Page 175 - Modern Control Systems

Problems 149

1
tf(.v) ' YU)
s + 1 s
1 K <• *•«
' ±l
K 2
X

FIGURE P2.35 Multiloop feedback system.

input. What is the time required for the step response
to reach 90% of its final value?
P2.36 A system is represented by Figure P2.36. (a) Deter- FIGURE P2.37 Two-mass system.
mine the partial fraction expansion and y{t) for a ramp
input, /(f) = t, t > 0. (b) Obtain a plot of y(t) for part
(a), and find y(t) for l = 1.0 s. (c) Determine the im-
pulse response of the system v(/) for 2 0. (d) Obtain
(
a plot of y(t) for part (c) and find y(i) for ( = 1.0 s.
-0.5 m-
24
RU) • •* n.v)
s* + 9s 2 + 26s + 24
Q- 4
FIGURE P2.36 A third-order system.
FIGURE P2.38 Winding oscillator.
P237 A two-mass system is shown in Figure P2.37 with an
l
input force u(t). When m | = m 2 = and^i = K 2 = 1,
find the set of differential equations describing the viscous 4 friction coefficient for the sphere in air is
system. 2 X 10~ N m s/rad. The sphere has a mass of 1 kg.
P2.39 For the circuit of Figure P2.39, determine the trans-
P238 A winding oscillator consists of two steel spheres
on each end of a long slender rod, as shown in form of the output voltage V 0(s). Assume that the cir-
Figure P2.38. The rod is hung on a thin wire that can cuit is in steady state when t < 0. Assume that the
be twisted many revolutions without breaking. The switch moves instantaneously from contact 1 to con-
= 0.
tact 2 at t
device will be wound up 4000 degrees. How long will
it take until the motion decays to a swing of only 10 P2.40 A damping device is used to reduce the undesired
degrees? Assume that the thin wire has a rotational vibrations of machines. A viscous fluid, such as a
4
spring constant of 2 X 10~ Nm/rad and that the heavy oil, is placed between the wheels, as shown in
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FIGURE P2.39 4ft
Model of an
electronic circuit.