Lecture 23
Electromechanical systems
Consider the system shown in the following figure.
θ
: angular displacement of moving part
T: electromechanical torque
T
ext
: external torque (e.g., a load)
To analyze this system we have to consider all the laws we have seen so far. Let us
introduce first the following notation,
11
1
1
,,
,
s
s
s
nn
n
n
E
ie
Ei
e
E
λ
==
=
=
±±
1
0
0
n
R
R
R
=
±
²»²
±
Note that R is a diagonal matrix.
1.
From KVL, KCL, and Ohm’s Law we know that
s
E
Ri
e
−=
2.
From Faraday’s Law we know that the induced voltages are
dd
i
d
L
d
d
i
d
L
eL
i
L
i
dt
dt
d
dt
dt
d
λθ
ω
θθ
+⋅
=
+
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From Ampere’s Law we can determine the relationship between flux and
inductance,
()
L
i
λθ
=
4.
Energy conservation describes the relation between torque and current.
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 Spring '09
 FRANCISCODGALIANA
 Angular Momentum, Trigraph, Elementary algebra, dt dt dθ

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