Implementation of High Order DAE for Matlab Solver
2 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
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).
0 commentaires
Réponse acceptée
Torsten
le 9 Mar 2015
I guess your DAE system is of higher index than 1.
You can check this:
Best wishes
Torsten.
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Ordinary Differential Equations dans Help Center et File Exchange
Produits
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!