Curious about some links posted for "Understand PID control"

Peter Nachtwey · 2005-11-06T19:26:44+00:00

I didn't want to confuse a someone and hijack a thread so I waited to start this one.Jerry posted this links don't see how the stated advantages 1 through 4 can be justified?This reminds of the threads posted a few years ago about the I-PD being the best form of PID.1. Is the damping determined by where the poles of the CLTF are place?2. I agree that the I-PD is almost problem free when it comes to integrator wind up but a PID can be implemented so its wind up will handle saturation nicely. I think this is implementation dependent.3. I would think a PID would follow a ramp better because the zeros in the CLTF introduced by the PID extend the CLTF's bandwidth.4. Again, I don't see how I-PD can respond to a disturbance better than a PID because the I-PD CLTF bandwidth is not as high as that of a PID.This will give the PID priest hood something to ponder.Peter Nachtwey

Nov 06, 2005 26 Replies

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Tim Wescott 20 years ago

- lots of back and forthing snipped -

I think the real item of interest here is that Peter's system is using a form of integrator bounding that ends up working the same as Jerry's circuit. The difference is that Jerry's way is easier to implement but more obscure in its operation for a beginner. Peter's way looks, with the exception of a rather complicated integrator limit, like a PID that you may see in a textbook.

I suspect that the two forms are essentially, if not exactly, the same behaviorally because of the way that Peter's method limits the integrator.

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Jerry Avins 20 years ago

I'm tempted to believe that, but if Peter's PID-style integrator has the same time constant as a classical PID integrator, then it's not equivalent to Phelan's. By time constant, I mean the time constant of an equivalently performing op-amp integrator; namely, the R-C consisting of the input resistor and the feedback capacitor.

Jerry

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Peter Nachtwey 20 years ago

Consider placing the closed loop poles on the real axis. That is safe. Then the response is either critically damped or over damped. However, one must be mindful of the location of the zeros since they are not placed.

Peter Nachtwey

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Peter Nachtwey 20 years ago

I don't understand this comment at all. However, I am not claiming that that the integrator limit I use makes a PID equivalent to Phelan's. I am just claiming and demonstrated that a PID doesn't need to overshoot and its response will be faster because a PID has zeros which extend the bandwidth. This contradicts the advantages the pages on your webpage. BTW, the incremental ( velocity ) form of PID doesn't need to overshoot either.

By time constant, I mean the time constant of an

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ The digital world allows one to do things that can't be done in the analog world.

Peter Nachtwey

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Tim Wescott 20 years ago

I have gotten into trouble even with that, in the case of a system consisting of two integrators and an adjustable low-pass stage. Anything with three poles on top of each other ended up with a poorly behaved controller (I _think_ it wasn't minimum phase, but I can't remember). I had to go to a pole-placement rule that put one pole closer to z = 1 than the other two, then everything was fine.

The point being that while I could make a pole-placement rule that worked, I had to do it by working backwards from a few example controllers that I reviewed for robustness using other means.

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