Curious about some links posted for "Understand PID control"



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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Peter Nachtwey wrote:

Pole-positioning -- blech. I can only make that work if I know ahead of time what pole locations are "safe". I think it was overenthusiastic pole positioning that led to the whole field of robust control.
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Tim Wescott
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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 wrote:

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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Tim Wescott
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I have had a lot of success with pole placement. If you check my equations you will see it is very simple.
Peter Nachtwey
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Peter Nachtwey wrote:

Hey Jerry -- could you toss a block diagram or two in there? I'm not sure I'm visualizing the two loops well enough.
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Tim Wescott
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Tim Wescott wrote:
...

+<<<<<<-bounds circuit-<<<<<<-+ | | || || || || | Command->| - |->|integral|->| - |->|power amp|->+->>> actuator |_____| |________| |_____| |_________| | | | | | +<<<<<<<-Kd-<<<<<<-+ | | +<<<<<<<<<<<<<<<-Kp-<<<<<<<<<<<<<<<<<<<-+
Kp is the proportional gain term. Kd is the derivative term. We could use a real differentiator fed back to the input, but bypassing the integrator has the same effect. Not needing to perform a real differentiation is a distinct advantage with digital implementations.
The bound circuit in an analog circuit is a pair of resistors and a diode for each of the positive and negative bounds. For digital implementations, it is even simpler. The integrator (which has become a summer) is adjusted to prevent the power amp's output from exceeding it's assigned limits. The limit can be motor current, available supply voltage, allowed acceleration, and even all of those.
There are other ways to analyze the loop(s), but they lead to the same equations.
Jerry
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