MEEN 364
Exam 1
1/9
Texas A&M University
Department of Mechanical Engineering
MEEN 364
Dynamic Systems and Controls
Exam 1 – October 9, 2003
7:00 – 9:00 PM; 124 HRBB
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
502 (T 8:0010:50 AM)
503 (T 2:205:10 PM)
504 (W 1:504:40 PM)
506 (R 2:205:10 PM)
NOTE:
No calculators are allowed. No open books or open notes.
Problem 1:
You are given a system with input
u
(
t
) and output
y
(
t
) described by the following set
of statespace equations:
dx
1
/
dt
= 3
x
2
+
u
dx
2
/
dt
= –
x
1
–
4
x
2
–
u
y
=
x
1
We are interested in solving for the response of the system (its output) for
t
> 0 when the state at
t
= 0 is given.
(a) [7 points]
Write an expression for the Laplace transform of the output,
Y
(
s
), in terms of the
Laplace transform of the input,
U
(
s
), and the initial conditions for the states,
x
10
and
x
20
.
(b) [6 points]
If
x
10
= 1,
x
20
= 0, and
u
(
t
) = 0, solve for the output as a function of time (
y
(
t
) for
t
> 0) using Laplace transform methods.
(c) [6 points]
If
x
10
= 0,
x
20
= 0, and
u
(
t
) = 2
e
– 2
t
, solve for the output as a function of time using
Laplace transform methods.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Garhic

Click to edit the document details