Solving a Delay Differential Qquations that involves a mass matrix

I have a DAE system with constant time delay that involves mass matrix (i cannot invert the matrix because it's singular). Now, without a delay, Matlab could solve it with ode23s but i really don't know how should i proceed with the current situation, because dde23 has no option for mass matrix. Thanks in advance.

[Torsten]

You should include your DAE system - maybe someone here has an idea.

[Furkan]

The Eq System in Matrix form is like this;

W*x_dot=U-G*x

Now since W has no inverse, i need to define W as mass matrix. The code below is giving error because i am desperately trying to multiply the right side of the Eq system with inv(W), to leave xdot alone.

R1=50;

L1=0.001;

ZL=120;

f=10000;

x0=zeros(6,1);

tao=11.55*1e-6;

G=[0 0 0 1 1 0; 0 0 0 0 0 0; 0 0 1/R1 0 0 1; 1 0 0 0 0 0; 1 0 0 0 -ZL 0; 0 0 1 0 0 -ZL];

W=[0 0 0 0 0 0; 0 0 0 0 0 0; 0 0 0 0 0 0; 0 0 0 0 0 0; 0 0 0 0 -L1 0; 0 0 0 0 0 0];

dxdt= @(t,X,XL) (inv(W)*([0; 0; 0; sin(2*pi*f*t); XL(3,1)+(ZL*XL(6,1)); XL(2,1)+(ZL*XL(5,1))]-G*X));

slv = dde23(dxdt, tao, x0, [0 0.0005]);

[Torsten]

I think you must have misunderstood something in the setup.

Your second equation reads 0=0 which can't be what you want.

It will be best to include the equations in mathematical notation, not as MATLAB code in order to avoid further errors.

[Furkan]

Hello sir, this is a homework i am trying to do, so i might have some miscalculations on the mathematical model, i come up with 2 different Eq systems which can be true, since you said first one is wrong, it should be the second one i find. Here is the model:

However when i implement this into code, the issue i am dealing with still there: i cannot inverse the first matrix to leave X_Dot alone. I need to describe this matrix as Mass matrix. Normally i could do it with ode23s, but this system has a time delay, so ode won't work with it and dde23 has nor option for mass matrix. I hope i could adress my problem here. Thank you for your time.

Answer 1

[Torsten]

Write out your system and you will find that

x3 = x6 = x7 = x8 = x9 = 0

and you are left with the equations

x1(t) = sin(2*pi*f*t)
-x4(t) + x5(t-tau) = 0
x4(t-tau) - x5(t) = 0
-x1(t) + x2(t) = 0

So no differential equations are left.

Better use pencil and paper than MATLAB to solve them.