tuning rules for the controller- how to?

[gary36]

Given the system with open loop TF G(s)= K* ((1+s/z)/(1+s/p))* (1/s^2). How to tune value of k, z and p based on frequency domain specifications (such as bandwidth). Could not find a good resource (even with AI tools)

 

[LvW]

Question: The expression (1/s^2) belongs to the numerator - which means: The denominator is multiplied with s^2 ?

 

[FvM]

First question, which part of the transfer function is representing the controller (compensator), which the plant?

A possible split is type II compensator (lead-lag + integrator) and integrator plant.

Second question, what are your frequency domain specifications?

With freely tunable gain and lead-lag corner frequencies, the transfer function itself doesn't impose a bandwidth limit. It should be noted that this isn't a very realistic control system model, real systems have additional poles or true dead time.

 

[gary36]

it is lead compensator for a double integrator plant. I have represented the open loop transfer function in #1. The question is generic. Given the bandwidth specifications for this system, how to arrive at the value of k, z and p.

 

[FvM]

Bandwidth specification isn't sufficient, phase margin or control error for specific excitation is a typical control quality criterion.

An empirical approach sets lead- and lag-corner frequencies symmetrically below and above intended crossover frequency to achieve maximal phase margin and tunes k to set the frequency.