Page 169 - Modern Control Systems

Problems 143

the necessary parameters M 2 and & 12 so that the mass [8,19]. An amplidyne is a power amplifying rotary am-
does not vibrate in the steady state when plifier. An amplidyne and a servomotor are shown in
M l
F(t) — a sin(&)o t). Figure P2.ll. Obtain the transfer function 9(s)/V c(s),
P2.ll For electromechanical systems that require large and draw the block diagram of the system. Assume
power amplification, rotary amplifiers are often used v d = k 2i q and v q = k {i c.

Control
field
it = Constant

l r / \ 2 (
P \ Motor 1
f-
1
4 V Load y, b

Am plidyne **

FIGURE P2.11 Amplidyne and armature-controlled motor.
P2.12 For the open-loop control system described by the the transfer function B L{s)fVf{s) and draw a block dia-
block diagram shown in Figure P2.12, determine the gram of the system. The generator voltage »„ can be as-
-
value of K such that y(t) * 1 as t —» oo when r(r) is a sumed to be proportional to the field current .
i f
unit step input. Assume zero initial conditions. P2.14 A rotating load is connected to a field-controlled
DC electric motor through a gear system. The motor is
assumed to be linear. A test results in the output load
Controller Process reaching a speed of 1 rad/s within 0.5 s when a constant
1 80 V is applied to the motor terminals. The output
Ms) • A: • -—- • YU) steady-state speed is 2.4 rad/s. Determine the transfer
K
s+20
function 0{s)/Vf(s) of the motor, in rad/V. The induc-
tance of the field may be assumed to be negligible (see
FIGURE P2.12 Open-loop control system. Figure 2.18). Also, note that the application of 80 V to
the motor terminals is a step input of 80 V in magnitude.
P2.13 An electromechanical open-loop control system is P2.15 Consider the spring-mass system depicted in Figure
shown in Figure P2.13. The generator, driven at a con- P2.15. Determine a differential equation to describe
stant speed, provides the field voltage for the motor. The the motion of the mass m. Obtain the system response
motor has an inertia J m and bearing friction />„,. Obtain x(t) with the initial conditions A(0) = Xg and i(0) = 0.

+ o-vV\A-| Motor

0 1 „ • N i
Gear ratio n = ——
No

Generator

FIGURE P2.13 Motor and generator.