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I am studying control theory (among other things) at a university. I know about linear, non-linear, continuous, discrete, robust, etc. control theory. However one thing that has never been adequately explained has been, how do we get the process model which to design the control for?

Simple electronic circuits and simple physical phenomena can be easily converted to mathematics, but what do I do if the real world process is very complicated? E.g. a multirotor RC helicopter or a space rover? There are probably two cases:

  1. Designing a new complicated process/device (and control for it).
  2. Designing a control for an existing complicated process/device.

Are there any organized or commonly used methods to get the model? Any books/resources/search term suggestions which I might find useful?

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This is a modeling question, not a mathematical question. –  Qiaochu Yuan Oct 17 '12 at 18:56
@QiaochuYuan Modeling is part of mathematics? –  Euler....IS_ALIVE Oct 17 '12 at 19:30
@QiaochuYuan The American Mathematical Society in its subject area classification for mathematics lists: 00A71 and 97Mxx as parts of mathematics. –  Joseph Malkevitch Oct 17 '12 at 19:51
Studying mathematical models is absolutely a part of mathematics, but I strongly disagree that deciding what model to use is a mathematical question. It's a question in whatever subject studies the thing you're modeling. –  Qiaochu Yuan Oct 17 '12 at 20:49
Mathematical modeling is in part about using mathematics in subjects outside of mathematics. Suppose I want to understand "fairness" in a certain situation X. There often will be different ways to measure or define fairness for the situation X, and one might think it necessary to invent a new way to measure fairness to get a better insight into X, different from those that have been looked at in the past. To me, this process is doing mathematics. –  Joseph Malkevitch Oct 18 '12 at 1:52

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