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School of Engineering Science
ENSC 483  Modern Control Systems
Spring 2007–Assignment 5
1.
Electrical circuit–
Obtain the state space description of the network shown in Figure 1. Use
the voltages across the capacitors and the current through the inductor as the state variables.
Note that
v
1
is the input and
v
2
is the output.
Figure 1: An electrical network
2.
MassSpring Systems
– Obtain the diﬀerential equations for the system shown in Figure
2. Draw a block diagram for this system and ﬁnd the transfer function
H
(
s
) =
X
2
(
s
)
F
(
s
)
. Write
the state variable formulation of this system using the state variables:
z
1
=
x
1
,z
2
= ˙
x
1
,z
3
=
x
2
,z
4
= ˙
x
2
.
Figure 2: A massspring system.
3.
Companion Matrices.
Consider the following
n
×
n
matrix in companion form:
A
=
0 0
···
0 0

a
0
1 0
···
0 0

a
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0 0
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This note was uploaded on 10/09/2009 for the course ENSC 1166 taught by Professor Mehrdadsaif during the Spring '07 term at Simon Fraser.
 Spring '07
 MehrdadSaif

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