Solution
EE105 HOMEWORK 3
Due Sept. 27,10
Using Matlab, make a Bode plot of the transfer function H1(s) =
1
s + 3s + 1
2
Using Matlab, make a Bode plot of the transfer function H2(s) =
s
s2 + 3s + 1
Find the transfer function that relates Vel1 to F in the
Solution
EE105 HOMEWORK 4
Due Oct. 4, 10
J1
Find the transfer function 1/Tin for the mechanical
arrangement of Fig.3.
1 = 1/sJ1(Tin-T1) T1 = B(1- 2 ) 2 = (1/sJ2)T1
-1/sJ1
B
J2
1
Tin
-B
T1
2
FIG 1
Tin
1/sJ1
1
B T1
1/sJ2 2
1 =
Tin
sJ2+B
s J1J2+Bs(J1+J2)
2
I
Name
EE105 HOMEWORK 5
Due Oct. 11, 10
The motor and generator of Fig.1 are identical machines. Measurements show that in the
steady state for Vin = 1V .
rm
Iin = 0.05 amps
Vin
Vo
V
Vo = 0.8
= 300 rad/sec
Iin
+
B
+
Em
J
Find the motor constants rm,
Solutions
EE105 HOMEWORK 6
Find the Laplace transform of f(t) = t
Due Nov.01, 10
Lcfw_t = 1/s2
Lcfw_tf(t) = -(d/ds)F(s)
Find the Laplace transform of f(t) = t2
Lcfw_t2 = 1/(2s3)
Find the Laplace transform of f(t) = t3
Lcfw_t3 = 1/(3!s4)
e(t)
In the system
Solution
EE105 HOMEWORK 7
Ko
s +4s +6s+16
Find the upper bound on Ko for which the system
is stable.
Due Nov. 8, 10
Given that GH in Fig.1 is GH=
3
P(s) = s3+4s2+6s+16+Ko
e(t)
2
r(t)
+
d(t)
H(s)
_
KoMAX = 4(6)-16 = 8
+
G(s)
+
c(t)
FIG 1
For KoMAX the syst
Solution
EE105 HOMEWORK 8
Due Nov 15, 10
A certain system has the
open-loop transfer function
GH = K(s+1.5)
s2
Locate the breakaway point.
s2- 2s(s+1.5) = 0
so=-3
2
-3
1
-1.5
2
Plot the loci.
Show the loci form a circle about the point s=-1.5.
By the angl
NAME
EE105 HOMEWORK 9
Due Nov 22, 10
A certain unity-feedback control system with the plant transfer function G(s) = 1/(s+4) 2 is
to be compensated with the controller H(s) = A/s.
Find the maximum value of A=A1 for which the three closed loop poles are ne
Solutions
EE105 HOMEWORK 10
Due Dec 06, 10
A certain control system has the open-loop transfer function
GH =
K
(1+s/z )
2
s (1+s/20)(1+s/p)
The closed-loop system is to have a unity gain frequency of 5 rad/sec.
Choose K, z, and p so that the closed-loop s
Name
QUIZ 1
EE105
Sept.20, 10
Given that for a certain system
[(d/dt)2 + 4(d/dt) + 3]c(t) = r(t)
find the system characteristic polynomial.
P(s) = s2 + 4s + 3
Given that the system input is r(t) = U(t), find c(t).
C(s) =
1
= 1/3 - 1/2 + 1/6
s(s+1)(s+3)
s
Solution
The position control system plant
of Fig.1 has the transfer function
Gp(s) = 1
s(s+6)
The system is to be compensated
by the control law
Hc(s) = Ao s + Ai.
s
Find the system order
QUIZ 5
EE105
Nov 9, 2010
e(t)
r(t)
+
d(t)
H(s)
_
+
G(s)
+
c(t)
FIG
NAME
QUIZ 4
EE105
Oct 11, 10
Given that C(s) = (s+1) find c(t).
s(s+2)2
C(s) = 1/4 - 1/4 + 1/2
s
(s+2) (s+2)2
c(t) = 1/4 - (1/4)exp(-2t) + (1/2)texp(-2t)
Complete the equations below that
describe the arrangement of Fig.1.
The machine constant is km and t