Seeking Textbook Suggestions

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'; J.R.Leigh; 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 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:

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 night do. A decent text for $10 is rare these days.

Jerry

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.

I would recommend:

Modern Control Engineering (4th Edition) by Katsuhiko Ogata

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)

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.

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.