encoders measurements in speed control loop

On Wed, 18 Feb 2015 20:38:24 +0800, Bruce Varley wrote:

> On Tue, 17 Feb 2015 13:03:50 -0600, Tim Wescott
> <seemywebsite@myfooter.really> wrote:
> 
>>On Tue, 17 Feb 2015 20:14:02 +0800, Bruce Varley wrote:
>>
>>> On 16 Feb 2015 09:22:17 GMT, al.basili@gmail.com (alb) wrote:
>>> 
>>>>Hi everyone,
>>>>
>>>>I have to control a sinusoidal BLDC through a PWM and an H-bridge,
>>>>following a profile written in a table.
>>>>
>>>> I have encoders reading as feedback but I have not quite well
>>>>understood how to measure the difference between the position table
>>>>and the encoders reading.
>>>>
>>>>In general if the encoder reading is in the same turn as the table
>>>>than everything is fine:
>>>>
>>>>p = 78 deg (position)
>>>>m = 75 deg (measure)
>>>>
>>>>e = p - m = 3 deg
>>>>
>>>>But when I cross the 0 deg (360 deg) I have some stupid issues with
>>>>signs:
>>>>
>>>>p = 359 deg m = 1   deg
>>>>
>>>>e = p - m = 358 deg
>>>>
>>>>while I would like to get -2 deg!
>>>>Even with modulo function I'd not be better off:
>>>>
>>>>e = mod(p - m, 360) = 358 deg!
>>>>
>>>>Should it be dependent on the quadrant I'm in?
>>>>
>>>>I'm missing some basics here. And yes, a pointer to elementary school
>>>>math is definitely appreciated!
>>>>
>>>>Al
>>> 
>>> Have just solved this very problem for filtering the signal from a
>>> wind indicator that sends an analog signal of 0 - 360 degrees. In
>>> order to remove the discontinuity, you need to determine when it's
>>> crossed, and in which direction, this requires a suitably fast
>>> scanning rate. Say then that the direction goes 355-358-2, then you
>>> know that the angle has 'increased'. So add 360 to get 362 degrees.
>>> You can then apply a modulo function to get 2. Going the other way,
>>> eg. 5-2-357, subtract 360 to get -3. The operation is fully
>>> symmetrical in each direction.  You extend the range of the angle to
>>> +/- infinity, then use modulus to bring it back to a real range.
>>> 
>>> If the rotation is always one way and the extended angle value is
>>> likely to get very large in one direction, you need to do a reset when
>>> it goes above a trigger value.
>>> 
>>> You can also deal with this using coss and sins and their inverses,
>>> but that's rather inelegant IMO.
>>
>>Yes, encoders can be an excellent way to measure motor speed, but only
>>if you can insure that you sample the encoder position faster than twice
>>per revolution.
> 
> Hey, that's a nice visualisation of Shannons theorem (I think).

I think it has some relation to Shannon's sampling theorem on more than a 
superficial level -- but I'm not sure what it is.  I don't think it's a 
1:1 correspondence.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com