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December 18th, 2017, 02:21 PM   #1
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This has me beat...

I have a function which takes an input between 1 and 6, and divides a variable (let's call it Z) by that number. The result is therefore a number between Z/6 and Z.
Z/6 is a result that is 16.6667% of Z, Z is 100% of Z.
What I want to do is linearise the control input so that I can specify a 0 to 83.3333% reduction in the result out of the original function. I cannot change the original function, this needs to be a new function which manipulates the control to the original.
To clarify, I want an input with range 0-83.33, this must control an input with range 1-6 which gives an output of 100% to 16.667% of a variable, Z.
Z is arbitrary.

If it's any easier, the control input can be thought of as a 0-5, I simply add 1 along the way.
I can't figure out how to generate the control signal from my 0-83.3% input, I've been playing with a table in Excel for ages and can't come up with a solution.

Any clues?

Last edited by skipjack; December 18th, 2017 at 03:54 PM.
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December 18th, 2017, 04:05 PM   #2
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Subtract the input value from 1 to give a value from 1/6 to 1, the reciprocal of which is your desired control signal.
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December 18th, 2017, 11:43 PM   #3
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OK, that works
Now to complicate the problem, I'm trying to do it without dividing by variables (vhdl).
The original function is a piece of analogue electronics which can't be changed, really, really annoying right now, lol.
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December 19th, 2017, 02:37 AM   #4
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How accurately do you need to approximate the result?
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December 19th, 2017, 03:49 AM   #5
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I honestly don't know but 0.1% sounds about right. I am looking into doing a reciprocal in vhdl but it's making me cry.
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December 19th, 2017, 05:31 AM   #6
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1/(1 - x) = 1 + x² + x³ + . . . could be used, but you might need dozens of terms.

I also tried 1.0039 + 0.7843x + 1.9062x^2 + 1.1937x^3 - 0.414x^4 - 1.5278x^5 - 0.8095x^6 + 2.9826x^7 + 11.052x^8, which seems to be within 1%, but not 0.1%.
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December 19th, 2017, 09:23 AM   #7
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Good grief! That's quite some numbering there. It's clear there's no easy solution, I shall attempt to weigh up the pro's and con's of this method and doing a proper divide, it could go either way! (tho the divide makes me die a little inside).
Thanks for the insight
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