PID regulator parameters for a known process

[Pero2912]

Hello guys,

I'm beginner in automatics and could use your advice.
So, I'm designing a PID regulator for oven and right now I'm trying to tune the Kp, Ki and Kd parameters. The oven has nice step response that gets easily approximated by the PT1 system with the dead time delay.


The system to which oven corresponds is :
\[\frac{1.1 }{420s+1 }\cdot\exp(-150s)\]

When I try to design PID components I use Ziegler Nichols Method which turns out to be bad. I use step response where rising time is 420sec, delay time 150s and K=1.1. The PID coefficients I get are somewhere around Kp = 2, Ki = 0 and Kd = 225. Happily I tried to simulate the closed loop and got -- disaster. What am I doing wrong? What is going bad with calculation? How would you tune this PID?

 

[D.A.(Tony)Stewart]

Looks like your system shut down at output = 100

When I measure rise time, and assume 1st order response, I put the intercept thru the 60% of full scale just like RC time constant, then best fit towards 0. This gives me Tr=650 ms instead of 420 , thus for Td=150 ms Xo=100? Mu=120?
**broken link removed**
Ko=100/120*650/150=3.6

How did you get Ki and Kd?

**broken link removed**

 

[Pero2912]

Hey thanks for answer.
First, system shuts down at 100°C, because I turn down the oven. I didn't want to cause any damage, nor wait too long.
Second, time is in seconds, not milliseconds.
Once you I the 60% of the full scale, and the best fit towards zero and than subtract delay time, that is 150s, what makes Tr 420 as mentioned earlier. Then, from your table I find Ti and Td, and from parallel model we have Ki = Kc/Ti, and Kd = Kc*Td. And it didn't work.