[DPRG] PWM Frequency and torque
Subject: [DPRG] PWM Frequency and torque
From: Chuck McManis
cmcmanis at mcmanis.com
Date: Tue Feb 27 00:19:36 CST 2007
Its not that complicated. You need to just remember some basic facts:
1) Torgue is proportional to current, more current = more torque.
2) Current is proportional to voltage, more voltage = more current = more
torque
3) Voltage is a function of the driver circuit's frequency bandwidth.
So you're pushing a square wave into a motor, the circuit looks something like:
+\/\/\/++
  
+++  (
V~   ) Effective Motor
+++ C ( Inductance
  )
  
+++
And what you're looking at is a "low pass" filter, where the frequency
determines what the output voltage is across the inductor (aka the motor).
What you get is a resonant circuit where the voltage across the coil is a
function of the duty cycle and frequency of the input and that changes the
motor's torque.
The simplest way to "tune" this circuit is to up the voltage. Basically the
motor's inductance is going limit the voltage ramp and if you can vary the
voltage (or build a chopper but more on that in a second) you can precisely
control the current through the motor and hence its torque.
I'd suggest for home lab users, put your Ammeter (multimeter set to amps)
in series with your motor. Vary the parameters of the circuit (input
voltage, frequency, and duty cycle) and watch how that affects the current
through the motor.
As you've noticed these circuits are not linear in their response to duty
cycle so if you want a motor controller where 10 is 10% and 50 is 50% and
100 is 100% of the motors torque, you need to compute the voltage/current
curve for the resonant circuit and fill in your values from there. what
you'll find is that 1% torque is like 33% duty cycle and the difference
between 75% torque and 100% torque is like 95% and 100% duty cycle.
So the simple answer is, there is no simple answer. You can finesse the
problem by using active feedback.
The simplest form of active feedback is called a chopper circuit. A chopper
is fairly simple in concept. Basically you apply a voltage across the motor
and measure the current through the motor using something like a shunt.
When the current reaches the desired set point you turn off the voltage,
when it drops below your minimum set point you turn on the voltage. What
this does is drive the motor with a PWM voltage wave form that is modulated
by the chopper feed back to provide the desired current. In this way you
can precisely control motor current, and precisely control motor torque.
Further, even as the mechanical load on the motor changes, the torque
output of the motor will remain constant because the chopper circuit will
compensate. I have to believe that there is probably a 50 line program you
could put into one of the 8 bit PICs or AVRs to do exactly this.
Chuck
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