Name
Given that
find y(n)
EE106
Quiz 3
Y(z) =
Feb. 16, 10
z(z-0.9)
(z-1)(z-0.3)
Y(z) = 3z + 6/7z
(z-1) (z-0.3)
y(n) = 3 + 0.857(0.3)n
Given an analog control law
H(s) = 200(s+15)
s (s+75)
map the two roots of H(s), s=-15 and s=-75 to the Z plane for the s
Name
EE106 HOMEWORK 10
The plant of Fig.1 is in the observer form. It has no
input but an initial conditions
Due Apr. 27.
1/s
+
1/s
x2
x1
+
X1(0)=0, X2(0)=1
-0.4
and the characteristic polynomial Pp(s) = s2+0.4s+1
-1.2
The model for the plant, shown in Fi
Solutions
EE106 HOMEWORK 9
Due Apr. 20, 10
A certain sample-data system has the state-space representation
zX =
0.8 -0.3 X + 1 u
0
0.2
1
y = [1 -1] X
Find the system characteristic polynomial
Find the system controllability matrix.
P(z) = det[zI-A] = (z-0
NAME
EE106 HOMEWORK 8
In the mechanical arrangement of Fig.1 the two
motors are identical with a motor resistance of rm
and a motor constant of km
Due Apr.6, 10
Vs
J1
1
Determine if the arrangement is controllable.
s1 = (1/J1r) (Vs - k1)
s2 = (1/J2r) (Vs
Solution
EE106 HOMEWORK 7
A state vector for the system of Fig.1 is X= [1, 2, 1, 2]T
Complete the matrix equation below using X.
1
0
2
0
0
0
-k/J1
k/J1
0
0
k/J2 -k/J2
0
0
s
0
1
0
2
Tin
J1
k
J2
T2
1, 1
2, 2
FIG 1
1
0
2
1
0
+
1/J1
2
0
1
=
1
Due Apr.06,10
Ti
Name
HOMEWORK 6
EE106
The plant of Fig.1 has the transfer function
r*(t)
Due, Mar. 09, 10
H(z)
zoh
G(s)
G(s) = 100
s
and the system sample rate is 200Hz.
FIG 1
Choose H(z) so that T(z) = C(z) = NT
R(z) (z-0.8)2
G(z) = 100T
(z-1)
H(z) = 200(z-1)
[0.4z-0.34
Name
HOMEWORK 5
EE106
The plant of Fig.1 has the transfer function
r*(t)
Due, Mar. 09, 10
H(z)
zoh
G(s)
G(s) = 100
s
and the system sample rate is 200Hz.
FIG 1
Choose H(z) so that T(z) = C(z) = NT
R(z) (z-0.8)2
G(z) = 100T
(z-1)
H(z) = 200(z-1)
[0.4z-0.34
Solution
EE106 HOMEWORK 4
The plant of Homework 3 is
Due Feb.23, 10
G(s) = 1/s
and the controller in the S plane is H(s) = 3124 (s+9.93)
s (s+99.3)
Convert the plant to a plant in the Z plane. Include the ZOH. The sample rate is to be
200Hz.
Find the tran
Solutions
EE106 HOMEWORK 3
Map the transfer function
Due Feb. 16,10
H(s) = 10(1+s)
(1+s/10)2
from the S plane to the Z plane using the pole-zero method. Let T=0.01
H(z) = 10[1- exp(-0.1)]2 [z- exp(-0.01)]z = 9.06 [z- 0.99]z
[z - exp(-0.1)]2 [1-exp(-0.01)]
Solutions
EE106 HOMEWORK 2
Due Feb.09, 10
Find the Z transform of the sequence cfw_y(n) = 1 0 1 0 0 0 0
Y(z) = 1 + 1/z2 = (z2+1)/z
The function f(t) = t exp(-2t) is sampled at the rate of 20 samples/second to generate the
sequence cfw_f(0.05n) find the Z
EE106
SPRING 10
PROBLEM 1
PROBLEM 2
PROBLEM 3
PROBLEM 4
PROBLEM 5
TOTAL
GRADE
PROBLEM 1
Find the Z transform of the signal x(t) = 1 exp(-t) sampled at T = 0.1.
X(z) =
zz
z-1 z-exp(-0.10)
Given the sequence cfw_x(n) = 1,2,3,0,0,0 find X(z). Express your an