Depth Information
5
5
u
(
t
)
y
(
t
)
6
3
2
4
Figure P8.7
8.8.
Figure P8.8 gives the simulation diagram of an automatic control system. The plant is
the system that is controlled, and the compensator is an added system to give the
closed-loop system certain specified characteristics.
(a)
Write the state equations for the plant only, with input
m(t)
and output
y(t).
(b)
Give the transfer function for the plant.
(c)
Write the differential equation for the plant.
(d)
Write the state equations for the compensator only, with input
H
p
(s)
e(t)
and output
m(t).
(e)
Give the transfer function for the compensator.
(f)
Write the differential equation for the compensator.
(g)
Write the state equations for the closed-loop system, with input and output
Choose as states those of parts (a) and (d). These equations can be written
directly from the simulation diagram.
H
c
(s)
u(t)
y(t).
Compensator
Plant
e
(
t
)
m
(
t
)
u
(
t
)
y
(
t
)
x
2
3
4
2
4
x
3
5
3
x
1
1
Figure P8.8
