Hi,

i have a theoretical question regarding controller design using bode, nyquist, and root locus. I can't seem to think of any additional benefit of using the nyquist and root locus plots over the bode. IIRC, the nyquist and root locus plot the closed loop response, while the bode is more for open loop. but in that case, wouldn't the advantage be to design in either nyquist or root locus, since a stable closed loop system would mean the open loop is inherently stable, unlike a stable open loop system, which may become unstable when the loop becomes closed. but at the same time, i think the design (finding the gain/phase margins with bode is alot simpler).

Does anyone have any other insight on when we should use one over the other?

tia

 

I think most of the methods you are mentioning were invented in an age where computational power was at a premium. Nowadays, I don't know if there is any advantage using one over another, although there may be advantages in building physical intuition about a system. I think most people stick to the Bode methods but it does not make the others any less applicable.

For example, the root locus method is based on being able to put the characteristic equation of the system in the form \(1 + K \frac{G(s)}{H(s)}\). Root locus tells you how the root locations change as \(K\) varies from \(0 \to \infty\) or \(0 \to -\infty\). If you cannot put the system in this form or you have multiple parameters, this might not be the best method.

--Vahe