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[DPRG] Processing unit for mobile robot
Subject: [DPRG] Processing unit for mobile robot
From: Randy M. Dumse
rmd at newmicros.com
Date: Fri Apr 25 15:32:25 CDT 2008
Eric Sumner said: Friday, April 25, 2008 10:37 AM
> If you have an unstable sampling period,
> you can't do that. So long as the sampling rate is fast
> enough, this formulation should produce the same results
> regardless of the sampling rate for any set of gains.
I'm not sure I can follow your point, but I suspect you are
dismissing mine.
The need to ease the gain on the K term is because of Delta-t
isn't dt. That is, Delta-t being finite in size means how often
we run determines how close the discrete value is to the
calculus value and so the shorter the time, the closer to
theoretical value.
As an example, let's say we get the a response where we run the
routine twice in a period and where we run it three times.
Let's say the error goes up linearly with time. So if we
calculate twice in 3mS, we have a Yp term based on 0 until 1.5mS
and and 1.5 until 3mS. If we do it three times, we get a Yp of 0
until 1, 1 until 2 and 2 until 3. So the Yp output average over
those 3mS will be 1.5/2 if we do it twice, and will be 3/3 if we
do it three times. Therefore a single Kp gain will not give the
correct output for irregular periods.
Or at least that's how it looks to me so far. I haven't studied
this officially, this is just my thinking on the subject over
the last week when the idea first occurred to me about why the
irregular update would cause problems.
Do you know the offical engineering text answer?
Randy
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