Implementation of High Order DAE for Matlab Solver

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Helge
Helge 2015-3-6
编辑： Helge 2015-3-24
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).

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采纳的回答

Torsten
Torsten 2015-3-9
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.
  1 个评论
Helge
Helge 2015-3-17
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!

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