Not sure if this is the right forum, but I'm an electrical engineer studying controls so here goes.(adsbygoogle = window.adsbygoogle || []).push({});

Here's my background on what I know. Lead or lag compensators generally have the form C(s) = K*(s+z)/(s+p), i.e. the controller has a DC gain and introduces a pole-zero pair. In the case of a lag compensator, the pole occurs before the zero, and the opposite for the lead compensator.

From what I understand, these compensators can help meet system specifications for steady-state error and phase margin (probably other stuff, but my course tends to focus on those two).

A lead compensator can help add phase around the critical point (where magnitude of the loop gain, |C(s)P(s)| = 1) to help with the phase margin; while the gain K of the controller can help with the steady-state error.

Alright, so what does a lag compensator do that's better/different that a lead compensator? As far as I can tell the phase added by the lag controller doesn't really help/is unwanted, and really you're just interested in the gain for steady-state error, while designing the pole-zero pair placement such that you fix the phase margin after adding your desired DC gain. That's my interpretation thus far.

Summaries of my confusion:

- When would one opt for a lead, vs a lag, vs a lead-lag dual compensator?

- How can a lag controller be better (more suitable, whatever) than a lead?

Thanks for any help, much appreciated

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# Control engineering: lead and lag compensators

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