Thanks gain for the details to face the problem I have experienced with my commuted circuit. In trying to make my DutyCycle a periodic function I have found a related discussion Periodic piecewise function where periodicity is achieved by the use of the function Mod. One has to be cautious with suggestions given there.

Regards Jesus Rico

Thanks. The option Trace Internal is not listed in the documentation, although it does show up when you do Options[Trace].

Frank,

I basically used Trace[NDSolve[Eqns1, {iL[t], vc[t]}, {t, 0, nc Ts}], TraceInternal -> True].

This can be helpful, tool: http://mathematica.stackexchange.com/questions/29339/the-clearest-way-to-represent-mathematicas-evaluation-sequence/29340#29340

The basic structure of the computation carried out by NDSolve is described in http://reference.wolfram.com/language/tutorial/NDSolveStateData.html. It helps me know where to look.

Part of the issue is that the problem is initialized wrong by NDSolve. Let sol[1] be one solution (the wrong one) and sol[2] be the other (the almost correct one). This is evident in the solutions themselves. The following pairs are the two sides of the equations passed to NDSolve at t == 0; they should be the same, but the derivatives are different. The LHS is wrong for both.

Eqns1 /. Equal -> List /. {iL[t] -> 3, vc[t] -> 30, t -> 0} /. sol[1]
Eqns1 /. Equal -> List /. {iL[t] -> 3, vc[t] -> 30, t -> 0} /. sol[2]
(*
  {{{79985., -74015.}, {-15000., 0.}, {3., 3}, {30., 30}}}
  {{{79985., -74015.}, {-15000., 0.}, {3., 3}, {30., 30}}}
*)

In the second solution, the derivatives are corrected at the first step.

iL'[Take[iL["Grid"] /. First@sol[1], 5]] /. First@sol[1]
iL'[Take[iL["Grid"] /. First@sol[2], 5]] /. First@sol[2]
(*
  {{79985.}, {79985.}, {79985.}, {79981.7}, {79978.5}}
  {{79985.}, {-74015.}, {-74015.}, {-74014.5}, {-74013.6}}
*)

But I cannot say why NDSolve is not deterministic, that is, why it does solves the system two different ways (seemingly at random).

The problem is that the condition 0 <= Mod[t, 1/10000] <= 0.000025 is translated to

Sign@Max[(-1 + NDSolve`CountableCrossingValue[t/Ts])/20000 - 
   t, -0.000025` + (1 - NDSolve`CountableCrossingValue[t/Ts])/20000 + t] < 0

This agrees with 0 <= Mod[t, 1/10000] <= 0.000025 except at t == 0 (and multiples of Ts). So that is the source of the error at the initial value at t == 0. That seems to be a bug.

Using PiecewiseExpand to convert If to Piecewise fixes it. (It has had been mentioned that NDSolve deals with Piecewise more readily than programming constructs like If.) For instance:

Eqns1 = {iL'[t] == PiecewiseExpand[-((Rs (1 - st1) + (Rd st1))/L) iL[t] - 
      st1/L vc[t] + (E1 - (st1 Vf))/L, Assumptions -> 0 <= t <= nc Ts],
   vc'[t] == PiecewiseExpand[st1/C1 iL[t] - 1/(R C1) vc[t], 
     Assumptions -> 0 <= t <= nc Ts],
   iL[0] == iL0, vc[0] == vc0} /. {R -> 10, L -> 0.2 10^-3, 
   C1 -> 0.2 10^-3}

An alternative, more interesting as a check on the analysis above than as a workaround, is to integrated from a small value near zero instead of zero:

NDSolve[Eqns1, {vc, IL}, {t, 1*^-10, nc Ts}]

Either of these approaches produces a consistent result.

Hi Frank,

you are quite right. $Mod$ also seems to cause problems. As you say:

DutyCycle[d_, Ts_, t_] := Piecewise[{{1, 0 <= Mod[t, Ts] <= d Ts}}];

does not seem to work. And

DutyCycle[d_, Ts_, t_] := Ceiling[-(Mod[t, Ts] - Ts d)]

does not work either. So there is a problem with $Mod$. But

DutyCycle[d_, Ts_, t_] := HeavisideTheta[Sin[2 Pi/Ts*t + Pi*d] - Sin[Pi*d]];

and

DutyCycle[d_, Ts_, t_] := If[Sin[2 Pi/Ts*t + Pi*d] - Sin[Pi*d] > 0, 1, 0];

do work; in spite of the latter having the "If". Curiously enough,

DutyCycle[d_, Ts_, t_] := HeavisideTheta[SawtoothWave[t/Ts - d] - (1 - d)];

does not work. In the following case, however, there is no $Mod$ and things still go wrong:

DutyCycle[d_, Ts_, t_] := If[IntervalMemberQ[IntervalUnion @@ Table[Interval[{k Ts, Ts d + k Ts}], {k, 0, 4}], t], 1, 0]; 

This last one, I couldn't even make work with Piecewise, i.e.

DutyCycle[d_, Ts_, t_] := Piecewise[{{1, IntervalMemberQ[IntervalUnion @@ Table[Interval[{k Ts, Ts d + k Ts}], {k, 0, 4}], t]}}];

does not work either.

DutyCycle[d_, Ts_, t_] := Evaluate[Piecewise[Flatten[Table[{{1, (k - 1) Ts < t < (k + Td) Ts}, {0, (k + Td) Ts < t < (k + 1) Ts}}, {k, -2,3} ], 1]]];

does work, but

DutyCycle[d_, Ts_, t_] := Piecewise[Flatten[Table[{{If[Evaluate[0 < Mod[t, Ts] < d Ts], 1, 0], (k - 1) Ts < t < (k + d) Ts}, { If[Evaluate[0 < Mod[t, Ts] < d Ts], 1, 0], (k + d) Ts < t < (k + 1) Ts}}, {k, -2, 3} ], 1]];

does not - making the case against $Mod$ even stronger.

If I have not made a mistake, all of these functions should be identical in the interval of interest, say from $0$ to $nc Ts$, which you can test by running

Plot[{DutyCycle[Td, Ts, t]}, {t, -nc Ts, 2 nc Ts}]

--- some work some don't.

Cheers,

Marco

PS: I had some other examples of writing this function, but unfortunately, the session died on me when I wanted to post.

...but not on my system :-)

When you went to the Piecewise function, you also got rid of the Mod function inside. Recently I was using CompilePrint to look at a compiled Piecewise function and an equivalent If statement and they looked the same. Could the Mod be the problem?

Marco, Excellent demonstration, big thanks!. I will use the suggested definition as the basis for my periodic DutyCycle function. Also, the solution you have obtained coincides with my semi analytical one.

Best regards Jesus Rico

Jesus, What operating system and what version of Mathematica are you using? That info may help understand the problem since Hans doesn't see it. Hans, same question to you.

I did 8 plots, and they were all the same (Mathematica Version 7) Regards H. Dolhaine