Hello Ali;

Basically, auto-tuner (self-tuner) algorithms in S7 CPUs work with estimation of a process with step changes, a form of recursive numerical optimization calculation.

When you encounter an implementation of the self-tuner functions, you must provide parameters that determine the initial values of the gains for the process (this will be the estimation) and the size of the step change that will be used for optimization.Then the tuner runs a loop ca;lculation, verifies if the process response is better, stes new calculation parameters and tries them again until the correct response if found.

Note that the specific implementation will be different depending on the specific software you use for autotune, the programming software version, the PLC family you are working with and the specific function of self-tune you choose. 

See the following discussion with useful information and links provided by hdhosseini:

https://support.industry.siemens.com/tf//ww/en/posts/auto-tuning-pid-algorithm-in-s7-300/112080/?page=0&pageSize=10

The screenshot below is taken form the PID Self-tuner v5 manual:

https://support.industry.siemens.com/cs/ww/en/view/1939235

Hope this helps,

Daniel Chartier

Dear Daniel

Thank you very much for the answer. 

do you have more information on the optimization and identification problem in auto tuning (for example TUN-ES)

I like to know what is the cost function for optimization and the system identification.

Best Regards

Ali Namadchian