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EML 4312
Spring 2009
Control of Mechanical engineering systems
University of Florida
Mechanical and Aerospace Engineering
Suggested exercises on State Space method
Issued: April 25, 2009
Problem 1.
Consider a dynamical system governed by the following set of coupled di±erential equa
tions:
˙
X
=
aX
2

bXY
(1)
˙
Y
=
Y

2
X
(2)
Is this a linear system? Verify that (
X
= 0
, Y
= 0) is an equilibrium point of this system. Is it the
only equilibrium point? Linearize the system around the equilibrium (
X
= 0
, Y
= 0).
Problem 2.
The linearized equation of motion of a highperformance helicopter are:
¨
θ
=

σ
1
˙
θ

α
1
˙
x
+
nδ
+
w
¨
x
=
gθ

α
2
˙
θ

σ
2
˙
x
+
gδ,
where
θ
(
t
) is the pitch angle of the helicopter,
x
(
t
) is its translation, the rotor thrust angle
δ
(
t
) is a
control input that is used to control the pitch
θ
, and
w
is an external disturbance.
n, g, σ
(
·
)
, α
(
·
)
are
constants.
1. Is this a linear system?
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This note was uploaded on 06/06/2011 for the course EML 4312 taught by Professor Dixon during the Fall '07 term at University of Florida.
 Fall '07
 Dixon
 Mechanical Engineering

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