Using ODE45 to solve a state space system.

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Francisco
Francisco 2014-7-16
评论： Francisco 2014-7-23
Hello there!
I stucked in how to use ode45. My problem is the following:
I have a ODE that i want to solve, the only difference is that my initial conditions are vector 3x1.
*function xdot = double_int2(t, y)
xd1 = y(2,:) % xdot = v
xd2 = temp2 + Td % temp2 and Td are vector 1x3
end*
and the other function
*
function [T,Y] = call_double_int2()
x01 = [10 0 0 ];
v01 = [1 0 0];
t_span = [0 5];
[T,Y]= ode45(@double_int2, t_span, [x01 v01])
end*
So, I don't know how to implent in wat that MatLab understand it`s a row vector, I tried to declare the funcion as double_int2(t,y(2,3)), but it always take it as a element.
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Francisco
Francisco 2014-7-23
% Position
x01 = [10 0 0 ]; x02 = [0 10 0 ]; x03 = [0 0 0 ]; x04 = [0 -10 0 ]; x05 = [-10 0 0 ]; x0 = [ x01; x02; x03; x04; x05 ];
% Linear Velocity
v01 = [1 0 0]; v02 = [0 1 0]; v03 = [0 0 0]; v04 = [0 -1 0]; v05 = [-1 0 0]; v0 = [ v01; v02; v03; v04; v05 ];
%% Parameters global alpha n kq Kw e3 b m A J g omega
n = 1; % Number of Vehicles
alpha = 3*n ; %%%% Verify
kq=50; Kw=10*eye(3); %dimension of matrix eye
e3 = [ 0 0 1 ] ;
b = 2; %%%% Verify
g = 9.806;
A = [0 1 0 0 0; 1 0 1 0 0; 0 1 0 1 0; 0 0 1 0 1; 0 0 0 1 0]; % Adjacency Matrix
m = 2; % mass
J = 1.2416*eye(n,n); omega = ones(1,3); % Vector that makes Ti no null
%% Thrust Vector
aux = zeros(1,3);
sum = zeros(1,3);
for i=1:n for j=1:n
if i == j
continue
end
xij = x0(j,:)-x0(i,:); %%x0 -> current x
vij = v0(j,:)-v0(i,:); %%v0 -> current v
aux = A(i,j) + ((xij)*tanh(norm(xij))/norm(xij) + (vij*tanh(norm(vij))/(b*norm(vij)) ) );
sum = aux + sum;
end
Ti = aux+alpha*omega;
Td(i,:) = Ti; % Recording Ti in a matrix [5,3]
%[t_temp,y_temp] = ode45(@double_int2, [0 10], [x0(i,:) v0(i,:)]);
aux = zeros(1,3); % clean aux for next iteration
end
%% t_span = [0, 5];
[t,y]= ode45(@double_int2, t_span, [x01 v01]);
%% Now the function %% %%
function xdot = double_int2(t, y) % x is the vector [ position , velocity ]
global Td m g e3
x=y(1:3);
v=y(4:6);
xd1 = v; % xdot = v
xd2 = m*g*e3 + Td; % m * vdot = m * g * e3 + Td
xdot = [xd1, xd2 ];
Francisco
Francisco 2014-7-23
My xdot is that cconcatenated matrix, but ode45 expect it to return a 1D vector as I think that is the only problem now. Thanks for you attention.

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Sara
Sara 2014-7-16
First, the size of the array of initial conditions has to be the same of the number of equations you want to solve. So, in your case, you either have 6 equations ([x01 v01] is an array 1 by 6) or you want only 1 element from x01 and y01. Given your ODE function, I think it's the second, but you tell us.
Then:
function xdot = double_int2(t, y)
expects that somewhere you define xdot, maybe as xdot = [xd1,xd2]. In addition, y is a 1D array, so replace y(2,:) with y(2).
You will also need to pass temp2 and Td to double_int2. You can do:
[T,Y]= ode45(@(x)double_int2(x,temp2,Td), t_span, [x01 v01])
function xdot = double_int2(t, y,temp2,Td)

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