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(7895 previous messages)
rshow55
- 08:27am Jan 22, 2003 EST (#
7896 of 7899)
Can we do a better job of finding truth? YES. Click
"rshow55" for some things Lchic and I have done and worked for
on this thread.
Gisterme raised some points about oscillations, and
how engineers strive to get rid of them in control systems -
as they have since the 1940's. I've made the point that
oscillatory solutions - where there are alternating
adjustments - alternating points of view - conflicts -
contradictions - and yet good adjustment and stability. The
Bush administration, and the US military-industrial complex of
interlocking, crosstalking, mutually reinforcing organizations
are continuing to have fundamental problems that were
of deep concern to the leaders of the US
military-industrial-intelligence affairs from 1942 on - that
is, since it became clear that control stability was an
intractable problem. I'm quoting from Analysis of Nonlinear
Control Systems by Dunstan Graham and Duane McRuer 1961 -
Dover ed 1971 (I wore out my original edition - and am
transcribing from the Dover edition.) This is a book I was
given to read, and did read, in preparation to meeting
Wolfgang Flugge, of Stanford, who had agreed to assist in my
instruction, so far as engineering mechancs went, if I
satisfied him with my mastery of this book. (I did, but Flugge
told me I had only done so by the skin of my teeth. He was,
however, willing to do me the great favor of flogging me into
near-presentable shape - something he later told me he thought
some of his associates and he had barely done. )
Chapter 10 - Epilog and Consequence
"Early investigators of feedback control systems, such as
Minorsky (1922) and Hazen (1934) pointed out and treated
important nonlinear characteristics. but in the explosive
expansion of control system technology which followed the
introduction of feedback amplifier design, attention was
concentrated almost exclusively on linear systems for more
than a decade (refs from 1932-47). During this time the
analysis of nonlinear systems was often considered to be
inordinately arcane, at least in the United States. Two survey
papers which approximately bracket this period and which
reflect the then-current view are the ones by Von Karman and
by Bennet. The appearence of the comprehensive book by
Minorsky, of hte english language editions of the source books
by Kryloff and Bogoliuboff and by Andronow and Chaikin, and
the papers by Goldfarb stimulated renewed interest in the
problems of nonlinear control systems, ans showed the paths
which have been followed since. (This statement, however, is
not to be construed to say that there were not numerous other
significant contributions to the theory of nonlinear mechanics
and its applications. Every investigation of nonlinear control
systems is, in fact, founded on the results of investigations
in other branches of mathematics and mechanics. Very extensive
historical bibliographies have been given by Higgens and by
Ku.) The points is that the engineering literature on the
subject of nonlinear feedback control systems is
practically nonexistent for any year prior to 1950. Beginning
in that year, there have been a continually increasing number
of reports, papers, and books on the subject of this book.
"In spite of the many words which have been used her to
elaborate the discussion, and perhaps to hide the fundamental
fact, both the study and the physical synthesis of nonlinear
control systems are, still today, in a somewhat unsatisfactory
state.
" The multidudinous methods of mathematical analysis are
amenable to particular problems, and there is no workable
general theory. Of course, a solution to any given linear
equation with given specific conditions or forcing functions
may be easily and rapidly found by machine methods, and both
analog and digital computers are common fixtures in industrial
research and design departments, as well as in engineering
schools. Where computing machinery is not available, step by
step numerical or graphical methods may be applied by human
computers to find one or more solutions. Eve
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