EECS 565, Winter 2011, Problem Set 1: SOLUTIONS1
issued: January 13, 2011
due: January 20, 2011
1. (a) Step responses for the system
G(s) =
2
n
,
2
s2 + 2n s + n
with = 0.5 and n = 1, 2, 5rad/sec, are plotted in Figure 1. Note that, as n increases, the sy

EECS 565, Winter 2011, Problem Set 3: SOLUTIONS1
issued: January 27, 2011
due: February 3, 2011
1. Note you are only required to hand in parts (a), (b), and (c). I included the solutions to the remainder
for your reference.
(a) We now derive a state space

EECS 565, Winter 2010, Problem Set 6: SOLUTIONS1
issued: February 18, 2010
due: February 25, 2010
1. (a) 0 = 2A + V 2 C 2 /W
(b) Solving the quadratic equation from (a) and taking the nonnegative solution yields optimal cost
=
2
AW
C2
AW
+
C2
+
VW
C2
The

EECS 565, Winter 2011, Problem Set 11
issued: Thursday January 13, 2011
due: Thursday January 20, 2011
1. Problem 2, Chapter 1.
2. Problem 3, Chapter 1.
3. Problem 4, Chapter 1.
4. There are several ways to enter transfer functions into Matlab, and to man

EECS 565, Winter 2011, Problem Set 01
issued: January 6, 2011
due: (not to be handed in)
The following problems are intended to help you review material that we will be using almost daily in
EECS 565: Nyquist, Bode, and root locus plots, and the theory of

EECS 565, Winter 2011, Problem Set 31
issued: January 27, 2011
due: February 3, 2011
1. Problem 5, Chapter 2. HAND IN: Parts (a), (b), and (c) only. The rest are optional.
2. Problem 1, Chapter 3. It is generally true, (not just in this example), that ref

EECS 565, Winter 2011, Problem Set 21
issued: Thursday, January 20, 2011
due: Thursday, January 27, 2011
Read Chapter 2 and Appendix A.1. Please note that you are expected to know and be able to use all
the identities stated in this appendix. Try to deriv

EECS 565, Winter 2011, Problem Set 41
issued: February 3, 2011
due: February 10, 2011
1. Problem 7, Chapter 3.
2. It is often desirable to reduce the order of a plant model by deleting some states from the system model.
In general, one always wants to wor

EECS 565, Winter 2011, Problem Set 61
issued: February 17, 2011
due: February 24, 2011
1. Problem 1, Chapter 5.
2. Consider again the magnetically suspended ball problem. The state equations have the form
x = Ax + Bu + Ed,
y = Cx
(1)
where d is a constant

EECS 565, Winter 2011, Problem Set 71
issued: March 10, 2011
due: March 17, 2011
1. Problem 2, Chapter 6.
2. Problem 4, Chapter 6.
3. Problem 5, Chapter 6.
4. Recall that the step response of a stable second order linear system with no zeros will overshoo

EECS 565, Winter 2011, Problem Set 81
issued: Thursday March 17, 2011
due: Tuesday March 24, 2011
1. Consider, as shown in Figure 1, the problem of stabilizing the inverted pendulum on a cart.
m
y
l
u
M
Figure 1: Inverted Pendulum on a Cart
Dene state var

EECS 565, Winter 2011, Problem Set 5: SOLUTIONS1
issued: Thursday, February 10, 2011
due: Thursday, February 17, 2011
1. (a) Plots of P (t) and K(t) for terminal times T = 5, 10, 15, 20 are shown in Figure 1. Note that, as
T , P (t) converges to a constan

EECS 565, Winter 2011, Problem Set 4: SOLUTIONS1
issued: February 3, 2011
due: February 10, 2011
1. (a) Place the state feedback eigenvalues at
30 + 30j
30 30j
100
(1)
and the observer eigenvalues at
60 + 60j
60 60j
200
5 .
(2)
Then setting G = (C(A + BK)

EECS 565, Winter 2011, Problem Set 2: SOLUTIONS1
issued: Thursday, January 20, 2011
due: Thursday, January 27, 2011
Note: I provide answers to all parts of Problem 1, not just those that you were required to hand in.
1. (a) The Matlab place command may be

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