Anti-lock braking systems...

[Ed Carryer]

>PWM
>How does one determine the optimum freq. for pwm.  Common sense (as
>opposed to theory) tells me that I would want the period of the pwm less
>than the time constant (T.C.) of the mechanical devive.

David,
I can't claim to be an expert,
but here's how I would approach the problem:

When using PWM to achieve intermediate levels of an output,
you are using the time constant of the driven device to
smooth (filter) the PWM input into something that resembles
a constant level at an intermediate value.
So why not approach it as a filter design problem ?
Ask yourself
'how much ripple due to the PWM drive signal can I tolerate in my output ?'
Given that, you can calculate the attenuation that the filter
(your mechanical system) will need to provide. If you know the time constant
of the system, you can figure out what the minimum drive frequency
should be to have no more than X amount of ripple.

For the upper frequency limit, you need to know something about
the effective 'inductance' of the device being driven. Here you are trying
to determine how long a signal must be applied to the input before
the output responds. For example:
If your friend who chose 20kHz as a drive frequency was driving a
highly inductive load, they would probably
not be very happy with the result. Implicit in the assumption of a linear
relationship between Duty Cycle (DC) and output is that the time for
the output to respond is very short relative to the peroid of the
drive signal. When this is not true (as it would not be if the period
of the PWM was similar to the rise time of the current in an inductor),
you do not get what you expect. i.e. 100% ouput is not the maximum
that the device is capable of.

To demonstrate this to my students, I hook up a signal generator
to a motor driver and drive a small DC motor. I set the duty cycle
of the generator's output to 50% and leave it there. Then I sweep the
frequency from very low ~1Hz up to 20kHz. What happens is this;
1) at very low F, the motor pulses, moving very quickly, many revs,in jerks
2) at moderate F, the motor smooths out somewhat
3) at a little higher F, the motor smooths out pretty much completely
(at the last two steps the motor speed was essentially constant)
4) at still higher F, the motor begins to slow down. This is due to the
inability to build full current in the motor windings and therefore
the average current falls, even though the duty cycle remains constant.

Operating anywhere between stages 3 & 4 will get you what you want.

I hope this helps
ed
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