//Example sec 11.9.2 a

//stability of linear continuous system

clear;clc;

xdel(winsid());

s=%s;

G=1/(s*(s+1)*(s+2))

G1=pfss(G)

//taking Z transform of G1

z=%z;

G2=(z/(2*(z+1)))-(z/(z+%e^(-1)))+(z/(2*(z+%e^(-2))))

//upon simplification we get the following characteristic equation

B=z^3-(1.3*z^2)+0.85*z-0.5

//substituting "z=(1+r/1-r)" in B

//the resultant equation is B1

r=poly(0,'r');

B1=3.65*r^3+1.95*r^2+2.35*r+0.05

routh_t(B1)

disp("The system is stable")

Hello Ankur 

maybe you can find something here :

1. Andrew D. Lewis "Tautological Control Systems", SpringerBriefs in Electrical and Computer Engineering 2014 (http://link.springer.com/book/10.1007%2F978-3-319-08638-5) or (http://www.mast.queensu.ca/~andrew/papers/pdf/2014c.pdf) also video lectures (https://www.youtube.com/watchv=F2rg4Uq6tNY&list=PLbPr5CUeh0DqEtMQ9M65v5QKDOGp0grSe)

2.  Eduardo D. Sontag, "Mathematical Control Theory: Deterministic Finite Dimensional Systems" Texts in Applied Mathematics (http://www.springer.com/us/book/9780387984896)

3. RW. Brockett "The early days of geometric nonlinear control", Automatica

Volume 50, Issue 9, September 2014, Pages 2203–2224 (http://www.sciencedirect.com/science/article/pii/S0005109814002386)

best regards

Hi Ankur,

It is difficult to get in one book things that have been developed over the years and by so many people with different background.

When as kids we learn that 1+2=3 or even 7+2=9, maybe is not too difficult, yet 8+7=15, not to mention 8*7=56, are pretty difficult and is not very clear why one would need this.

One of the miracles of Electrical Engineering in general and Control in particular is that you write some apparently abstract mathematical formulas, and... it works in real systems.

What makes Control more difficult is the "damn" feedback.

It is not too difficult to understand why you need a filter in order to clean your music of unwanted noise. The fact that the clean music comes to you 50 msec or even 1 sec later is not too relevant.

Instead, the same 50 msec delay in  closed-loop may mean total disaster, unless you have a good representation of the system under Control, etc., etc., and this brings you to some serious mathematics. 

So, my own experience has taught me that you better learn all mathematical stuff you are taught, even if (in the beginning) you don't know why. The understanding of why and how comes later, when and if you really have to deal with real systems.

In this respect, some books are written by people with real-world background, who may try to add a few whys, or by people with mathematical ground, who care most about the math. Both approaches are good to get.

The references in the messages above are good, yet they may deal with the mathematical aspects of things more than your question seems to ask for.

I would think that such a book as

Gene F. Franklin, J. David Powell, Abbas Emami-Naeini:

Feedback Control of Dynamic Systems

may contains a bit more about the practical motivation behind the mathematical theory of Control.

Best regards,

Itzhak

《Feedback Systems An Introduction for Scientists and Engineers》

Really a good book to provide an introduction to the basic principles for control

If you're interested in the psychology and human factors angle, use Google Scholar to look up Thomas Sheridan at MIT

Hi Ankur,

 For an excellent insight into Control, video lectures of "Brian Douglas" [1] are awesome. Analysis/Design from practical perspective, I have found two books to be very helpful

(i) Modern Control Systems (12th Edition): Richard C. Dorf

(ii) Feedback Control of Dynamic Systems (7th Edition) by Franklin et al.

 I taught two courses from (ii) and found it full of learning for the students. In case, you need, I will be happy to share Slides for the book made personally by me. 

[1] https://www.youtube.com/user/ControlLectures

You should definitely read Chapter 4 of "Cybernetics: Or Control and Communication in the Animal and the Machine" (1948!)  by Norbert Wiener.

He discusses the motivation and methods of feedback control, back when the idea was still in its infancy. He refers to a lot of Bode's work. I imagine that would also be an interesting read, if you can find it.

You might be able to find some other stuff here ...

http://21stcenturywiener.org/reading-corner/

Hi Ankur,

    The first researcher who developed control theory is the British scientist Maxwell. He adopted the differential equation to describe a control system and found the stability condition about the location of roots in complex plane. A nice example to explain the intuition is the feedback mechanism in steamer.  Hope this helps.

Regards,

Chao

Hi Jamshed Iqbal , It would be great if you can share the sides which you made for teaching with me. Your help is greatly appreciated. Thanks in advance. If you need my contact details, please let me know.

Regards

Venkatesh