Seeking Textbook Suggestions

George wrote:


Most of automatic control theory is about clever ways to manipulate
polynomials after you've done the Laplace transform, so I don't think
that you'd have much luck.

I would certainly expect a math student to eat the Laplace transform
right up, and a physics student shouldn't have too much more trouble.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I would highly recommend you obtain a copy of 'Control Theory, a guided tour';
J.R.Leigh;
Pub. Peter Peregrinus for the IEE: ISBN:0863413390. Find it at:
<http://www.iee.org/Publish/Books/Control/index.cfm>
since Prof. Leigh appears to have already done much of your work for you.

However: can students be familiar with differential equations, but at the same
time not yet
familiar with their solution by means of the Laplace Transform; given that the
Laplace
transform was developed by mathematicians as an extension to the Fourier
Transform precisely
to assist in the solution of differential equations by making the solution an
exercise in
algebra - and all this more than 100-years before the topic of Control
Engineering and was
even thought of? Control Engineers are concerned with the dynamic responses of
systems - as
are Electrical/Electronic's Engineers and Mechanical Engineers (to name a few);
so they
simply borrow the use of the Laplace Transform, Fourier Transform, etc. from the
mathematics
of dynamic systems, to make their lives richer and easier.

The appropriate educational sequence (and as I experienced it in my own
first-degree in
Control Engineering) would therefore be (IMHO):
1) Understanding Differential Equations and their solution in the time domain
(transient
solution + particular integral).
2) Understanding Fourier Series and the Fourier Transform (transformation
between
time-domain and frequency domain) ánd the Dirichlet Conditions.
3) Understanding how the Fourier Transform was extended to create the Laplace
Transform and
why it was done.
4) Understanding how the Laplace Transform and Inverse Transform are used to
solve
differential equations easily, by algebra.
5) Understanding of how the frequency-response of systems relates to time-domain
dynamics;
which arises from understanding of the Fourier and Laplace Transforms and their
inverses.
(Note: The above is all basic Engineering Maths, I haven't said anything about
Control
Engineering, yet.)
Now, here's the 1st bit of Control Engineering-related stuff:
6) Understanding how 'Transfer Functions' (TFs, which derive from Laplace
Transforms) and
block-diagrams are used by Control Engineers (and others) as a short-hand for
describing and
visualising the responses of dynamic systems in terms of standardised
differential equation
responses (1st-order, 2nd-order, phase-lead and lag, etc.) and TF parameters,
such as gains,
time-constants, etc.

As for Control Engineering texts, in my experience, they mostly start at point
(6) above,
i.e. they assume that the maths of dynamic systems, including Fourier and
Laplace
Transforms, has already been comprehensively covered elsewhere in a maths course.

Frankly: " a book that uses  ordinary differential
equations for much of the development and introduces Laplace transform late (if
at all)."
could be making the students jump through tedious mathematical hoops and
difficulties that
the mathematicians of past centuries (Fourier, Laplace, etc.) made such an
effort to
simplify through their work. What's more, nobody is ever going to have a good
grasp of the
behaviour of dynamic systems (feedback or otherwise) without understanding the
equivalence
between frequency-response and time-response. Even a visit to the local Hi-Fi
dealer will
have them talking about frequency-response of amplifiers, etc. An engineer,
especially a
Control Engineer, should understand how that relates to steady-state and
transient
performance.

Another possibility might be to look for books written for engineers who,
traditionally, are
not taught the maths of dynamic systems. For example: all of Shinskey's books on
Process
Control are written using differential equations and time-domain responses (with
never a
mention of the Laplace Transform); because they are written for Chemical
Engineers (and
therefore sometimes make very laborious long-winded reading for Control
Engineers). Do an
Amazon search for 'Shinskey'.

Overall, though, I think Leigh would meet and exceed your requirements.
Recommended!

Kelvin B. Hales
Kelvin Hales Associates Limited
Consulting Process Control Engineers
Web: www.khace.com

wrote:


J.R.Leigh;

I am in the process of getting a copy of that book.
OK. Now suppose I am convinced that the Laplac transform is the way to
go.
What (aside from Leigh) is a good, basic introductory text?
The idea is to introduce the topic to physics and math sutdents.

George wrote:

The Laplace transform is so useful for control theory that you probably
won't find what you want. The controlled systems are specified in the
time domain, and the controller circuits are designed in the frequency
domain.

Laplace transforms are closely related to Fourier transforms, which your
students probably understand. They are little more than a formalization
of Heaviside's operational calculus, which is likely a part of any
dif-eq course. I think Laplace could easily be worked in in easy stages.

My Laplace text (in technician school) was by J. C. Jaeger, one in the
series of "Methuen's Monographs on Physical Subjects" It's 130 pages are
4.5 by 6.5 inches, and it contains more than your students will need to
know. We didn't have assignments in it, using it as a reference and home
reading instead. That was enough. Is there a Dover reprint? The material
in http://store.yahoo.com/doverpublications/0486406784.html  night do. A
decent text for $10 is rare these days.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

I would recommend:

Modern Control Engineering (4th Edition)
by Katsuhiko Ogata

http://www.amazon.com/exec/obidos/tg/detail/-/0130609072/qid 14703204/sr=8-2/ref=pd_csp_2/103-2899561-3327027?v=glance&s=books&nP7846

It is more practical than theoretical, and has lots of real-world
examples worked out in detail, with lots of Matlab code examples.
Targeted for senior level undergrad, or working professional.

Only drawback is there is no digital control section, Ogata has a
separate book for that.  But for real-world analog linear control
system analysis, it is pretty good.  Though, I would imagine 99% of
implementations these days are DSP based, not analog opamp based, so a
supplementary digital control book is really mandatory, e.g. Franklin
and Powell Digital Control of Dynamic Systems (3rd Edition)

http://www.amazon.com/exec/obidos/tg/detail/-/0201820544/ref=pd_sim_b_4/103-2899561-3327027?%5Fencoding=UTF8&v=glance

Hi George,

I could suggest you a book in german, but I guess
its easier for your students to learn the laplace-
transformation than german ;)

Thomas

Can you suggest some German textbooks anyway - I have found a wealth of
good material in books of other languages.

I know of Isermann's book but it is also available in English. Surely
there are some real gems out there still untranslated?

Fred.

"Fred Stevens" wrote:

It's a pity how people tend to forget that loads of material
comes from non-english speaking countries (IMHO more than 75 %)


The book I was having in my mind is called
"Regelungstechnik 1" (Control Theory 1) from
Jan Lunze. The specialty of this book is, that
it first explains the basics of control in time
domain only and introduces Laplace quite late. Sorry,
I dont know the ISBN # or if it is also available in English.

Thanks Thomas. I  heard of Lunze many years ago when I was looking for
a good MIMO control textbook.
I think he published his about the same time as Jan Maciejowski. I'll
investigate further. Also, there are some excellent
French books on control, for example the books by Landau at Grenoble.
It seems that many authors from other countries (e.g. Holland and
Sweden) write their books directly in English, but I'm
sure there are some really interesting ones in Russian, Czech, Italian
etc.

Fred.