Relationship of Relay Tuning Result and Different Forms of PID Controller


Thread Starter


I have to adjust 10 PID loops and done some relay tuning exercises with my S7 program.

I had obtained the Ultimate Gains (Ku) and Ultimate Periods (Pu) of my PID's with relay tuning method.

I would like to know, what is the relationship between my relay tuning results and the Siemens PID parameters. I am using some FB58 and some FB41.

For example one of my relay tuning result for FB58 is:

Ku = 101.86% per deg C

Pu = 120 sec

According to Zeigler-Nichols rule of tuning constants, I get:

Gain = 61.12% per deg C(by 4d/a.pi), Ti = 60 sec (by Pu/2) , Td = 15 sec(by Pu/8)

What are the corresponding parameters for implementation in FB58, if the cycle time of PID is 0.4 sec:

Gain =?, TI =?, TD=?

The official formula of FB58 is as follow.

The step response in the time range is:
LMN_Sum(t) = GAIN*ER(0)[1+(1/TI)*t+D_F*e**(-t/(TD/D_F))]

LMN_Sum(t) is the manipulated variable in automatic mode of the
ER (0) is the step change of the normalized error
GAIN is the controller gain
TI is the integral time
TD is the derivative time
D_F is the derivative factor</pre>
In the FB58, there is a parameter D_F which is quite interesting in this case.

Thank you for your help in advance.