为什么我在 Octave 的 ODE45 仿真中只得到 NaN och Inf？

Question

我使用带有 ODE45 的 Octave 来模拟 ODE 方程组。但问题是 ODE 模拟给出了错误的值。看看这个 Octave 代码：

function dx = dynamik(t, x)
b1 = 1000;
b2 = 2000;
m1 = 10;
m2 = 7;
M = 2000;
g = 9.82;
mu = 0.3;
L = 0.1;
Ap = 0.004;
Am = 0.002;
Pp = 2*10^6;
Pm = 2.1*10^6;
k1 = 1.78e+4;
k2 = 4.04e+4;
k3 = 8.86e+3;

dx= [ x(2);
    -k1/m1*x(1) + k1/m1*x(3) - b1/m1*x(4) + b1/m1*x(4) + Ap/m1*Pp - Pm*Am/m1*x(2);
    x(4);
    k1/M*x(1) - k1/M*x(3) + b1/M*x(2) - b1/M*x(4) - g*mu*x(4) - k2/M*x(3) + k3*L/M*sin(x(5));
    x(6);
    3*k2/(m2*L)*x(3) - 3*k2/m2*sin(x(5)) - 3*k3/(m2*L^2)*x(5) - 3*b2/(m2*L^2)*x(6) + 3*g/(2*L)*sin(x(5))];
endfunction

tspan = 0:0.5:10;
init = [0, 0, 0, 0, 0, 0];
[t, y] = ode45(@dynamik, tspan, init);

这给出：

>> y
y =

0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00
1.6659e+08   -6.9253e+10   -1.9336e+05    8.0380e+07   -4.4787e+07    3.8388e+12
5.9331e+18   -2.4665e+21   -6.8864e+15    2.8628e+18   -1.3333e+32    1.1428e+37
2.1131e+29   -8.7843e+31   -2.4526e+26    1.0196e+29   -3.9691e+56    3.4019e+61
7.5258e+39   -3.1286e+42   -8.7350e+36    3.6313e+39   -1.1816e+81    1.0127e+86
2.6803e+50   -1.1142e+53   -3.1110e+47    1.2933e+50  -3.5174e+105   3.0148e+110
9.5460e+60   -3.9684e+63   -1.1080e+58    4.6060e+60  -1.0471e+130   8.9747e+134
3.3998e+71   -1.4134e+74   -3.9461e+68    1.6404e+71  -3.1171e+154   2.6717e+159
1.2109e+82   -5.0337e+84   -1.4054e+79    5.8425e+81  -9.2794e+178   7.9533e+183
4.3125e+92   -1.7928e+95   -5.0054e+89    2.0808e+92  -2.7624e+203   2.3676e+208
1.5359e+103  -6.3849e+105  -1.7827e+100   7.4109e+102  -8.2234e+227   7.0482e+232
5.4701e+113  -2.2740e+116  -6.3491e+110   2.6394e+113  -2.4480e+252   2.0982e+257
1.9482e+124  -8.0989e+126  -2.2612e+121   9.4003e+123  -7.2875e+276   6.2461e+281
6.9386e+134  -2.8844e+137  -8.0534e+131   3.3479e+134  -2.1694e+301   1.8594e+306
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN
       NaN           NaN           NaN           NaN           NaN           NaN

但是在 OpenModelica 中，我有这个代码：

model Hydraulik_System_1
// Types for variables
type PositionCylinder = Real(unit="m");
type Position = Real(unit="m");
type Velocity = Real(unit="m/s");
type DegreesPosition = Real(unit="rad");
type DegreesVelocity = Real(unit="rad/s");
type pressure = Real(unit="Pa");
type flows = Real(unit="l/min", min=0.0);

// Types for parameters
type spring = Real(unit="N/m");
type damper = Real(unit="Ns/m");
type mass = Real(unit="kg");
type friction = Real(unit="%");
type length = Real(unit="m");
type gravitation = Real(unit="m/s^2");
type area = Real(unit="cm^2");

// Parameters
parameter spring k1 = 1.78*10^4;
parameter spring k2 = 4.04*10^4; 
parameter spring k3 = 8.86*10^3;
parameter mass m1 = 10;
parameter mass m2 = 7;
parameter mass M = 2000;
parameter damper b1 = 1000;
parameter damper b2 = 2000; 
parameter gravitation g = 9.82;
parameter friction mu = 0.3;
parameter area Am = 0.002;
parameter area Ap = 0.004;
parameter length L = 0.1;
parameter pressure Pp = 2*10^6;
parameter pressure Pm = 2.1*10^6;

// Variables
PositionCylinder x1;
Position x3;
Velocity x2 , x4;
DegreesPosition x5;
DegreesVelocity x6;
initial equation
x1 = 0;
x2 = 0;
x3 = 0;
x4 = 0;
x5 = 0;
x6 = 0;
equation

der(x1) = x2;
der(x2) = - k1/m1*x1 + k1/m1*x3 - b1/m1*x4 + b1/m1*x4 + Ap/m1*Pp - Pm*Am/m1*x2;
der(x3) = x4;
der(x4) = k1/M*x1 - k1/M*x3 + b1/M*x2 - b1/M*x4 - g*mu*x4 - k2/M*x3 + k3*L/M*sin(x5);
der(x5) = x6;
der(x6) = 3*k2/(m2*L)*x3 - 3*k2/m2*sin(x5) - 3*k3/(m2*L^2)*x5 - 3*b2/(m2*L^2)*x6 + 3*g/(2*L)*sin(x5);

end Hydraulik_System_1;

结果如下所示：

你能告诉我为什么我的模拟会发生这种情况吗？ OpenModelica 仿真结果和Octave 仿真结果有很大的不同。为什么？我是否更改 ODE 求解器并不重要。结果几乎一样。

Answer 1

我使用了lsode，也得到了正确的答案，但是调用参数必须切换，并且更小的tspan。

首先，交换了函数中的参数：

function dx = dynamik(x, t)

设置 tspan:

tspan = 0:0.0625:2;

然后lsode调用：

[y,t] = lsode(@dynamik, init, tspan );

更新：已安装 odepkg，并且能够重现您的错误。还看到 ode23 的错误，但 ode23s 没有。这表明您的 ODE 是 "stiff,"，因此 Runge-Kutta 4/5 并不是真正合适的算法。

为什么我在 Octave 的 ODE45 仿真中只得到 NaN och Inf？

Why do I only get NaN och Inf at ODE45 simulation in Octave?

matlab

nan

octave

openmodelica

ode45