where zeta = 0.707 and wn = 15. The transfer function of the power amplifier is approximately G₁(s) = ka TS + 1 where tau = 0.15 s. (a) Determine the sensitivity of the system to a change of the parameter ka. (b) The system is subjected to a disturbance Td(s) = 10/s. Determine the required magnitude of ka in order to maintain the steady-state error of the system less than 0.10° when the input R(s) is zero. (c) Determine the steady state error of the system when subjected to a disturbance Td(s) = 10/s when it is operating as an open-loop system ks = 0 with R(s) = 0.
where zeta = 0.707 and wn = 15. The transfer function of the power amplifier is approximately G₁(s) = ka TS + 1 where tau = 0.15 s. (a) Determine the sensitivity of the system to a change of the parameter ka. (b) The system is subjected to a disturbance Td(s) = 10/s. Determine the required magnitude of ka in order to maintain the steady-state error of the system less than 0.10° when the input R(s) is zero. (c) Determine the steady state error of the system when subjected to a disturbance Td(s) = 10/s when it is operating as an open-loop system ks = 0 with R(s) = 0.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Hi, please solve the following problem showing all steps in detail. I am reviewing this for an upcoming exam, and I want to make sure I have everything down correctly.
Transcribed Image Text:where zeta = 0.707 and wn = 15. The transfer
function of the power amplifier is
approximately
G₁(s)
=
ka
TS + 1
where tau = 0.15 s.
(a) Determine the sensitivity of the system to
a change of the parameter ka.
(b) The system is subjected to a disturbance
Td(s) = 10/s. Determine the required
magnitude of ka in order to maintain the
steady-state error of the system less than
0.10° when the input R(s) is zero.
(c) Determine the steady state error of the
system when subjected to a disturbance Td(s)
= 10/s when it is operating as an open-loop
system ks = 0 with R(s) = 0.
Transcribed Image Text:Large microwave antennas have become
increasingly important for radio astronomy
and satellite tracking. A large antenna with a
diameter of 60 ft, for example, is susceptible
to large wind gust torques. A proposed
antenna is required to have an error of less
than 0.10° in a 35 mph wind. Experiments
show that this wind force exerts a maximum
disturbance at the antenna of 200,000 ft lb at
35 mph, or the equivalent to 10 volts at the
input Td(s) to the amplidyne. One problem of
driving large antennas is the form of the
system transfer function that possesses a
structural resonance. The antenna
servosystem is shown in the figure below. The
transfer function of the antenna, drive motor,
and amplidyne is approximated by
R(s)
where
G(s)
=
Power
amplifier
G₁(s)
T/(s)
Sensor
k,= 1
Antenna, drive motor,
and amplidyne G(s)
w/1
s(s² + 25w,s + w²/1)
0(s)
Position
(radians)
where zeta = 0.707 and wn = 15. The transfer
function of the power amplifier is
approximately
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