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I have a strange problem. We have an actuator which was controlled using varying voltage. For example, to achieve setting 1 we measured that the resistance of the coil is 32 Ohms and 2.09 V is supplied. That should see a current of 65.33mA and power of 0.136 W. Now we have to change it to a PWM control with constant 4.5 v supply. But how to calculate the duty cycle. The resistance remains the same. We need the same power. Is there any formula which can be used to calculate the effective current which is needed to drive in this case 0.136W?

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If your frequency is high enough (like period 20 times shorter that actuator's time constant), you can consider your voltage just average: V = Vbus * D. So duty cycle would be D = V / Vbus.

This is based on the fact your actuator is a solenoid with inductance and resistance, making up time constant.

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