Hi Sai,

It depends on which design rule (Modulus optimum or Symmetrical optimum) you use. 

Optimisation of transient response with the strategy:

- try-tuning (evolution strategy)

- simulation (computer aided)

- controller parameter with frequency response

- design rules (modulus optimum or Symmetrical optimum)

The best way is to find out the values using Simulink. also see attachment (.jpeg)

regards

Check the book by Dorf and Bishop.  These formulas are engineering formulas, so they are correct up to 10% error.  

Book Modern Control Systems, 13th Edition

IF you have modeled the system, then compare the transfer function of modeled one with theoretical formula for second order system. Find out how your design parameters are linked to basic second order system parameters and verify the same in practical result.

if your variation in parameters are less you have to just optimize your modelling scheme using simulation technique.

If high variation then practical is right and you have remodel the system

In fact, if there is no coincidence between the theoretical and measured values, then some thing wrong, either in system identification data or in measuring these parameters  

Hi, Sai

I agree with Jobby C Johnson

If the results and data are not agreed.

First of all try to fit a parametric model on your data.

Then through your parametric model you can find rise time ,...

I think your data is noisy.

I suggest you to study "system Identifacation " of Dr,Karrari 's book (faculty of AUT)

Dear Coleg,

Usually practical experiments needs supplemental operations like filtering to obtain similar theoretical evolution. Firstly, try filter real data. But, depending on filter parameters, it is possible that the obtained transfer function to contain filter model.

The formulas present calculating settling time, Tr, etc are very idealististic as they are valid only for a second order system with no zeros.

your experimental setup may have some (extra ) components e.g. filters etc whose model is when included may your system no longer remains second order or may have zeros, which can be a reason for difference between theoritical and measured results.

REGARDS