I'm trying to find the approximate solution of a system by using polynomials as an ansatz.
Minimize does not seem to be doing its job.
I'm trying to solve a nonlinear system by using its taylor expansion instead.
Trying to find a minimum of an integral over time of RHS*RHS.
(* :: Package :: *)
gs=1;
rs=10.000000000000000;
vte=0.025864186384551461;
csat=1.0000000000000000*10^-014;
cktCKTgmin=9.9999999999999998*10^-013;
hereDIOtBrkdwnV=-0.65509939013317497;
hereDIOtDepCap=0.50000000000000000;
modelDIOjunctionPot=1.0000000000000000;
modelDIOgradingCoeff=0.50000000000000000;
modelDIOtransitTime=9.9999999999999998*10^-013;
modelDIOf2=0.35355339059327379;
hereDIOtF1=0.58578643762690485;
czero=2.0000000000000000*10^-012;
modelDIOf3=0.25000000000000000;
omega=2*Pi*10^6;
(*
t0=0;
h=10^-8;
*)
smoothMax[tx_, tm_, ts_]:=tm + Log[1 + Exp[(tx - tm)*ts]]/ts
smoothMin[tx_, tm_, ts_]:=tm - Log[1 + Exp[(tm - tx)*ts]]/ts
glue[tx_, ts_]:=((Exp[tx*ts] - Exp[-tx*ts])/(Exp[tx*ts] + Exp[-tx*ts] + 1)+1)/2
current[VD_]:=(csat*(Exp[VD/vte] - (1)) + cktCKTgmin*VD)
charge1[VD1_]:=(czero*hereDIOtF1 + czero/modelDIOf2*(modelDIOf3*(VD1 - hereDIOtDepCap)+ (modelDIOgradingCoeff/( modelDIOjunctionPot+ modelDIOjunctionPot))*(VD1*VD1 - hereDIOtDepCap*hereDIOtDepCap)))
charge0[VD0_]:=(modelDIOjunctionPot*czero*(1- Exp[(1 - modelDIOgradingCoeff)*Log[1 - VD0/modelDIOjunctionPot]]) /(1 - modelDIOgradingCoeff))
charge2[x_]:=glue[-(x - hereDIOtDepCap), gs]*charge0[smoothMin[x, hereDIOtDepCap, gs]]+ glue[x - hereDIOtDepCap, gs]*charge1[smoothMax[x, hereDIOtDepCap, gs]]
charge3[current_]:=(modelDIOtransitTime*current)
charge[VD_]:=charge3[current[VD]] + charge2[VD]
chargecurrent[v2_, v2t_]:=(D[charge[v22], v22]/.v22->v2)*v2t
v[t_, omega_]:=Sin[omega*t]/2
rest11[t_, i1_, v1_, v2_, v2t_, omega_, current1_, chargecurrent1_, v_]:=(i1 - (v1 - v2)/rs)^2+ (v - v1)^2+ ((v1 - v2)/rs - current1 - chargecurrent1)^2
i1[t_, t0_, a1_, b1_, c1_, d1_]:=a1+b1*(t-t0) + c1*(t - t0)^2 + d1*(t - t0)^3
v1[t_, t0_, a2_, b2_, c2_, d2_]:=a2+b2*(t-t0) + c2*(t - t0)^2 + d2*(t - t0)^3
v2[t_, t0_, a3_, b3_, c3_, d3_]:=a3+b3*(t-t0) + c3*(t - t0)^2 + d3*(t - t0)^3
v2t[t_, t0_, a3_, b3_, c3_, d3_]:=D[v2[tt, t0, a3, b3, c3, d3], tt]/.tt->t
rest22[t_, t0_, a1_, b1_, c1_, d1_, a2_, b2_, c2_, d2_, a3_, b3_, c3_, d3_, omega_]:=rest11[
t,
i1[t, t0, a1, b1, c1, d1],
v1[t, t0, a2, b2, c2, d2],
v2[t, t0, a3, b3, c3, d3],
v2t[t, t0, a3, b3, c3, d3],
omega,
current[
v2[t, t0, a3, b3, c3, d3]
],
chargecurrent[v2[t, t0, a3, b3, c3, d3], v2t[t, t0, a3, b3, c3, d3]],
v[t, omega]
]
SERIES1[a1_, b1_, c1_, d1_, a2_, b2_, c2_, d2_, a3_, b3_, c3_, d3_, t1_, h_]:=Integrate[
Series[
rest22[t, t1, a1, b1, c1, d1, a2, b2, c2, d2, a3, b3, c3, d3, omega],
{t, t1, 8}],
{t, t1, t1 + h}];
Print["start"];
h=10^-8;
a1=0;
b1=0;
c1=0;
d1=0;
a2=0;
b2=0;
c2=0;
d2=0;
a3=0;
b3=0;
c3=0;
d3=0;
For[t1=0.0, t1 < 10^-5, t1 = t1 + h,
(*
result=FindMinimum[
SERIES1[a1, b11, c11, d11, a2, b21, c21, d21, a3, b31, c31, d31, t1, h]/h,
{{b11, b1}, {c11, c1}, {d11, d1}, {b21, b2}, {c21, c2}, {d21, d2}, {b31, b3}, {c31, c3}, {d31, d3}}
];
*)
result=Minimize[
SERIES1[a1, b11, c11, d11, a2, b21, c21, d21, a3, b31, c31, d31, t1, h]/h,
{b11, c11, d11, b21, c21, d21, b31, c31, d31}
];
Print[result];
b1=Last[result[[2]][[1]]];
c1=Last[result[[2]][[2]]];
d1=Last[result[[2]][[3]]];
b2=Last[result[[2]][[4]]];
c2=Last[result[[2]][[5]]];
d2=Last[result[[2]][[6]]];
b3=Last[result[[2]][[7]]];
c3=Last[result[[2]][[8]]];
d3=Last[result[[2]][[9]]];
(*
Print["t1=", t1];
Print[",a1=", a1, ",b1=", b1, ",c1=", c1, ",d1=", d1];
Print[",a2=", a2, ",b2=", b2, ",c2=", c2, ",d2=", d2];
Print[",a3=", a3, ",b3=", b3, ",c3=", c3, ",d3=", d3];
Plot[i1[t, t1, a1, b1, c1, d1], {t, t1, t1+h}];
*)
a1=a1 + b1*h + c1*h^2 + d1*h^3;
a2=a2 + b2*h + c2*h^2 + d2*h^3;
a3=a3 + b3*h + c3*h^2 + d3*h^3;
];
