system of differential equations

Hello All,

I am wondering how to solve system of differential equations using simulink?

plz do help me how to make a simulink model.

regards,

Answer 1

[Titus Edelhofer]

Hi,

you could open the vdp model as a typical second order differential equation. The way to go stays the same when you have a system: put as many integrators per row of your system as you have orders of differentiation, and feed them with the variables that make up the differential equation.

Titus

Answer 2

[Arnaud Miege]

Write down the equations on paper and then implement them using the various blocks available in Simulink. A tip: it's generally better to start with the highest order derivative and integrate rather than the other way round and differentiates. Have a look at Modeling Best Practises in the Simulink documentation and also at the interactive tutorials on the MathWorks web site.

HTH,

Arnaud

Answer 3

[Seba]

is it possible to find solution of this system with simulink:

x''(t)+ x'(t)+ z''(t) = 0

x(t)+ x'(t)+ z'(t) + 1 = 0

[Arnaud Miege]

That system does not have a solution. If you differentiate the second equation once more, you have:

x'' = -x' - z''

z'' = -1 - x'' - x'

If you then substitute the expression for z'' in the second equation into the first, you get:

x'' = -x' + 1 + x'' + x'

in other words, 1 = 0.

I suggest you check these equations, they're probably wrong.

[ikhlas]

how can I solve this system using Euler's method in matlab

u'=p

v'=q

p'=0

q'=0

such that u(0)=0 , v(0)=0, p(0)=0, q(0)=1?

Answer 4

[Seba]

here is a system of equations. Is it possible to find solution of this system with Simulink ?

Id, Iq,Ia,Ib,w,Me are unknown functions, Ud an Uq are known functions, other are constants

http://imageshack.us/photo/my-images/684/98585262.jpg/

[Arnaud Miege]

Yes, as long there is a solution, you can represent any system of ODEs in Simulink. Start working out the higher order derivatives and use integrator blocks to work your way up. Read the documentation, e.g.:

http://www.mathworks.com/help/releases/R2011a/toolbox/simulink/ug/bra6ae8.html

Answer 5

[Seba]

do you have any examples on how to solve equations with complex numbers in Simulink?

[Arnaud Miege]

It's the same as with real-valued signals, see the documentation:

http://www.mathworks.com/help/releases/R2011a/toolbox/simulink/ug/f15-99132.html#f15-82250

There are blocks to combine the real and imaginary parts into a complex number and conversely, to split a complex number into its real and imaginary parts.

[Seba]

how can I solve equations with real-valued signals with simulink, do you have any documentation on that?

[Arnaud Miege]

Like I said before (read my previous answers/comments), you can represent any system of ODEs in Simulink. Start working out the higher order derivatives and use integrator blocks to work your way up. Read the documentation, e.g.:

http://www.mathworks.com/help/releases/R2011a/toolbox/simulink/ug/bra6ae8.html.

Also work through the tutorials I suggested and look at Modelling Best Practises in the documentation.

Answer 6

[Seba]

I don't understand why the first example doesn't work and second example works

http://imageshack.us/photo/my-images/543/unledneim.jpg/

[Arnaud Miege]

There are two problems with the first example. The first one is a fairly simple syntax error: the correct MATLAB syntax is 10+10*i, not 10+10i (notice the *).

The second one is more subtle: even with the correct syntax, you'll get an error because you have an algebraic loop with a complex signals, which is not allowed. You will need to break the algebraic loop in some way. For example, adding a unit delay block with a sample time of say 1e-3s (or whatever is appropriate for your application), allows the model to run.

[Walter Roberson]

Hmmm?

>> 10+10i

ans =

10 + 10i

[Arnaud Miege]

OK, fair enough.

Answer 7

[Seba]

I have tried with delay block but i can't get the solution of the equation(which is -2.5-2.5*i)??

http://imageshack.us/photo/my-images/837/clipboard01fn.jpg/

[Arnaud Miege]

This is an algebraic equation. Typically when you have a system of differential & algebraic equations, you would eliminate the algebraic variables and reduce the number of equations to the differential equations only before implementing in Simulink.

[Seba]

so, how can i solve this equation with Simulink (10 + 10*i + 5*k = k)?

Should i put another delay loop or should i put this one on some other place?

[Seba]

Could this equation be solved with simulink?

[Arnaud Miege]

I have just told you this is an algebraic equation and k is an algebraic variable. If you have k in another (differential) equation, substitute for k the solution of this equation and then solve the differential equation in Simulink rather than what you're trying to do.

[Walter Roberson]

10 + 10*i + 5*k = k

implies that

10 + 10*i + 5*k - k = 0

which implies that

10 + 10*i + 4*k = 0

which implies that

4*k = -10 - 10*i

which implies that

k = (-10 - 10*i)/4

which is

k = -2.5 - 2.5*i

Any simple variation on this problem can be solved with a math block.

[Seba]

what is a math block? Is that a block in Simulink?

[Walter Roberson]

http://www.mathworks.com/help/toolbox/simulink/slref/mathfunction.html