Page 34 - Modern Control Systems

Chapter 1 Introduction to Control Systems

Parkinson had a dream about an antiaircraft gun that was successfully felling
airplanes. Parkinson described the situation [13]:

After three or four shots one of the men in the crew smiled at me and beckoned me to
come closer to the gun. When I drew near he pointed to the exposed end of the left
trunnion. Mounted there was the control potentiometer of my level recorder!

The next morning Parkinson realized the significance of his dream:
If my potentiometer could control the pen on the recorder, something similar could,
with suitable engineering, control an antiaircraft gun.

After considerable effort, an engineering model was delivered for testing to the
U.S. Army on December 1, 1941. Production models were available by early 1943,
and eventually 300() gun controllers were delivered. Input to the controller was pro-
vided by radar, and the gun was aimed by taking the data of the airplane's present
position and calculating the target's future position.
Frequency-domain techniques continued to dominate the field of control follow-
ing World War II with the increased use of the Laplace transform and the complex fre-
quency plane. During the 1950s, the emphasis in control engineering theory was on the
development and use of the s-plane methods and, particularly, the root locus ap-
proach. Furthermore, during the 1980s, the use of digital computers for control com-
ponents became routine. The technology of these new control elements to perform
accurate and rapid calculations was formerly unavailable to control engineers. There
are now over 400,000 digital process control computers installed in the United States
[14, 27]. These computers are employed especially for process control systems in
which many variables are measured and controlled simultaneously by the computer.
With the advent of Sputnik and the space age, another new impetus was imparted
to control engineering. It became necessary to design complex, highly accurate control
systems for missiles and space probes. Furthermore, the necessity to minimize the
weight of satellites and to control them very accurately has spawned the important
field of optimal control. Due to these requirements, the time-domain methods devel-
oped by Liapunov, Minorsky, and others have been met with great interest in the last
two decades. Recent theories of optimal control developed by L. S. Pontryagin in the
former Soviet Union and R. Bellman in the United States, as well as recent studies of
robust systems, have contributed to the interest in time-domain methods. It now is
clear that control engineering must consider both the time-domain and the frequency-
domain approaches simultaneously in the analysis and design of control systems.
A notable recent advance with worldwide impact is the U.S. space-based ra-
dionavigation system known as the Global Positioning System or GPS [82-85]. In
the distant past, various strategies and sensors were developed to keep explorers on
the oceans from getting lost, including following coastlines, using compasses to point
north, and sextants to measure the angles of stars, the moon, and the sun above the
horizon. The early explorers were able to estimate latitude accurately, but not longi-
tude. It was not until the 1700s with the development of the chronometer that, when
used with the sextant, the longitude could be estimated. Radio-based navigation sys-
tems began to appear in the early twentieth century and were used in World War II.
With the advent of Sputnik and the space age, it became known that radio signals
from satellites could be used to navigate on the ground by observing the Doppler
shift of the received radio signals. Research and development culminated in the