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Topic: Stochastic differential equations with Simulink?
Replies: 4   Last Post: Aug 29, 2013 8:15 AM

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Tikkuhirvi Tietavainen

Posts: 94
Registered: 4/22/08
Stochastic differential equations with Simulink?
Posted: Aug 6, 2013 10:03 AM
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Hi,

is it possible to simulate stochastic differential equations with Simulink? The one I'm working with is an inverted pendulum with two PD-controllers. The other controller has time delay in input and works only when certain criteria is met. This is the equation:

I*A''(t)=m*g*h*A(t)-[P1*A(t)+D1*A'(t)+f1(A(t-d))+f2(A'(t-d))]+s*n(t),

f1(A(t-d))=P2*A(t-d) & f2(A'(t-d))=D2*A'(t-d), when A(t-d)*[A'(t-d)-a*A(t-d)]>0 and
f1(A(t-d))=0 & f2(A'(t-d))=0 otherwise.

A(t) is the pendulum angle, I,m,g,h,s,P1,D1,P2,D2,a are constants, n(t) is Gaussian noise (mean=0, variance=1), t is time and d is time delay.

After some reformulation I believe this is what should be simulated:

x(n+1)=x(n)+f(x(n),x(n-k))dt+s*n(t)*sqrt(dt)

k=d/dt. The initial state is x0=[A(0),A'(0)]=[0.01,0].

Apparently the sqrt(dt) instead of just dt is the key problem here. If this is not doable with Simulink, any hint about how to make this happen is appreciated.

Thank you,
Aino



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