Test for Semester 2003/2004
Principles of Automatic Control (A)
Institute of Automation, College of Information Engineering, Zhejiang University of Technology
Name: , Student Number: , Scores: .
1、(8 Points)
Suppose that a signal can be expressed as following:
?
?
?
?
?
≤≤
≤≤
=
?
otherwise
TtTe
Tt
tf
at
,0
2 ,
0 , 0
)(
Please find its Laplace transform.
2、（10 Points）
Please find the current i(t) of the system after the closure of the switch at t=0 with the
initial conditions: i
L
(0)=0. e(t)=V and V is a constant.
3、(12 Points)
Please find the transfer function between the input V
i
and the output V
o
.
4、(10 Points)
For the loop transfer function
)50)(1(
)(
++
=
sss
K
sGH . Please use the Nyquist criterion
to find the range of gain K, so that the closed loop system is stable.
5、(8 Points)
For the loop transfer function
)20)(2(
)1(
)(
2
++
+
=
sss
sK
sGH .
Please sketch the root locus.
6、 (14 Points)
For the loop transfer function
)1(
)1)(12(
)(
2
+
++
=
Tss
ssK
sGH ， 0,0 >> TK .
(1) Please determine the condition, which must be satisfied for KT, , so that the
closed loop system is stable.
(2) For unit negative feedback system, please find the steady state errors when the
reference input signals are unit step, unit ramp and unit acceleration respectively.
7、(14 Points)
Please use the Nyquist criterion to analysis the stability of the closed loop system
with the loop transfer function 0. 0,T ,
)1(
)1(
)(
2
>>
+
+
= τ
τ
Tss
sK
sGH . And then check with the
Routh criterion.
8、(12 Points)
For the Bode plot, please find the loop transfer function of the system.
9、(12 Points)
For the discrete time control system, with sampling period T=1s, and a=1, k=10.
Please analysis the stability of the system.
C(s)
)(
as
k
+
R(s)
_
ZOH
