Re: Optimize pow() function

From	rickman <gnuarm@gmail.com>
Newsgroups	comp.arch.embedded
Subject	Re: Optimize pow() function
Date	2016-09-22 17:44 -0400
Organization	A noiseless patient Spider
Message-ID	<ns1jc0$igt$1@dont-email.me> (permalink)
References	<ns0mo1$7j2$1@dont-email.me> <ns0p5g$ggu$1@dont-email.me> <ns1hbm$c75$1@dont-email.me>

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On 9/22/2016 5:10 PM, pozz wrote:
> Il 22/09/2016 16:17, Don Y ha scritto:
>> On 9/22/2016 6:36 AM, pozz wrote:
>>> I have to convert voltage measure (Volt) into power (Watt).  As you
>>> know, the
>>> physics says I need to square the voltage measure.
>>>
>>> I have to calibrate the mathematical law and I have two points:
>>> 0W -> 0V
>>> <nominal power> -> <voltage at nominal power>
>>>
>>> That could be enough, but we noticed a different relation between volt
>>> and watt
>>> at intermediate points. I, as the software engineer, have to try to
>>> compensate
>>> differences from the theory, without increasing complexity during
>>> calibration.
>>>
>>> My idea is to calibrate the exponent: it is normally 2.00, but I can
>>> calibrate
>>> from 1.00 to 3.00.
>>> In this way, the two old calibration points are the same as before.
>>> So the
>>> exponent (the third calibration measure) can be changed at last.
>>>
>>> The problem is pow() function with double arguments takes a lot of
>>> time to
>>> finish.  Do you suggest a mathematical method to reduce its complexity?
>>>
>>>
>>> uint16_t power_nominal = 1500;   // In Watt
>>> uint16_t volt_nominal;   // Volt measured at nominal power
>>> signed uint8_t exp_corr = -100 to +100;
>>> double exp = 2.00 + exp_corr;
>>>
>>> uint16_t volt = adc_convert(...);  // Actual volt measure
>>> double alpha = (double)power_nominal / pow((double)volt_nominal, exp);
>>> uint32_t watt = alpha * pow((double)volt, exp);
>>>
>>>
>>> alpha can be pre-calculated, because power_nominal, volt_nominal and
>>> exp are
>>> constant (after calibration). The last instruction is the problem.
>>
>> No, the "problem" lies in your transducer/measurement error.
>> The definition of a "watt" (power) doesn't change just because your
>> observations of that APPARENT relationship (V ~ W) "has issues".
>>
>> Perhaps your load's characteristics are changing as a function
>> of operating point.  Or, nonlinearities in your measurement system.
>> Or, ...
>>
>> Ask yourself WHY the exponent needs to be changed.  I suggest you
>> don't have an accurate model of your load and its excitation.
>> Until you do, how will you know that this is the CORRECT means of
>> compensating your model to agree with your observations?
>
>
> I know the problem is in the poor quality of the transducer, but I'm
> only in charge of the software and the hardware engineer can't fix it
> (often the software solves hardware issues).
>
> So I need a more complex law. The quadratic law (one parameter) can be
> calibrated with a single measure (nominal value). The generic power law
> (exponent not exactly equals to 2, two parameters) needs two calibration
> measures and has a nice feature: it's very simple to calibrate in two
> steps.
>
> The input section has an hardware calibration, a simple digital trimmer.
> So the first step is to calculate the power from the measured voltage
> with the following formula:
>   P = Pn / (Vn ^ 2) * (V ^ 2)
> where Pn is the nominal power and Vn is the voltage needed at nominal
> power.  The user increase/decrease the trimmer pot until the correct
> power is displayed.
>
> Second step. Change the power to another value (half of nominal power,
> for example). If the transducer works as in theory, the measured power
> is correct. Otherwise the user increase/decrease the exponent until the
> power displayed is correct. The power is calculated as:
>   P = Pn / (Vn ^ exp) * (V ^ exp)
>
> After the second step, we are sure the first calibration point is yet
> valid, because that formula is correct when V=Vn, even if exp isn't 2.

I think your equation is not written in a clear way.  I think what you 
mean is this...

P = Pn * (V ^ exp) / (Vn ^ exp)

Now the equation makes sense to me.  But that still doesn't mean it will 
give close to correct values anywhere other than the calibration points.

Have you considered...

P = Pn * (V / Vn) ^ exp

Then there are an infinite set of other corrections you could use.  The 
question is which ones are more accurate?

Have you looked at a range of data to see what the correction curve 
needs to be?

-- 

Rick C

Thread

Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-22 15:36 +0200
  Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-22 07:17 -0700
    Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-22 23:10 +0200
      Re: Optimize pow() function rickman <gnuarm@gmail.com> - 2016-09-22 17:31 -0400
        Re: Optimize pow() function lasselangwadtchristensen@gmail.com - 2016-09-22 14:44 -0700
        Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-23 09:03 +0200
          Re: Optimize pow() function Paul Rubin <no.email@nospam.invalid> - 2016-09-23 00:17 -0700
          Re: Optimize pow() function Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2016-09-23 22:45 +0300
      Re: Optimize pow() function rickman <gnuarm@gmail.com> - 2016-09-22 17:44 -0400
        Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-23 09:08 +0200
          Re: Optimize pow() function rickman <gnuarm@gmail.com> - 2016-09-24 01:54 -0400
      Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-22 14:50 -0700
        Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-23 09:23 +0200
          Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-23 00:32 -0700
          Re: Optimize pow() function Evgeny Filatov <e.v.filatov@ieee.org> - 2016-09-23 12:56 +0300
            Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-23 10:41 -0700
          Re: Optimize pow() function Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2016-09-23 21:07 +0200
          Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-23 12:12 -0700
    Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-22 23:12 +0200
      Re: Optimize pow() function Don Y <blockedofcourse@foo.invalid> - 2016-09-22 14:58 -0700
  Re: Optimize pow() function Tim Wescott <tim@seemywebsite.com> - 2016-09-22 10:01 -0500
    Re: Optimize pow() function Jack <jack4747@gmail.com> - 2016-09-22 08:08 -0700
      Re: Optimize pow() function Tim Wescott <seemywebsite@myfooter.really> - 2016-09-22 11:53 -0500
        Re: Optimize pow() function pippo2@disney.com (Jack) - 2016-09-22 21:12 +0200
          Re: Optimize pow() function lasselangwadtchristensen@gmail.com - 2016-09-22 13:12 -0700
          Re: Optimize pow() function Tim Wescott <seemywebsite@myfooter.really> - 2016-09-22 15:51 -0500
    Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-22 23:15 +0200
      Re: Optimize pow() function Tim Wescott <seemywebsite@myfooter.really> - 2016-09-22 17:52 -0500
      Re: Optimize pow() function David Brown <david.brown@hesbynett.no> - 2016-09-23 09:32 +0200
    Re: Optimize pow() function David Brown <david.brown@hesbynett.no> - 2016-09-23 09:28 +0200
      Re: Optimize pow() function Paul Rubin <no.email@nospam.invalid> - 2016-09-23 00:47 -0700
        Re: Optimize pow() function David Brown <david.brown@hesbynett.no> - 2016-09-23 11:05 +0200
        Re: Optimize pow() function Tim Wescott <tim@seemywebsite.com> - 2016-09-23 11:44 -0500
  Re: Optimize pow() function Jack <jack4747@gmail.com> - 2016-09-22 23:15 -0700
    Re: Optimize pow() function Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2016-09-23 20:49 +0200
  Re: Optimize pow() function Richard Damon <Richard@Damon-Family.org> - 2016-09-25 06:50 -0400
    Re: Optimize pow() function Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2016-09-25 16:36 +0300
      Re: Optimize pow() function Chris <xxx.syseng.yyy@gfsys.co.uk> - 2016-09-26 17:30 +0000
        Re: Optimize pow() function Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2016-09-26 21:49 +0300
      Re: Optimize pow() function pozz <pozzugno@gmail.com> - 2016-09-26 23:30 +0200
        Re: Optimize pow() function Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2016-09-27 18:58 +0300
  Re: Optimize pow() function Robert Wessel <robertwessel2@yahoo.com> - 2016-09-26 22:44 -0500

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