Using ode45 to solve matrix/vector form of state space diff eq

I currently have two state space equations in matrix/vector form

The first is Ydot4=[a 0 0 0;0 0 0 0; 0 0 b 0;0 0 0 0 c]*[y1;y2;y3;y4]

The second is Ydot2= [d 0 0 0;0 e 0 0;0 0 f 0;0 0 0 g]*[y1;y2;y3;y4]+[h 0 0 0]*V0(t)

I would like to know how to solve these equations using ODE45 over a timespan of 0 to 1 seconds with intervals of 1ms. And V0(t)=5cos(40t)

Ydot4=V2doubledot

Y4=V2dot

Y3=V2

Y2=V1dot

Ydot2=V1doubledot

Y1=V1 .

[Birdman]

This is 5th time you open the same question. Please delete it because you already opened it 38 minutes ago.

[Reed Garion Williams]

You close it every time so i have to reopen it... Allow someone else to answer it even if you may not think it belongs

[Birdman]

But one question is enough. Why you keep opening it? It will not improve your chance of getting answer.

[Reed Garion Williams]

If you close the question i cannot receive answers therefore i have to ask again

[Birdman]

One question is enough. If someone who knows about this topic come across your question, he/she will answer, don't worry. Please do not open the same question again. I am closing it.

[Reed Garion Williams]

How will someone answer the question if it is closed???

[Birdman]

By the time I was closing this, you also closed your initial question as well. Keep this question here and eventually someone will answer.

Answer 1

[James Tursa]

Trying to understand your nomenclature, and using your element ordering, here is the layout I would normally start with for a 4-element state vector y:

y(1) = Y1 = V1
y(2) = Y2 = V1DOT = d(V1)/dt = d(Y1)/dt
y(3) = Y3 = V2
y(4) = Y4 = V2DOT = d(V2)/dt = d(Y3)/dt

This is not the way I would have done it, btw. I would usually prefer to keep all of the "position" elements next to each other and then all of the "velocity" elements next to each other, rather than interleaving them as you have done. But, continuing with your element ordering, the derivatives would be:

d(y(1))/dt = d(Y1)/dt = d(V1)/dt = y(2)
d(y(2))/dt = d(Y2)/dt = d(V1DOT)/dt = d^2(V1)/dt^2 = V1doubledot
d(y(3))/dt = d(Y3)/dt = d(V2)/dt = y(4)
d(y(4))/dt = d(Y4)/dt = d(V2DOT)/dt = d^2(V2)/dt^2 = V2doubledot

So the first and third element derivatives are easy of course. For the second and fourth derivative elements, that would be obtained from your state space equations in vector form.

But at this point I am confused. Your Ydot4 state space matrix equation seems to map the [y1;y2;y3;y4] back to V2 (as a vector and not as an element), but then your Ydot2 state space matrix equation seems to map [y1;y2;y3;y4] back to V1 (again as a vector and not as an element). So they seem to map to two different variables, and those variables seem to be vectors? Which leads me to believe that all the stuff I just wrote is not valid and doesn't really apply to your problem.

Can you clarify what the variables in your system are, what their dimensions are, and what the derivative equations for these variables are? Your current nomenclature is hard for me to follow.

Answer 2

[Bilal sadiq]

Reed Garion Williams can you provide matlab script or some further explanation so that one can better understand to help you....