Problem solving ODE system in Simulink

Question

Oscar Espinosa 2020-11-7

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https://ww2.mathworks.cn/matlabcentral/answers/639520-problem-solving-ode-system-in-simulink

评论： Oscar Espinosa 2020-11-7

采纳的回答： Stephan

Hi, I'm having some troubles when trying to solve a system of ODE.

This is the equation that I'm trying to solve:

with initial conditions

.

When solving the equation numerically I obtained the next plot in the interval from

to

.

I tried to do the same with Simulink, but the resulting graph from the scope its the next one:

The Simulink diagram is the next:

Thanks in advance.

Oscar Espinosa

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Answer 1

Stephan 2020-11-7

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I think something went wrong, when you solved numeric:

syms y(t)
eq = diff(y,t,4) + 3 * diff(y,t,2) - sin(t) * diff(y,t,1) + 8 * y == t^2;
[V,S] = odeToVectorField(eq);
fun = matlabFunction(V,'Vars',{'t','Y'});
[tsol, ysol] = ode45(fun,[0 20], [1 2 3 4]);
plot(tsol, ysol(:,1))

result is:

The equation in Simulink:

gives:

Which is the same result. I think you have to switch the x0-Inputs with the signal inputs of your 4 integrators to solve the issue.

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Oscar Espinosa 2020-11-7

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Hi, Stephan

That helped to me, thank you. By the way I'll like to show how I tried to solve the ODE like a system of ODE, so:

xconds = [1;2;3;4];
function dxdt = ode_4th_order(t,x)
dxdt(1,1) = x(2,1);
dxdt(2,1) = x(3,1);
dxdt(3,1) = x(4,1);
dxdt(4,1) = -3*x(3,1)+sin(t)*x(2,1)-x(1,1)+t^2;
end
[t,x] = ode45('ode_4th_order',tspan,xconds);
plot(t,x(:,1));

But this give a completely different graph, the one that you see in the original post. Does this approach work? I mean, there is something that I did wrong or something missing?

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