I want to control the temperature of an electric oven. To do this, I must find its mathematical model, or transfer function.

To control the temperature of the oven I use PWM, which goes into a circuit with optocoupler and TRIAC. In this way, the input voltage to the resistors has the following waveform:

enter image description here

On the other hand, I have a temperature vs. time curve with the PWM at maximum power (100%).

enter image description here

With this curve I can identify the model using the ident or procest (MATLAB) commands. When the PWM is at 100%, the input voltage to the resistors is 220 V AC and 60 Hz; so, the input is 311.127 × sin(377t)

Can this input be considered equivalent to its root mean square voltage, that is, to 220 V in direct current? It seems so to me, due to how high the frequency is (60 Hz).

If I consider the input waves as DC signals, it would be easier to simulate and tune a PID control.

  • \$\begingroup\$ what kind of oven? \$\endgroup\$
    – jsotola
    Feb 13 at 4:09
  • \$\begingroup\$ As the "time constant" is vey long, you should use, at start on, "anticipative" control. Some delay is also present, about 200 s (?). \$\endgroup\$
    – Antonio51
    Feb 13 at 10:07
  • 1
    \$\begingroup\$ What are the units for the graph timebase? \$\endgroup\$
    – Andy aka
    Feb 13 at 10:37

1 Answer 1


The RMS value of any voltage waveform is equal to the magnitude of a DC voltage that produces the same amount of heat in a resistor. Indeed, the RMS function was created to do just that. Therefore, the answer to your question is yes. If you want to apply it to your PWM waveform you will have to calculate its RMS value as a function of the conduction angle.


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