Case studies for CT systems - Continuous and Discrete Time Signals and Systems - page 377

Fig. 8.7. Impulse responses of
the spring damping system for
M

x =2.0
x =1
x =4

0.2

h ( t )

0.1

= 10 and ω n = 0.3.

0

−0.1

0 5 10 15 20 25 30 35 40 45 50

t (s)

overall duration over which the steady state value is achieved is much longer.
Such systems are referred to as overdamped systems.
For Case 3 with ξ n = 0 . 2, the spring acts as a flexible system. The impulse
response approaches the steady state value of zero after several oscillations.
Such systems are referred to as underdamped systems. Since the fundamental
frequency ω n is 0.3 radians/s, the period of oscillation is given by

= 2 π
ω n

= 2 π
0 . 3

T = 21 . 95 seconds . (8.28)

Based on Eq. (8.28), parameter ω n is referred to as the fundamental frequency of
the spring damping system. Since parameter ξ n determines the level of damping,
it is referred to as the damping constant.

8.3 Armature-controlled dc motor

Electrical motors form an integral component of most electrical and mechan-
ical devices such as automobiles, ac generators, and power supplies. Broadly
speaking, electrical motors can be classified into two categories: direct current
(dc) motors and alternating current (ac) motors. Within each category, there are
additional subclassifications covering different applications. In this section, we
analyze the armature-controlled dc motor by deriving its transfer function and
impulse response.
Figure 8.8(a) shows an armature-controlled dc motor, in which an armature,
consisting of several copper conducting coils, is placed within a magnetic field
generated by a permanent or an electrical magnet. A voltage applied across the
armature results in a flow of current through the armature circuit. Interaction
between the electrical and magnetic fields causes the armature to rotate, the
direction of rotation being determined by the following empirical rule, derived
by Faraday.
Extend the thumb, index finger, and middle finger of the right hand such that
the three are mutually orthogonal to each other. If the index finger points in the
direction of the current and the middle finger in the direction of the magnetic
field, then the thumb points in the direction of motion of the armature.