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I am highly interested in the study of control systems theory. However it seems that almost all books are written by electronics or mechanical engineers.

Due to this they generally omit many things. For instance every single textbook in controls explains the DC motor, the RC circuit state space models. However I yet have to see a book that says something like,

Feedback loops in nature: When a car is being driven air resistance is proportional to speed and constitutes a 'natural' feedback without any op-amps or sensors etc...

and feedback loops in weather

https://www.theguardian.com/environment/2011/jan/05/climate-change-feedback-loops

if anyone knows of a book that addresses such matters that will be great!

Urb
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3 Answers3

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Here is a (free) book that you may be looking for:
Feedback Systems: An Introduction for Scientists and Engineers by Karl J. Åström and Richard M. Murray

From its preface I quote:

This book provides an introduction to the basic principles and tools for the design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information and social systems. We have attempted to keep the mathematical prerequisites to a minimum while being careful not to sacrifice rigor in the process. We have also attempted to make use of examples from a variety of disciplines, illustrating the generality of many of the tools while at the same time showing how they can be applied in specific application domains.

Zeta.Investigator
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Nonlinear physics
One area of physics that studies control systems is the nonlinear theory... although some may treat it as a branch of mathematics. The physics textbooks on nonlinear theory are usually full of the examples of systems with a feedback - from various types of generators and amplifiers, to non-linear equations (e.g., Korteweg-de Vries) for waves in liquids, to equations describing patterns formation (such as Swift-Hoheberg equation, with applications in clouds and QFT alike).

Generators
I have mentioned amplifiers and generators - these are the areas where the feedback is explicitly designed and studied. This ranges from simple motors to the circuits used in radio communication (where Vand-der-Pol equation is the model par excellence) and to quantum generators, such as lasers and masers.

Decision theory
Another very mathematical prospective on control systems is from the point of veiw of statistics. Serious texts dealing with hypothesis testing and Bayesian statistics are essentially physics-speak for control theory.

Summary

  • The feedback is so ubiquitous in physics, that it is likely to be covered in a separate book: one should either look for appropriate problems in a specific domain, or address the texts that are more mathematical but less specific about applications.
  • Control theory often passes in physics under different names and with different terminology (e.g., nonlinear physics/oscillation theory, decision theory/statistics).
Roger V.
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Well, there are control systems build for physical devices that need to be controlled. For instance, controlling an airplane or a missile requires control loops, where the forces one is dealing with are real physical effects (eg, the airflow past the aircraft, at each control surface). I remember doing some control theory for satellite attitude and orbit control. Do aerodynamics and you'll find plenty physical loops. Look up aircraft control books or papers and you'll find those. And actually, generalizing this applies to anything that moves (eg robotics, or your car example). Going further, it applies to any physical system that is changing.

The issue is that most control theory books generalize the theory, so you have to be able to find the mathematical expressions for your physical interactions. In any case it's normally implemented electronically (abstracting the control circuits to control eg aircraft control surfaces). The in depth control theory was developed for those kinds of applications.

I did not try to find the references, but wanted to place your question and a possible way to search in a broader context.

Bob Bee
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