Relevant Mathematics and Physics in Control Theory

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Discussion Overview

The discussion centers on the relevant branches of mathematics and physics for students interested in control theory, particularly from the perspective of an undergraduate majoring in electrical engineering and physics. Participants share insights on mathematical concepts and subjects in physics that may be beneficial for understanding and applying control theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants emphasize the importance of differential equations, particularly Laplace transforms, as foundational for control theory.
  • Complex numbers and logarithms are noted as essential tools, with one participant sharing their experience of needing to strengthen their understanding of complex numbers before taking control systems classes.
  • Numerical methods are suggested as useful, with specific mention of methods like Runge Kutta for solving ordinary differential equations (ODEs).
  • Linear algebra is highlighted as critical, especially regarding matrices and vectors for state-variable modeling in modern control theory.
  • One participant mentions the relevance of chaos theory in understanding nonlinearities and instability in control problems.
  • Connections between control theory and digital signal processing (DSP) are noted, with a recommendation to take a DSP course for insights into digital control.
  • Participants discuss parallels between control algorithms and filter representations, indicating that feedback control systems can be modeled similarly to standard filters.

Areas of Agreement / Disagreement

Participants generally agree on the importance of differential equations, linear algebra, and numerical methods in control theory. However, there is no consensus on a definitive list of subjects or the extent of their relevance, as various perspectives and additional topics are introduced.

Contextual Notes

Some participants mention specific mathematical techniques and concepts without detailing their assumptions or the contexts in which they apply. The discussion reflects a range of experiences and educational backgrounds, which may influence the perceived relevance of different mathematical branches.

Who May Find This Useful

Undergraduate students in electrical engineering, physics, or mathematics considering a focus on control theory, as well as educators seeking to understand student perspectives on relevant mathematical foundations.

snakeize
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Hi, I'm an undergrad major in electrical engineering and physics; I am also minoring in mathematics. I am thinking of going into the field of control theory. I was wondering what branches of mathematics are particularly relevant to the field of control theory (I had a mathematics professor who was a control theorist)? And, also subjects in physics I may find particularly useful, directly or indirectly? I thank you all for your input in advance.
 
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Differential Equations,

Specifically Laplace Transforms.

Almost the entire class was in "Laplace World" as my professor put it.

Also be sure to live, learn, and love logarithms and complex numbers. It may sound like I'm talking down to you, but when I took my control systems class, I was a little shaky on complex numbers since I hadn't done anything with them since high school. You use them a lot.
 
thx enigma, i'll keep that in mind. i'll definitely take that "functions of a complex variable" class in the math department. any other input from anyone else?
 
I expect that numerical methods would probably also be usefull.

In addition, you'll obviously have to deal with the usual suspects -- trigonometry, calculus, and maybe linear algebra.
 
You should be good at ODEs (modern control theory), lin algebra (also for modern control theory), Laplace transforms, and numerical methods for solving ODEs (Runge Kutta 4) But all this was said above anyway.

I would suggest taking a DSP course (Digital signal processing) as it will give you insight into digital control and open a new door of possibilities for you.
 
mmwave said:
Become an expert at linear algebra...

specifically matrices and vectors. this is necessary for state-variable modelling of anything. much of modern control systems are based on the state-variable model.
 
differential equations initially, linear algebra is used a lot in state space (matrices, linear independence, systems of equations, eigenvectors/values) later on in addition to diff eq. My controls professor also had to take a chaos theory math course in grad school because controls deals a lot with nonlinearities and instability which is sometimes chaotic, and these are factors in any real world control problem. Also numerical methods where you learn about euler's method and more sophisticated ways of representing continuous signals as discrete signals (z domain, w domain, bilinear transformation, etc.), and also simulation.

You will see a lot of parallels to your signals and systems and DSP courses, because in the end it is all based on the same ideas. A PID control algorithm will look almost identical to a standard IIR/FIR filter. You will see that your feedback control and even your systems are filters and can be represented by transfer functions when simplified and approximated.
 

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