public void NoRoot()
{
Func <double, double> f1 = x => x * x + 4;
Assert.Throws <NonConvergenceException>(() => Brent.FindRoot(f1, -5, 5, 1e-14, 50));
}
private MaxtorqueCapabilityCurve buildMaxtorqueCapabilityCurve(int count = 50, double Imax = 55, double Umax = 140, double max_speed = 6000)
{
var mtpa = buildTableMaxtorquePerAmple();
MaxtorqueCapabilityCurve mtcc = new MaxtorqueCapabilityCurve()
{
Imax = Imax,
Umax = Umax,
MaxSpeed = max_speed,
};
// Look for beta to get max torque
double max_t = mtpa.GetMaxTorqueWithCurrentMagnitude(Imax);
Fdq idq = mtpa.GetCurrentForTorque(max_t);
// Create PointPairList
// look for speed1
var speed1 = Brent.FindRoot(s =>
{
var data_ = calculatePointdata(idq.d, idq.q, s);
var u_ = Math.Sqrt(data_.ud * data_.ud + data_.uq * data_.uq);
return(u_ - Umax);
}, 100, max_speed, 1e-3);
// speed by speed
int count1 = (int)(speed1 / max_speed * count) + 1;
int count2 = count - count1;
for (int i = 1; i < count1 + 1; i++)
{
double speed = speed1 * i / count1;
var data = calculatePointdata(idq.d, idq.q, speed);
mtcc.speeds.Add(speed);
mtcc.maxtorques.Add(data.torque);
mtcc.currents.Add(idq);
mtcc.voltages.Add(new Fdq()
{
d = data.ud, q = data.uq
});
mtcc.power.Add(data.power);
mtcc.effs.Add(data.efficiency);
}
double t = max_t;
for (int i = 1; i < count2 + 1; i++)
{
double speed = speed1 + (max_speed - speed1) * i / count2;
// find beta which make U=Umax
//double beta = 0;
//bool success = Brent.TryFindRoot(b =>
//{
// var data_ = calculatePointdata(Imax * Math.Cos(b * Math.PI / 180), Imax * Math.Sin(b * Math.PI / 180), speed);
// var u_ = Math.Sqrt(data_.ud * data_.ud + data_.uq * data_.uq);
// return u_ - Umax;
//}, 100, 180, 1e-5, 100, out beta);
// Here:
// Find Id,Iq that bring max torque at speed
// it is intersect of circle Imax and ellipse Umax/w if Imax < ellipse center (-psiM/Ld)
// or ellipse center itself if Imax > ellipse center
Fdq idq2 = default(Fdq);
bool found = false;
var vle = buildVoltageLimitEllipse(speed, 1000, Imax, Umax);
var maxtorque_point = vle.curve[vle.maxtorque_point];
var minid_point = vle.curve[vle.minid_point];
if (maxtorque_point.Magnitude <= Imax)
{
idq2 = new Fdq {
d = maxtorque_point.d, q = maxtorque_point.q
};
found = true;
}
else if (minid_point.Magnitude > Imax) //Imax out of ellipse
{
found = false;
}
else
{
var range = Enumerable.Range(0, vle.maxtorque_point);
LinearSpline spline = LinearSpline.Interpolate(range.Select(k => vle.curve[k].Magnitude), range.Select(k => vle.curve[k].d));
double id = spline.Interpolate(Imax);
double iq = Math.Sqrt(Imax * Imax - id * id);
idq2 = new Fdq {
d = id, q = iq
};
found = true;
}
if (found)
{
//double id = idq2.d;//Imax * Math.Cos(beta * Math.PI / 180);
//double iq = idq2.q;//Imax * Math.Sin(beta * Math.PI / 180);
var data = calculatePointdata(idq2.d, idq2.q, speed);
mtcc.speeds.Add(speed);
mtcc.maxtorques.Add(data.torque);
mtcc.currents.Add(idq2);
mtcc.voltages.Add(new Fdq()
{
d = data.ud, q = data.uq
});
mtcc.power.Add(data.power);
mtcc.effs.Add(data.efficiency);
}
}
return(mtcc);
}
/// <summary>
/// Compute the time duration for a <see cref="EbisuModel"/> to decay to
/// a given percentile.
/// </summary>
/// <param name="model">Given model for the fact.</param>
/// <param name="percentile">Target percentile for the decay.</param>
/// <param name="coarse">If true, use an approximation for the duration returned.</param>
/// <param name="tolerance">Allowed tolerance for the duration.</param>
/// <returns>Duration in time units (of provided model) for the decay to given percentile.</returns>
private static double ModelToPercentileDecay(
this EbisuModel model,
double percentile,
bool coarse,
double tolerance)
{
if (percentile < 0 || percentile > 1)
{
throw new ArgumentException(
"Percentiles must be between (0, 1) exclusive",
nameof(percentile));
}
double alpha = model.Alpha;
double beta = model.Beta;
double t0 = model.Time;
double logBab = BetaLn(alpha, beta);
double logPercentile = Math.Log(percentile);
Func <double, double> f = lndelta =>
{
return((BetaLn(alpha + Math.Exp(lndelta), beta) - logBab) -
logPercentile);
};
double bracketWidth = coarse ? 1.0 : 6.0;
double blow = -bracketWidth / 2.0;
double bhigh = bracketWidth / 2.0;
double flow = f(blow);
double fhigh = f(bhigh);
while (flow > 0 && fhigh > 0)
{
// Move the bracket up.
blow = bhigh;
flow = fhigh;
bhigh += bracketWidth;
fhigh = f(bhigh);
}
while (flow < 0 && fhigh < 0)
{
// Move the bracket down.
bhigh = blow;
fhigh = flow;
blow -= bracketWidth;
flow = f(blow);
}
if (!(flow > 0 && fhigh < 0))
{
throw new EbisuConstraintViolationException($"Failed to bracket: flow={flow}, fhigh={fhigh}");
}
if (coarse)
{
return((Math.Exp(blow) + Math.Exp(bhigh)) / 2 * t0);
}
// Similar to the `root_scalar` api with bracketing
// See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root_scalar.html#scipy.optimize.root_scalar
var sol = Brent.FindRoot(f, blow, bhigh);
return(Math.Exp(sol) * t0);
}