Page 322 - Modern Control Systems

296 Chapter 4 Feedback Control System Characteristics

Disturbance
T/s)
Controller Dynamics
K
K(s) "• Y(s)
.y+ 1
Sensor
K, = i

FIGURE AP4.7
Feedback system N{5)
with noise. Sensor noise

W
Controller Machine
— i t
b
K .v + 2 • Y(s)
1^
l
FIGURE AP4.8
Machine-tool K ft l —- '
control. Laser sensor

DESIGN PROBLEMS
CDP4.1 A capstan drive for a table slide is described in DP4.1 A closed-loop speed control system is subjected to
f £> CDP2.1. The position of the slide x is measured with a a disturbance due to a load, as shown in Figure DP4.1.
yH|1^ capacitance gauge, as shown in Figure CDP4.1, which The desired speed is <o d{t) = 100 rad/s, and the load
is very linear and accurate. Sketch the model of the disturbance is a unit step input T d{s) - l/s. Assume
feedback system and determine the response of the that the speed has attained the no-load speed of 100
system when the controller is an amplifier and rad/s and is in steady state, (a) Determine the steady-
H(s) = 1. Determine the step response for several state effect of the load disturbance, and (b) plot a>(t)
selected values of the amplifier gain G c(s) = K a. for the step disturbance for selected values of gain so

W
Controller Motor and slide
R(s) G {{s) GAs) t—*-
FIGURE CDP4.1
The model of the
feedback system Tachometer
with a capacitance
measurement
sensor. The Switch
tachometer may be normally
mounted on the open Capacitance sensor
motor (optional),
and the switch will His) = l
normally be open.