EEL 205 Control Engineering
Practice Problem Set 2
1. Determine the transfer functions Vo(s)/Vi(s) for the two electrical networks shown in Fig. P1a and P1b. Also
obtain the impulse response vo(t) for impulse applied as vi(t).
1
RCs +1;R[(L2s/C)+R/C]
(L2s+R)L1L2s3+RL1s2+[(L1+L2)/C]s+R/C
2. Determine the time variation of the outputs from the following transfer functions when they are fed with the
specified inputs.
(a) Steady state output of H(s)= (s+1)2
(s+2)(s+3);u(t)=10sin5t
(b) Complete output of H(s)= (s+1)(s+2)
s(s+3)(s+4);u(t)=1fortm0; 0 otherwise.
y(t)=8.28sin 5t+
6;y(t)= 1
8+1
6t2+2
9e−3t−3
8e−4t
3. Obtain the block diagram and signal flow
graph for the circuit in Fig. P3. By either
way, obtain the transfer function of the
network as Vo(s)/Vi(s).
Either way you should get a transfer function H(s)= R1R2
L1L2s2+[R2/L2+R1/L1+R1/L2]s+(R1R2)/(L1L2)
4. By dividing the numerator and denominator of
H(s)= s2+3s+3
s3+2s2+3s+1
by s3, and converting the numerator to a cascade of integrators
with feedforward paths, realise the signal flow graph for H(s)
in phase variable form. This is a form in which each state
(represented by a node in the signal flow graph) is connected
to the next by an integrator 1/s.
[You should primarily get three states cascaded by integrators,
i.e., each involves the derivative of the last one, together with appropriate feedforward and feedback paths.]
5. Obtain the Y/X transfer function of the block shown in Fig. P5.
EEL 205/PS2
v t
( )
R
L
C
P1a
iv t
( )
o
L
v t
( )
iCR
12v t
( )
o
P1b
v t
( )
R
L
C
P1a
iv t
( )
o
L
v t
( )
iCR
12v t
( )
o
P1b
v t
( )
R
L
C
P1a
iv t
( )
o
L
v t
( )
iCR
12v t
( )
o
P1b
v t
( )
R
L
C
P1a
iv t
( )
o
L
v t
( )
iCR
12v t
( )
o
P1b
( )
LL
v t
( )
iR
12
v t
( )
o
P3
2
R1v t
( )
m
i t
i( )
i t
o
f
a
b
c
d
e
+
++
++
+
X
Y
P5
fc +ac
1−ace −ab −dc +abcd
