ME 4673 - Modern Control Theory
Homework 4 Solution
1. Consider the system given by
200
01
x = 0 2 0 x + 1 0 u
031
01
"
y=
100
010
#
x.
Is the system completely state controllable and completely observable? Is the system output controllable?
Solution:
U=
ME 4673 - Modern Control Theory
Homework 1 Solution
1. Determine the ranks of the following matrices.
"
100
500
32
(a) A = 6 1
30
(c) A =
(b) A =
2408
1263
#
(d) A =
#
"
"
1001
0050
#
Solution:
(a) rank(A) = 2
(b) rank(A) = 2
(c) rank(A) = 1
(d) rank(A)
ME 4673 - Modern Control Theory
Homework 5 Solution
Consider the plant
s+2
.
s (s 2) (s + 1)
We want the plants step response to have a 10% overshoot relative to its steady-state value
and a peak time of 1 sec.
G(s) =
1. Design a pole-placement controller
ME 4673 - Modern Control Theory
Homework 2 Solution
1. Write the state-space equations representing the following systems. Assume y is the output.
.
(a) 2 y +3 + 5y + 2y = u
y
y
(b) y (4) + 6 = 3 u +7u
Solution:
0
1
0
0
x1
x1
0
0
0
1 x +
x2 =
2
1
5
3
ME 4673 - Modern Control Theory
Homework 3 Solution
1. Given the state-space equations
"
#
=
"
y=
x1
x2
h
11
2 3
i
22
#"
"
#
x1
x2
x1
x2
#
+
"
#
0
1
u
+ u,
change the state variables to
z1 = 3x1 + 2x2
z2 = 7x1 + 5x2
and write new equations for the variabl