>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>> module's name: fnc >>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>----------------------------------------------------------------------->
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
fnc: > treatment function >
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>----------------------->----------------------------------------->
> > >
1 > f = g * pow(X1, p1) * pow(X2, p2) * ...
> > >
> ................................................................>
60 >g< > scaling factor
2 >N< > number of pow(X, p) term
>----------------------->----------------------------------------->
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
powxp: > individual function >
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>----------------------->----------------------------------------->
> Note:
> 1. "t" is relative to injection starting time
> 2. this section may be repeated N times if N > 1
>
>----------------------->----------------------------------------->
> > >
> 1 > type 1, sinewave
> > >
> ................................................................>
> X = k + sin(2 * PI *(t/T + alpha))
> ................................................................>
> 1 >p< > power factor for X
> 2 >T< > period, in sec
> 0. >alpha< > phase lead/delay, in fraction of period
> 0 >k< > offset value for the waveform
> ................................................................>
>----------------------->----------------------------------------->
> > >
> 2 > type 2, triangular
> > >
> ................................................................>
> x = alpha + t/T
> x = x - INT(x) # INT(x) is the integer portion of X
> if (x >= 0 && x < 0.5) X = (k2 - k1) * x * 2 + k1;
> if (x >= 0.5 && x < 1.0) X = k2 - (k2 - k1) * (x-0.5) * 2;
> ................................................................>
> 2 >p< > power factor for X
> 4.0 >T< > period, in sec
> 0.5 >alpha< > phase lead/delay, in fraction of period
> -1 >k1< > minimum value of X, -1, or 0
> 1 >k2< > maximum value of X, 0 or 1
>----------------------->----------------------------------------->
> > >
> 3 > type 3, linear ramp
> > >
> ................................................................>
> if (t <= t1) X = k1;
> if (t > t1 && t < t2) X = (k2 - k1) * (t-t1)/(t2-t1) + k1;
> if (x >= t2) X = k2;
> ................................................................>
> 1 >p< > power factor for X
> 0.5 >t1< > time ramp starts, in sec
> 7.5 >t2< > time ramp ends, in sec
> -1 >k1< > starting value of X, -1, 0 or 1
> 1 >k2< > ending value of X, -1, 0 or 1
>----------------------->----------------------------------------->
> > >
> 4 > type 4, square wave
> > >
> ................................................................>
> x = alpha + t/T
> x = x - INT(x) # INT(x) is the integer portion of X
> if (x >= 0 && x < 0.5) X = k2; # positive half comes first
> if (x >= 0.5 && x < 1.0) X = k1;
> ................................................................>
> 1 >p< > power factor for X
> 4 >T< > period, in sec
> 0 >alpha< > phase lead/delay, in fraction of period
> -1 >k1< > minimum value of X, -1, or 0
> 1 >k2< > maximum value of X, 0 or 1
>----------------------->----------------------------------------->
> > >
5 > type 5, exponential function
> > >
> ................................................................>
> X = k1 + k2 * exp((t-t0)*u(t-t0)/tau)
> i.e.
> if (t < t0) X = k1 + k2;
> else X = k1 + k2 * exp((t-t0)/tau)
> ................................................................>
1 >p< > power factor for X
0 >t0< > delay time, in sec
-0.5 >tau< > time constant, in sec
1 >k1< > -1 to 1
-1 >k2< > -1 to 1
>----------------------->----------------------------------------->
5 > type 5, exponential function
> ................................................................>
1 >p< > power factor for X
0 >t0< > delay time, in sec
-0.24 >tau< > time constant, in sec
0 >k1< > -1 to 1
1 >k2< > -1 to 1
>----------------------->----------------------------------------->
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