CNC acc/dec look ahead algorithm

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The discussion revolves around implementing an acceleration/deceleration look ahead algorithm for a CNC controller in C#/F#. The main confusion lies in understanding the role of Ts, the sample period, in relation to the interpolation periods and the acceleration/constant/deceleration regions. The original poster seeks clarification on whether Ts represents the duration of these interpolation periods or something else, as the referenced white paper does not provide clear definitions. They have already formulated some equations in F# but are uncertain about how to proceed with Ts. The conversation emphasizes the need for precise definitions in algorithm implementation for effective CNC control.
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Homework Statement


I`m having some trouble with an acceleration/deceleration look ahead algorithm I`m trying to implement in a CNC controller written in C#/F#, specifically the algorithms treatment of time.

Homework Equations


The white paper can be found at:
https://www.researchgate.net/publication/258401146_Look-Ahead_Algorithm_with_Whole_S-Curve_Acceleration_and_Deceleration
Page 2 describes T as the interpolation periods and Ts as the sample period. T1, T5, max acc/dec and max jerk are prespecified so I`m guessing I`m supposed to figure out the duration of the other interpolation periods. If that`s the case, than what does Ts represent exactly?? Duration of the interpolation periods? Duration of the acc/const/dec regions? The paper doesn`t say...

The Attempt at a Solution


I`ve written out all the equations in f#, I just have no idea what Ts is supposed to be?

Code: 
// Number of interpolation periods in acceleration region (Na):
let calcNa (Vs : double, Vm : double, Ts : double) : double =
Math.Round(Math.Sqrt(Vm - Vs / (1.0 + K) * J1 * Math.Exp(Ts)) + 1.0)

Thanks,
Liam
 
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lionliam96 said:
Ts as the sample period
"Sample period" is the length of time you're sampling?
 

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