Implementation of High Order DAE for Matlab Solver

Hi,

I got three variables y1(t), y2(t) and y3(t) which I want to solve for. Moreover I have two ODEs in explicit and coupled form and one algebraic equation , which look as follows:

 1. Eqn: y1''' = f(y1'', y1', y1, y2'', y2', y2, u)
 2. Eqn: y3''  = f(y1', y1, y2'', y2', y2,  y3', y3, u)
 3. Eqn: y1 = y2 + y3

u is my input which is a cosine function with amplitude U_g

I want to use ode15s() to solve this system if its correct, with a Mass Matrix M and a form like

 M(t,y)*y′ = f(t,y)

Therefore I have to reduce the order of the above equations first.

Now my function looks like the following, where "d" represents first differential and "dd" the 2nd differential:

 function out = myodefunc(t, y, U_g, R_e, L_e, M_m, bl_0, bl_1, ...)

 out = zeros(8, 1);
 % Reduce Order of Diffenrential Equations
 y1    = y(1);
 dy1   = y(2);
 ddy1  = y(3);
 y2    = y(4);
 dy2   = y(5);
 ddy2  = y(6);
 y3    = y(7);
 dy3   = y(8);
 % Define Output
 out(1) = y1 - y2 - y3;
 out(2) = dy1;
 out(3) = ddy1;
 out(4) = -(bl_0^3*dy1 - bl_0^2*U_g*cos(2*pi*f0.*t) + bl_1^3*y1^3*dy1 + bl_2^3*y1^6*dy1 - bl_1^2*U_g*cos(2*pi*f0.*t)*y1^2 -  ...
 out(5) = dy2;
 out(6) = ddy2;
 out(7) = dy3;
 out(8) = (L_e*bl_0*s_s_0*dy2 - L_e*bl_0*s_v_0*dy3 + R_e*bl_0*r_s_0*dy2 - R_e*bl_0*r_v_0*dy3 + R_e*bl_0*s_s_0*y2 - R_e*bl_0*s_v_0*y3 + -...

 end

With a Mass Matrix :

 M =

     0     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0
     0     0     1     0     0     0     0     0
     0     0     0     1     0     0     0     0
     0     0     0     0     1     0     0     0
     0     0     0     0     0     1     0     0
     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     0     1

Do you guys think, that I implemented this in the right way?

Mainly I am concerned about the algebraic equation, which is in the first line of the output. It's because I get zero output for out(2), out(3), out(5) and out(6).

Answer 1

[Torsten]

I guess your DAE system is of higher index than 1.

You can check this:

http://de.mathworks.com/help/symbolic/check-and-reduce-differential-index.html

Best wishes

Torsten.

[Helge]

Hi Torsten, just a quick reply on your answer. I succesfully implemented my DAE system by walking through the following manual: http://de.mathworks.com/help/symbolic/set-up-your-dae-problem.html

This is avaible for Symbolic Math Toolbox users in Matlab2015a. It is very straight forward method for implementing equation systems in Matlab and super helpful, Well Done!