I am looking for an introductory textbook in automatic control theory.
The book would be used by physics and math students who are
familiar with differential eqs but not with the Laplace transform.
I am especially interested in a book that uses ordinary differential
equations for much of the development and introduces Laplace transform
late (if at all).
To reply directly to me, replace all 'z' with 'a' in email address.
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.
I would highly recommend you obtain a copy of 'Control Theory, a guided tour';
Pub. Peter Peregrinus for the IEE: ISBN:0863413390. Find it at:
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
transform was developed by mathematicians as an extension to the Fourier
to assist in the solution of differential equations by making the solution an
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);
simply borrow the use of the Laplace Transform, Fourier Transform, etc. from the
of dynamic systems, to make their lives richer and easier.
The appropriate educational sequence (and as I experienced it in my own
Control Engineering) would therefore be (IMHO):
1) Understanding Differential Equations and their solution in the time domain
solution + particular integral).
2) Understanding Fourier Series and the Fourier Transform (transformation
time-domain and frequency domain) αnd the Dirichlet Conditions.
3) Understanding how the Fourier Transform was extended to create the Laplace
why it was done.
4) Understanding how the Laplace Transform and Inverse Transform are used to
differential equations easily, by algebra.
5) Understanding of how the frequency-response of systems relates to time-domain
which arises from understanding of the Fourier and Laplace Transforms and their
(Note: The above is all basic Engineering Maths, I haven't said anything about
Now, here's the 1st bit of Control Engineering-related stuff:
6) Understanding how 'Transfer Functions' (TFs, which derive from Laplace
block-diagrams are used by Control Engineers (and others) as a short-hand for
visualising the responses of dynamic systems in terms of standardised
responses (1st-order, 2nd-order, phase-lead and lag, etc.) and TF parameters,
such as gains,
As for Control Engineering texts, in my experience, they mostly start at point
i.e. they assume that the maths of dynamic systems, including Fourier and
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
could be making the students jump through tedious mathematical hoops and
the mathematicians of past centuries (Fourier, Laplace, etc.) made such an
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
between frequency-response and time-response. Even a visit to the local Hi-Fi
have them talking about frequency-response of amplifiers, etc. An engineer,
Control Engineer, should understand how that relates to steady-state and
Another possibility might be to look for books written for engineers who,
not taught the maths of dynamic systems. For example: all of Shinskey's books on
Control are written using differential equations and time-domain responses (with
mention of the Laplace Transform); because they are written for Chemical
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.
Kelvin B. Hales
Kelvin Hales Associates Limited
Consulting Process Control Engineers
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
What (aside from Leigh) is a good, basic introductory text?
The idea is to introduce the topic to physics and math sutdents.
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
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.
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
(Amazon.com product link shortened)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)
(Amazon.com product link shortened)
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?
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
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