Dear Carmine Melillo

In general, raising the Proportional Gain will speed up the control system's reaction and reduce the steady-state error, which is the ultimate difference between the Process variable and the Set Point. However, if the Proportional Gain is set to a value that is too high, the Process Variable will begin to oscillate.

Manual tuning is accomplished by raising the gain until the loop oscillates at a constant amplitude and setting the reset time to its maximum value and the rate to zero. (A greater gain can be employed when the reaction to an error correction happens fast. If the reaction is sluggish, a slight increase is preferable).

System identification use statistical approaches to construct mathematical models of dynamical systems from measurable data. The optimal design of experiments for efficiently generating informative data for fitting such models, as well as model reduction, are also part of system identification.

Look here for more examples: https://www.mathworks.com/help/control/getstart/system-identification-of-plant-models.html

Best Regards

Dr. Fatemeh Khozaei

Thanks for your help Dr. Khozaei.

Dear Camine Mellilo,

Also i suggest you to see links on topic.

http://www.ece.northwestern.edu/local-apps/matlabhelp/toolbox/ident/ch1sip15.html

https://www.sciencedirect.com/science/article/abs/pii/S1468121808000047

https://link.springer.com/article/10.1007/s13272-021-00499-6

Best regards

A step signal is applied to the original system and with the I / O data collected in a file, the Identification Tool from Matlab can be used to approximate the transfer function. Then the PID Regulator can be granted.