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I have a hard time understanding the differnce between the two techniques that are introduces in my textbook, a PID controller and Lead/Lag compensation.

Ultimately we add a new box to our "loop" and change the transfer function of our system(by multiplying the new box's transfer function with the old). And then tune the parameters to get the properties we want.

Are there examples of things that we can accomplish with a PID which we cant with a Lead or Lag or vise versa? To me it looks like not.

If they are really different could someone try to explain the difference between these control techniques?

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  • \$\begingroup\$ I think it is the case that all lead-lag can be converted, by rote, to PID. But not all PID can be converted, by rote, to lead-lag. I think there are areas where PID can reach that lead-lag can't (by itself.) A lead is just a low-pass followed by a PD. The lag adds a following PI. So memory serving a lead-lag is a low-pass, then PD, then PI. I don't have time now to go back to the math to be sure (or sure of the boundaries), though. Maybe search for a paper? \$\endgroup\$ – jonk Feb 23 '18 at 6:33
  • \$\begingroup\$ Oh, and I never have tried to "tune" a lead-lag. Usually lead-lag is applied when you have a fairly detailed model handy. At least, I've no experience with tuning one. Plenty with PID, though. \$\endgroup\$ – jonk Feb 23 '18 at 6:41
  • \$\begingroup\$ @jonk I guess one easier accomplish finer and other kinds of "tuning" with the lead/lag then a PID, right? \$\endgroup\$ – user21312 Feb 24 '18 at 11:05
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It can be said that PID is a special case of combination of lead lag controller. So a combination of lead-lag will do what a PID can but for a different combination of lead-lag, single PID will not be able to satisfy the condition.

Although sometimes two or three PID (with different values) are used in series rather than designing a new controller as it is simpler. Here is the link for limitation of PID ... though I guess using multiple PID's can achieve whatever we want.

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