Question

我正在使用带有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);

这给出了：

>> 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

但在OpenModelica中，我有这段代码：

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：

你能告诉我为什么我的模拟会发生这种情况吗？ OpenModelica仿真结果与Octave仿真结果之间存在巨大差异。为什么？如果我更改ODE求解器并不重要。结果几乎相同。

Answer 1

我使用了lsode，并得到了正确的答案，但是必须切换调用参数，并且需要更小的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来电：

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

更新：已安装odepkg，并且能够重现您的错误。另见ode23错误，但ode23s错误。这表明你的ODE很僵硬，＆＃34;所以Runge-Kutta 4/5并不是一个合适的算法。

为什么我只在Octave的ODE45模拟中获得NaN och Inf？

1 个答案: