PID tuning with delay - strange graph

Hello, I have GUI made in App Designer where are some PID tuning methods. I use simulink model via below and when plotting "actuating variable" I recieve a strange graph - its not smooth and I don't know why.

Simulink model:

Result of Scope - graf regulace1 (red marked on previous picture) of "actuating variable" for model (1/(6*s + 1))*exp(-1s) - using Cohen-Coon method which is working fine:

I have no idea what causes this problem.. I would be grateful for any help with this issue.

[Milan Hrstka]

@Sam Chak I have you in my mind, you already helped me once :D. Please don't you know where the problem is?

[Sam Chak]

@Milan Hrstka, Can you share the Simulink file?

[Milan Hrstka]

@Sam Chak There it is but It takes parameters from App Designer GUI, so there are variables.

[Milan Hrstka]

@Sam Chak Did you find out something? :/

[Stefanos Charkoutsis]

This is a very late response to things and possibly you already figured it out, but for future people looking into this. I was studying delay systems today and I came across a case where if there is a crossing in the phase of the system with the 180 degrees line (looking at frequency response bode phase) then it generates these bumps in the time response.

Please check this MATLAB link i am refering to: https://uk.mathworks.com/help/control/ug/assessing-gain-and-phase-margins.html

I believe that the cohen-coon method of tuning your controller is perfectly fine for finding fast response, but if you need better methods here is a very interesting paper from 2003 that compares some basi tuning methods for such delay systems:

“ PID Tuning Rules for First Order plus Time Delay System” by [Authors: Diwakar T. Korsane1 , Vivek Yadav2 , Kiran H. Raut3]

I really hope this helps someone. Also, it may not be exactly the answer, unfortunately i do not have the simulink files to test the theory and my MATLAB version is not compatible with the file provided, but it seems to be something that needs checking out.

Kind Regards

Stefanos