CNC acc/dec look ahead algorithm

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lionliam96
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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?