Given a plant's transfer function, G_o(s), how would one be able to choose the choice of a controller using Q-design method, where Q(s) = F_{q}(s)*G_o^{i}(s), where G_o^{i}(s) is the inverted signal of the plant? More specifically, how would one justify whether to use first, second, or third-order model for F_{q}(s)? Thanks in advance
Practically or academically? (Where have I used that before?)
I'm not sure what you mean by the order of the model, but I assume that you're constraining the behavior of your F_{q}(s) to keep the plant drive within bounds -- so do some analysis on the plant transfer function, or try things out in simulation, and see what works best. You want the simplest system that will still attain your goals.
It isn't clear what you are really trying to do? One could do many things. if the controller is 1/G_o(s) then F{q}(s) could be a low pass filter to reduce output noise. Why not simply make F({q}(s) a constant to increase the gain and get the closed loop control closer to unity?
You need to give a precise example as the question is vague. Why bother with Q design in the first place is a better question?
Peter Nachtwey
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