Homework 2  MAE143B Spring 2010: due Thursday April 15
Question 1 — State Variable Realization
Consider the system from input,
u
(
t
)
, to output,
y
(
t
)
, described by the transfer function
4
s
+ 4
s
3
+ 2
.
4
s
2
+ 25
.
84
s
+ 50
.
08
.
Provide a statevariable description of this system. That is, write down a ﬁrstorder vector ordinary
differential equation together with an output equation which represents this relationship between
u
and
y
.
Check your answer in matlab using the
tf
command. That is, create a system with your
A
,
B
,
C
and
D
matrices from your statevariable description via
sys = ss(A,B,C,D),
then compare matlab’s reverse computation to the above system via the command
tf(sys).
Plot the frequency response of the statevariable realization of this system using the matlab
bode(sys)
command. Label your plot well.
Question 2 — Simulation with sinusoidal input
Use the statevariable description of the system from Question 1 to construct a numerical simu
lation of the system with an input
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 Winter '10
 Bitmead
 Daniel, statevariable description

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