Tuesday, 25 June 2013

Preparing for Control Theory

With almost 2 years of experience in control theory, I would say that control theory is definite a tough area to work when you compare to other field of engineering. If you follow my blog, you might me complaining about control theory sometimes because sometimes it is troublesome for engineers prove various small details. Therefore, if you decided to pursue your studies, read on for information on how to better prepare yourself for control theory.

The main reason control theory is hard to study is because there are a lot different kind of mathematics involved in control theory. I have previously mentioned 2 fundamental fields of mathematics that show up almost always in different field of control theory, namely (a) discrete mathematics, and (b) linear algebra. If you don't have much exposure to this topics, it would be best to study them a bit prior to starting your studies. My previous post covers a good detail on where to get resources for studying this topic.

From now on, the advices given out is only applicable to conventional control theory that uses differential equations to represent systems. Note that field of research like Discrete Event System will use very different mathematics (math that is more related to computer sciences).

At the same time, you would also want to review some classical control theory (if your supervisor works a lot with differential equations). Any third year course or introductory courses to control theory would be considered to be classical. Typical classical control theory would use transfer function and the notion of poles to describe system stability. Review of transfer function and the notion of stability would be sufficient.

Next, you want to study modern linear control theory. The major difference is modern control theory uses a lot of linear algebra to study system behavior. A lot of proofs will also be involved when you study this topic. You will see a bit of discrete mathematics as you progresses along. Two good resources to study this topic would be Chen's Linear System Theory and Design and Zhou's Essentials of Robust Control.

That's probably a good amount of preparation if you can/have study the above material. There a lot of other material to prepare depending on which area you go into. But, my experience tells me the above are the fundamental for control theory that uses a lot of differential equations.

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