非线性电感的梯形积分
非线性电感的梯形积分
提问于 2019-11-06 05:36:25
我已经用Modelica建立了非线性电感的模型，但是这个电路不能用梯形积分来求解，感谢有人能帮我解决这个电路。
model NonlinearInductor
import Modelica.SIunits.MagneticFlux;
extends Modelica.Electrical.Analog.Interfaces.OnePort;
parameter Real T[:,2]=[-1.0015,-1200;-0.0015,-200;0,0;0.0015,200;1.0015,1200]
"piecewiselinear current versus flux relation";
Integer nbPoints = size(T,1) "Number of interpolation points";
Real L; //Slop of line flux-Current; inductance
MagneticFlux flux( start=0);
equation
v = der(flux); // Faraday's Low
algorithm
// Definition of Piecewise nonlinear inductance
if i < T[2,1] then
L := ((T[1,2] - T[2,2]) / (T[1,1] - T[2,1]));
flux := L * (i-T[1,1]) + T[1,2];
elseif i >= T[nbPoints-1,1] then
L := (( T[nbPoints-1,2] - T[nbPoints,2]) / (T[nbPoints-1,1] - T[nbPoints,1]));
flux := L * (i-T[nbPoints-1,1]) + T[nbPoints-1,2];
else
for iter in 2:(nbPoints-2) loop
if i >= T[iter,1] and i <T[iter+1,1] then
L := (( T[iter,2] - T[iter+1,2]) / (T[iter,1] - T[iter+1,1]));
flux := L * (i-T[iter,1]) + T[iter,2];
end if;
end for;
end if;
end NonlinearInductor;我准备了一个例子，如下所示：
model NonlinearInductorTest
Modelica.Electrical.Analog.Sources.CosineVoltage cosineVoltage1(V = 25e3 * sqrt(2), freqHz = 50,
phase=1.5707963267949) annotation (
Placement(visible = true, transformation(origin = {-80, 20}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
Modelica.Electrical.Analog.Basic.Resistor resistor1(R = 1000e6) annotation (
Placement(visible = true, transformation(origin = {-14, 20}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
Modelica.Electrical.Analog.Basic.Ground ground1 annotation (
Placement(visible = true, transformation(origin = {-80, -12}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
Modelica.Electrical.Analog.Basic.Capacitor capacitor1(C=0.4e-9) annotation (
Placement(visible = true, transformation(origin = {-50, 42}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
NonlinearInductor L annotation(
Placement(visible = true, transformation(origin = {28, 20}, extent = {{-10, -10}, {10, 10}}, rotation = -90)));
equation
connect(L.n, ground1.p) annotation(
Line(points = {{28, 10}, {28, 10}, {28, -2}, {-80, -2}, {-80, -2}}, color = {0, 0, 255}));
connect(L.p, capacitor1.n) annotation(
Line(points = {{28, 30}, {28, 30}, {28, 42}, {-40, 42}, {-40, 42}}, color = {0, 0, 255}));
connect(capacitor1.p, cosineVoltage1.p) annotation(
Line(points = {{-60, 42}, {-80, 42}, {-80, 30}}, color = {0, 0, 255}));
connect(capacitor1.n, resistor1.p) annotation(
Line(points = {{-40, 42}, {-14, 42}, {-14, 30}}, color = {0, 0, 255}));
connect(resistor1.n, ground1.p) annotation(
Line(points = {{-14, 10}, {-14, -2}, {-80, -2}}, color = {0, 0, 255}));
connect(ground1.p, cosineVoltage1.n) annotation(
Line(points = {{-80, -2}, {-80, 10}}, color = {0, 0, 255}));
annotation (
uses(Modelica(version="3.2.2")),
experiment(StartTime = 0, StopTime = 0.1, Tolerance = 1e-6, Interval = 2e-05));
end NonlinearInductorTest;请通过求解程序梯形运行示例，StopTime = 0.1，Interval = 2e-05
回答 1
Stack Overflow用户
发布于 2019-11-11 19:47:16
通过使用MSL的插值功能，您的模型可以大大简化。据我所知，您的代码与此函数的功能相同:在定义的区间内使用线性插值，在区间外使用线性外推。
以下是更新后的代码：
model NonlinearInductor2
extends Modelica.Electrical.Analog.Interfaces.OnePort;
parameter Real T[:,2]=[-1.0015,-1200;
-0.0015,-200;
0,0;
0.0015,200;
1.0015,1200] "piecewiselinear current versus flux relation";
Modelica.SIunits.MagneticFlux flux( start=0);
protected
final parameter Real[:] i_vec = T[:, 1];
final parameter Real[:] flux_vec = T[:, 2];
equation
v = der(flux); // Faraday's Law
flux = Modelica.Math.Vectors.interpolate(i_vec,flux_vec,i);
end NonlinearInductor2;除了使您的模型更易于理解之外，插值函数的使用还带来了以下好处：
- 该函数定义了
smoothOrder注释，它允许Modelica转换程序以分析的方式区分flux变量。
(通过注释continuous)
- Instead和
smooth，您可以定义导数是算法部分的哪个顺序，我们可以使用单个smoothOrder部分。
(应避免使用算法部分来描述物理行为，因为它会限制Modelica转换器处理方程式以创建可求解的系统。使用算法部分，您可以强制代码按照您编写的代码进行评估，这违背了非因果物理建模的原则(
不幸的是，OpenModelica在使用您的模拟设置(梯形规则，公差=1e-6)模拟新模型时仍然存在一些问题。通过将容差减小到1e-4，模拟结束，但仍显示警告
重新启动Kinsol:将线性解算器更改为KINDense。
很多很多次。也许OpenModelica专家可以在这方面提供帮助。
顺便说一句，无论选择哪种求解器，Dymola对新代码都没有问题。
页面原文内容由Stack Overflow提供。腾讯云小微IT领域专用引擎提供翻译支持
原文链接：
https://stackoverflow.com/questions/58719825
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