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How can I compute new pid coeff from old ones based on #147

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@JulienDevillers

Hello

I'm driving the pwm of an electric motor with a pid controler.
It works pretty well.

After some testings, I realized that the fact that the motor is powered by a battery
makes the system behave differently depending on the battery voltage.

I will change the system in order to make the pid system control the voltage provided to the motor instead of the pwm ; another
system will do the conversion V -> PWM based on the battery voltage.
Therefore, I expect the same behaviour whatever the battery voltage (if of course, the pid does not ask for a voltage
more than battery voltage)

Concretely, PID will not control values from 0 to 20k (pwm period) but 0 to 8400 (mV).

My question is:
Is there a mathematical way to compute the new PID coefficients from the old ones to get the same behaviour with the
new actuator without having to go again to a new pid tuning session?

Thanks.

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