Re: ScanTesla program -> Optimization

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:
> Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>

> Wow Cool!!  You know far far more than me at this point!!  I find I have 
> forgotten most of the mesh equation and complex number stuff over the 
> years.  I will press on just to refresh my knowledge there in any case.
> Jim also strongly suggested this "matrix stuff" too so it is probably a 
> "real good idea" ;-))  As far as I can tell, the C language has all the 
> function built in and ready to play.
> The step function and input square wave (Fourier series) should be about 
> 10000X faster to compute than a pure say 10-nS stepwise number grinder.
> For the linear time-invariant case, that is the way to go.  Program like 
> MathCad can also reduce the equations to run faster.  But the equation are 
> not super bad.

Hummm. Complex analysis is for steady state solutions, even with Fourier
series to represent a square wave input. You need a time-domain solution, 
that requires only real computations, to find the solution
with the transient, and with arbitrary input waveform.
What I am doing is (identical to what I have implemented in the sstcd
program):
Formulate a set of state equations with the form:
dX/dt = [A]X(t)+B*vin(t)
where X is a vector with 5 elements (Vc1,Vc2,Vc2,Il1,Il2), [A] is a
5x5 real matrix, and B is a vector with 5 elements. This is quite easy.
Solve it by numerical integration with the trapezoidal rule:
X(t0+dt)=X(t0)+(dt/2)*([A]*X(t0)+B*vin(t0)+[A]*X(t0+dt)+B*vin(t0+dt))
where t0 is the present time, dt is a small time interval ahead, X(t0)
is the present state, and X(t0+dt) is the next state.
The required calculation is:
X(t0+dt)=[[I]-(dt/2)*[A]]^(-1)*(dt/2)*([A]*X(t0)+B*(vin(t0)+vin(t0+dt)))
The matrix inversion has to be done just once.
This results in good precision if you put about 50 "dt" for each cycle.
If I find time I will make a starting code with these calculations
available soon.

Antonio Carlos M. de Queiroz