1. Why is the largest time constant always compensated in the case of pole compensation and not the smallest, for example?

2. Why do you have a good disturbance behavior with a phase reserve of less than 30 degrees and a good reference behavior with greater than that?

 

1. Why is the largest time constant always compensated in the case of pole compensation and not the smallest, for example?

2. Why do you have a good disturbance behavior with a phase reserve of less than 30 degrees and a good reference behavior with greater than that?

Hi,

To answer your first question, in a nutshell the largest time constant is considered the dominant one because it dominates the response. That is, it is the slowest and therefore has the greatest effect on the overall response.

If you look at some real systems you will see that usually the faster stuff is also smaller in amplitude. For example a voltage regulator if you have a slow recovery after a short circuit is relieved you can end up with a pretty large output voltage surge which can ruin the externally connected equipment, and the longer the surge (longer time constant) the more damage it can cause. Compensating for that will help make the regulator design much better.
On the other hand if you have a wild response due to some higher frequency components, then you probably have a bad design to begin with so you'd probably have to start over before you do any compensation.

What you could do is draw up a couple systems each with both slow and fast time constants and look at the time responses. You'll see how the slower responding time constants dominate. The faster ones seem to 'ride' on the slower ones in most systems and are usually of lower amplitude so we concentrate more on the slower ones. If the faster ones dominate then there is a gross error in the design that needs to be corrected first.

Little interesting story. Long time ago i went to the chief engineer and owner of the company with a design idea to help compensate for a then slow responding power converter. He rejected it outright i think because he did not understand the significance of needing such a thing. Some years later a client that used one of our converters for a large computer system had their system power input section blow up because the converter had surged probably more than once. It cost the company a lot of money to fix the clients equipment as well as our own, only to have the same thing happen again!
Some years later we went to a much more robust design which inherently included faster recovery sub cycle responding feedback. The base design was done by yours truly. It also included circuitry for greatly reducing DC current in the output circuit. It was accepted without any argument

 

A fine answer from MrAl.
I like to underline his explanation with an example:
In many feedback systems we have one (or more) local loops and one "outer" overall feedback loop. Now - when discussing stability properties, the question comes up which of the various loops (with different loop gains) must be opened.
(Intuitively, we tend to open the "outer loop)...is this correct?
The answer is Yes - because intentionally the "inner loops" have smaller time constants (and smaller reaction times) if compared with the outer loop (which has the largest time constant). It is the outer (overall) loop with the largest time constant which mostly determines the response of the whole system and which should be analyzed regarding the stability margin.