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There are two big working areas in control theory: robust control and optimal control.

  • In optimal control, only state-space models are used.
  • In robust control, only transfer functions are used.

But why are transfer functions used in robust control? Or am I wrong? Can I use state-space models in robust control, too? Give me an example, please!

Rodrigo de Azevedo
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euraad
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1 Answers1

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Note that every state space system can be written as a transfer function, and every transfer function as a state space system.

But my straightforward answer: The reason why state-space systems, in general, are used for optimal control is simply because it is more intuitive to use them because of how cost functions are defined and how mathematical optimization techniques work. You can simply deal with it better by using state-space representation then transfer functions.

Furthermore robust control techniques also often relies on the physical interpretation of the system and frequency area's where you want the controller to be "robust" (note there is no clear definition for robust, it is whatever you will say it is). But when rewriting your system from a transfer function to a state-space system you loose every physical interpretation of the system and frequencies analysis is also not intuitive anymore.

WG-
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  • What do you recommend. Optimal control or robust control? – euraad Jul 09 '17 at 15:15
  • Robust. You will never ever have true optimality. Furthermore, always try to use frequency domain techniques. There are cases where you can better use optimal controllers but they are rare. 99% of all the controllers in the world are frequency domain (transfer function) based, 1% is optimal control (state-space) based. See also the very good answer in my opinion to your other question: https://math.stackexchange.com/a/2348863/41569. – WG- Jul 09 '17 at 15:17
  • Thank you for the answer. I hope that LQG can be robust with LTR. – euraad Jul 09 '17 at 15:55