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I have to determinate the power (Watts) for an oven to reach the Temperature Reference. And I have been given only the function to apply power to the oven and read the temperature.

I've reading the Ziegler-Nichols method. And the first step is to obtain the tangent in the inflection point, and then check the values of:

  1. L : The point where the tangent intersect the x axis
  2. T : The point where the tangent intersect the reference line

But I do not understand one thing, the range of the power I can apply power from 0 to 10,000(W).

Do I have to calc this tangent for a static random Power? But which value, because it will be the same in "production mode", when the power is vary because of the controller?

Calculation of L & T for Ziegler-Nichols PID method

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There are two answers here. First answer is the theoretical one. It doesn't matter what static power you apply. You could apply any number. The reason is that the plot of y(t) that you end up drawing will be normalized to an input of 1.

In other words, compare slides 12 and 13 in this presentation

PID control - Simple tuning methods

If you apply an input power of 1, then the output plot you get gives you the value $K_p$ (you called it just K in your plot above). But if you input a power of $\Delta$u, then the output plot gives you the value $\Delta$u$K_p$. So to find the true value of $K_p$ you will divide by whatever power you input.

Second answer is the practical one. In reality you will never measure your parameters perfectly. There will always be some error or noise in the measurement. If you use a step of 1W on a 10,000W oven, you aren't going to get a very good measurement. So higher power will always be a better measurement. But, on the other hand, if you are unfamiliar with this system, you might not want to try full power right away. You might want to have a reasonable idea of the open loop system behavior before going to full power. If it were me, I would probably start by doing a 1000W (i.e. 10% full scale) step, making sure that I understood how the system was behaving and that I liked the answer. Then I would work up to full power in a few steps. I would take the final Z-N parameters from a run at full power.

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