EE 141 – Midterm
Winter 2010
02/10/10
Duration: 1 hour and 40 minutes
The midterm is closed book and closed lecture notes. No calculators.
You can use a single page of handwritten notes.
Please carefully justify all your answers.
Problem 1:
Consider two rooms in a house as depicted in Figure 1 . The temperature in
the left room is denoted by
x
1
and the temperature in the right room is denoted by
x
2
. The
left room is equipped with a heater and we are interested in controlling the heater to regulate
the
x
2
.
x
1
x
2
Figure 1: Two rooms in a house. The room in the left is equipped with a heater.
We assume that the evolution of
x
1
is described by the following diﬀerential equation:
d
dt
x
1
=

αx
1

β
(
x
1

x
2
) +
u
(1)
where the term

αx
1
describes heat lost to the exterior of the building,

β
(
x
1

x
2
) represents
the heat lost to the room in the right, and
u
represents the heat generated by the heater.
1. Knowing that the room in the right loses heat to the exterior of the building at the same
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 Spring '07
 Balakrishnan
 Digital Signal Processing, Thermodynamics, Signal Processing, 1 Hour, 3k, 20 degrees Celsius

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