When optimizing simple PID controllers, usually stability criteria like the amplitude reserve and phase reserve are applied to the transfer function of the open loop to assure stability of the closed loop. In my understanding, the goal of these considerations is to avoid high values (significantly above 0dB) in the closed loop transfer function. However, this could also be achieved by calculating the closed loop transfer function directly and trying to optimize its values.
In some cases, there can even be maxima in the closed loop transfer function where there is neither an amplitude value of 0dB nor a phase value of 180°. These go generally unnoticed when only the mentioned stability criteria are used.
So my question is: Is there any particular reason, that one should not just optimize the closed loop transfer function and disregard the open loop?
Thank you for your answer! You are right, I did mean gain and phase margins, that was a misnomer from my side.
I am not sure if we understand each other correctly here, I should have elaborated further on the boundary conditions that I am considering, I apologize for that.
I am considering the case, that we only have the open loop transfer function as a measurement, not in strict mathematical form. The transfer function is also not a simple case, since it has several local minima and maxima, so it is not easy to derive a strict mathematical form either. In this case, the optimization of PID parameters will be based a bit more on trial and error and looking at the effective values than in most other cases. This can of course be done in the open loop, I totally agree. This is also what I have done thus far.
To be quite frank, I simply do not see the reason to look at the open loop values if we can just calculate the closed loop transfer function and get all the important information directly. With Gcl=Gol/(1+Gol), one can calculate the closed loop gain from the measurement and the properties of the PID-controller (Gcl=closed loop gain; Gol= open loop gain). From this calculation, one can see directly if there are poles in the closed loop, by looking at the closed loop gain. One can also see if there are small maxima that might lead to unwanted oscillations etc..
I guess my question would be if you would think that this approach leads to similar results as an optimization of the open loop, or if I have overlooked something. Thank you again for your answer!
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