Solving state space equation by ode45
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Basetsana Sebolao
on 12 May 2021
Commented: Star Strider
on 17 May 2021
Helo everyone
I am trying to solve a state space matrix using ode45. My A matrix is a 4 x 4, my B matrix is a 4 x 4 and my input matrix, v is a 4 x 1. I am expecting a matrix of 4 x 1 however when I run my code Matlab indicates that my t and y arrays have 185853 rows in my workspace, which is befuddling because I do not understand why my matrix has a lot of rows.I have attached a picture of my code. Pease kindly assist, thank you in advance.
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Star Strider
on 12 May 2021
Please copy and paste all the relevant code to either an edit to your original post here or to a Comment. Screenshots can be appropriate for plots and other images, however not for code.
Accepted Answer
Star Strider
on 12 May 2021
The MATLAB ODE solvers are adaptive, and so will solve with as narrow a difference in the time steps as necessary to produce a stable solution. In your differential equation solution, there are very rapid oscillations with increasing amplitudes beginning at about time units.
tspan = [0 0.005];
iniCon = [0 0 0 0];
[t,y] = ode45(@sys, tspan, iniCon);
getSizes = [size(t); size(y)]
figure
plot(t, y)
grid
figure
cols = size(y,2);
for k = 1:cols
subplot(cols,1,k)
plot(t, y(:,k))
grid
xlim([0 1.5E-4])
title(sprintf('y_{%d}',k))
end
xlabel('t')
function di = sys(t, i)
Rs=1.115;Rr=1.0830; Wr=1150; Lm= 76.79; Ls=79.04; Lr=79.04; Ws=376;
R=[Rs 0 0 0; 0 Rs 0 0; 0 0 Rr 0; 0 0 0 Rr];
G=[ 0 0 0 0; 0 0 0 0; 0 -Lm 0 -Lr; Lm 0 Lr 0];
L=[Ls 0 Lm 0; 0 Ls 0 Lm; Lm 0 Lr 0; 0 0 0 Rr];
k=1/(Ls*Lr-Lm*Lm);
%A is a 4x4 matrix
A=-L*(R+(Wr*G));
%B is a 4x4 matrix
B= k*[Lr 0 -Lm 0; 0 Lr 0 -Lm; -Lm 0 Rs 0; 0 -Lm 0 Ls];
%V is a 4x1 matrix
v = [t; 0; 0; 0];
%state equation
di = A*i + B*v;
end
.
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