EE571
Solution to HW#3
0. Have you picked a lab partner to work with you? Your first lab is coming soon! 1a) The analogous circuit for the first problem is: Original Circuit Analogous Circuit
w=input
Due Monday, February 8
1. a)
EE572
HW #6
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Use the fact that the solution to, x k +1 = Ax k is x k = A k x 0 to find the Ztransform of A k (hint: take the Z$
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$
transform of both x k +1 = Ax k a
EE572  Solution to HW #6
1. a)
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$
Use the fact that the solution to, Zcfw_x k +1 = Ax k = zX ( z ) zx 0 = AX ( z ) or X ( z ) = [ zI A]1 zx 0 to find the Z$
$
$
transform of A k (hint: take the Z
EE572
HW #7
Due Wednesday, February 10
^
^
1. a)
If x k+1 = A x k + B w k , find the eigenvalues and eigenvectors then use the similarity transformation, xk
= Pzk, to determine which of the eigenvalue
EE572  Solution to HW #7 1. a) i) Solution: Find eigenvalues from det[sIA] = 0 = (s3)(s1). Therefore, eigenvalues are s1= 3 and s2= 1. The eigenvectors are found from [siIA]Pi=0. The eigenvectors
Due Wednesday, February 17
1.
EE572
HW#9
Consider the following discretetime multiinput state variable model:
 2 2
2  1
x k+1 =
xk +
wk 0
0  2
 1 1
a)
Find the eigenvalues of the openloo
EE572  Solution to HW #8
1. a)
Solution: Consider the following discretetime state variable model (don't use Matlab):
4 4
1
x k+1 =
x k + w k 1
4 4
2
0 1
0
$
$
The characteristic equation is
Solution
1.
EE572
HW#9
Consider the following discretetime multiinput state variable model:
 2 2
2  1
x k+1 =
xk +
wk 0
0  2
 1 1
a)
Find the eigenvalues of the openloop system. Solution
Due Monday, March 22nd (Happy Spring Break)
1.a)
EE572
HW #15
Sketch the root locus of the following splane openloop pole zero configurations (Use Matlab's rlocus() command to check your
answers) :
EE572
0.
1.a)
Solution to HW #15
Check your scores under the grades option and make sure all records are correct!
Sketch the root locus of the following splane openloop pole zero. Solution:
j
i)
60
Due Monday, March 29
EE572
HW #17
1. Keep working on your project!
2. Consider the system from HW#16:
T
s
W(s) +
G c (z)
G zoh(z)
10
s( s + 8)
Y(s)

Recall that we have already designed a lead compen
Solution
2.
EE572
HW #16
Given the system:
Ts
W(s) +
G lead(z)
G zoh(z)
10
s( s + 8)
Y(s)

a) Find an sdomain model for the openloop system including the ZOH if Ts = 10 msec.
Solution: From class w
Due Wednesday, April 7
EE572
HW #18
Note: PreLab 4 is also due next Monday. You should be able to do it, now.
1.a)
Determine the type number of the following openloop Zdomain transfer functions:
i
EE572 Solution to HW #17
1. Consider the system from HW#16:
T
s
W(s) +
G zoh(z)
G c (z)
10
s( s + 8)
Y(s)

Recall that we have already designed a lead compensator, Gc(z), to meet the following specif
EE572  Solution to HW #18 1.a) Determine the type number of the following openloop Zdomain transfer functions:
i ) G( z ) =
10( z + 1) 2 z ( z 1)
ii ) G( z ) =
10( z + 1)3 z 2 ( z 1)
iii ) G ( z )
EE572
Soln to RISHW #5*
1 0
1
5
x=
x + 2 w, x(0) = 6 , and
Given the continuous state variable model,
0 3
y = [3 4]x
the corresponding discrete nextstate approximation to this model,
x k +1
EE572
RISHW #5*
Due Wednesday, February 2nd (Happy Ground Hogs Day)
0. Please complete Lab 1 that we took data for after class today. It's due on Wednesday, too! On
days when you have a lab due, I usu
EE572
HW#2
Due Monday, January 24
0.
Pick a Lab partner and form a group of 45 people for the project. It is helpful if at least one of your
group members has some experience in assembly language pro
EE571 Solution to HW#1 1. a) Find the state variable model of the form
& x = Ax + Bw, x( 0+ ) for the following electrical network:
1 ohm
+
iL
1 0 u( t)+ w ( t) u( t)
Amp s
Vc 
1 /3 F
2 o hm s 1 /2
EE571  Solution to HW#2 1. a) Find the state variable model of the form
& x = Ax + Bw, x ( 0 + ) y = Cx + Dw
for the following electrical network:
1/3 F
1 ohm + Y2 1/2 H 10u(t)+w2(t)u(t) Y1
10u(t)+
Due Wednesday, September 11
0.
EE571
HW#3
Pick a lab partner to work with. Your first lab is coming soon.
1. a) Find an analogous circuit then a state variable model for the rotational system shown
be
Due Monday, Sept. 9th
1. a)
EE571
Find the state variable model of the form
HW#2
x Ax Bw, x( 0 )
for the following electrical network:
y Cx Dw
1/3 F
1 ohm
+ Y2 
1/2 H
2 ohm
10u(t)+w1(t)u(t) +

10u(
EE571
Solution to HW#4
1a) The solution to the state equation is x(t)=eAt x(0). To evaluate, first lets find the eigenvalues of A:
s 2 1
2 1
2
A=
sI A = 1 s 2 = s 4 s + 3 = ( s 1)( s 3) = 0 s1 = 1 an
Due Monday, September 1
EE571
HW#4
0.
Go back and finish HW3 Problem 2 now that you know how to do it.
1. a)
Recall the first matrix from HW#3, problem 2. Since you have already found the
eigenvectors
Due Monday, September 19
EE571
Easy 1 Problem Assignment! HW#7
0.
Lab 1 (the in lab portion) is due Monday. Each person should email his/her own lab.
1.
Given the following state variable model (see
EE571
Solution to HW#7
t
1a) The solution is x(t) = e
A(t t 0 )
e
x( t 0 ) +
A(t )
Bw( )d . To evaluate eAt, first lets find the eigenvalues of A:
t0
s + 4 2
4 2
A=
sI A =
= s2 + 8s + 12 = ( s +
Due Wednesday, September 21
EE571
HW#8
Since it is football season, you have decided to invest in a satellite dish. Rather than pay for a DirectTV technician to come and
align your dish antenna, you d
EE571
Solution to HW#8
1a) The block diagram for the satellite tracking system is:
1
2
comm
+

5
1+s/(40
)
V in
Ka
+

1/Ra
Va +
60

Motor Ckt
Amplifier
Receiver
Ia
1
Vb
(J L/Na +J )s
m
Kt
T
0.5
142