I am working on the temperature control of an electric oven. I had the idea of obtaining the temperature-time curve when the oven is fed with the alternating wave at maximum power (220 V 60 Hz). According to the Ziegler-Nichols tuning method, my curve would be the response of the system (oven) to a "unit step". But here I have a doubt. To control the power, I am using a BT136 triac, which receives a 5 volt PWM wave at its gate. When this 5 volt PWM signal is at 100% duty cycle, could I consider it as a unit step?
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2 Answers
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When the PWM is at 100%, the input to the oven is sinusoidal (220 V AC 60 Hz):
\$A \times \sin(\omega t) = 220V \sqrt2 \times \sin(2 \pi \times 60 Hz) = 311.127 \times \sin(377 t)\$
This cannot be considered as an unit step.
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1\$\begingroup\$ @Velvel The general form would be: Asin(wt), where A is the maximum value and w is the velocity or angular frequency. Since we know that 220 V is a root mean square value, then A=220*sqrt(2)=311.127. Finally, the angular velocity w is equal to 2*pi*f, where f is the frequency in Hertz. Since f=60 Hz, then w=377, approximately. \$\endgroup\$ Jan 31 at 22:29
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If you set a PWM to 100% duty, it will go high and be high forever and will not change until PWM duty is set to something else than 100%.
It is up to you to interpret that as unit step or not. Just like you can think of each edge of PWM signal as unit step or not.
