Page 309 - Modern Control Systems

Exercises 283

e. Disturbance The ratio of the change in the system transfer function to the
signal change of a process transfer function (or parameter) for a
small incremental change.
f. Transient The response of a system as a function of time.
response
g. Complexity A system with a measurement of the output signal and a
comparison with the desired output to generate an error
signal that is applied to the actuator.
h. Error signal A measure of the structure, intricateness, or behavior of a
system that characterizes the relationships and interactions
between various components.
i. Closed-loop The parts, subsystems, or subassemblies that comprise a
system total system.
j . Loss of gain An attribute of a system that describes a tendency of the
system to depart from the equilibrium condition when
initially displaced.
k. Open-loop A reduction in the amplitude of the ratio of the output
system signal to the input signal through a system, usually
measured in decibels.

EXERCISES
E4.1 A closed-loop system is used to track the sun to obtain which controls the arm [8,9]. The transfer function for
maximum power from a photovoltaic array. The track- the process is
ing system may be represented by Figure 4.3 with
H(s) = 1 and G(s) = K
(s + 5) 2
100
G(s) (a) Calculate the expected steady-state error of the grip-
TS + r per for a step command A as a function of K. (b) Name
where r = 3 seconds nominally, (a) Calculate the sensi- a possible disturbance signal for this system.
tivity of this system for a small change in r. (b) Calculate
A
the time constant of the closed-loop system response.
Answers: (a) e, v =
Answers: S = -3s/(3s + 101); r,. = 3/101 seconds 1 + K/25
E4.4 A magnetic disk drive requires a motor to position a
E4.2 A digital audio system is designed to minimize the
effect of disturbances as shown in Figure E4.2. As read/write head over tracks of data on a spinning disk,
an approximation, we may represent G(s) = K 2- as shown in Figure E4.4. The motor and head may be
(a) Calculate the sensitivity of the system due to K 2- represented by the transfer function
(b) Calculate the effect of the disturbance noise T d{s)
on V 0. (c) What value would you select for K\ to min-
imize the effect of the disturbance?
where r = 0.001 second. The controller takes the dif-
E4.3 A robotic arm and camera could be used to pick ference of the actual and desired positions and gener-
fruit, as shown in Figure E4.3(a). The camera is ates an error. This error is multiplied by an amplifier
used to close the feedback loop to a microcomputer, K. (a) What is the steady-state position error for a

FIGURE E4.2
Digital audio
system.