I'm trying to solve a nonlinear differential equation using ode45 I have a nonlinear system in the following form x = A*x + B*u and u is a function of the states x. Here is my function file,
function xprime = myode(t, x)
global g hs m S Cd Cl r0 rho0 h u
L = 0.5*rho0*exp(-(x(1)-r0)/hs)*x(3)^2*S*Cl/m;
f1 = x(3)*sin(x(6));
f2 = x(5);
f3 = -x(2) - g*sin(x(6));
f4 = x(3)*cos(x(6));
f5 = -x(5)*x(3)*sin(x(6))/hs + x(2)*(x(2) + g*sin(x(6)))*sin(x(6))/hs +...
x(2)*cos(x(6))^2*(g-x(3)^2/x(1))/hs -...
2*x(5)*(x(2) + g*sin(x(6)))/x(3) -2*x(2)*(x(2) +...
g*sin(x(6)))^2/x(3)^2 - 2*x(2)*x(5)/x(3) +...
2*x(2)*g*cos(x(6))^2*(g-x(3)^2/x(1))/x(3)^2;
f6 = -(g-x(3)^2/x(1))*cos(x(6))/x(3);
x2r = -.1221*t.^2 + 5.9859*t - 5.7866;
x5r = -.2442*t + 5.9859;
x2rdot = x5r;
x5rdot = -.2442;
x2rddot = x5rdot;
w1 = -x(2)*cos(x(6))*(1/hs + 2*g/x(3)^2)*L;
w2 = -x(2)*cos(x(6))*(1/hs + 2*g/x(3)^2)*L;
W = [w1;w2];
Delta = [h^2/2 0;0 h];
e1 = x(2) - x2r;
e2 = x(5) - x5r;
e = [e1;e2];
z1 = h*x(5) + (h^2/2)*f5;
z2 = h*f5;
z = [z1;z2];
d1 = h*x2rdot + h^2/2*x2rddot;
d2 = h*x5rdot;
d = [d1;d2];
u = -((Delta*W)'*Delta*W)^(-1)*(Delta*W)'*(e + z - d);
if( abs(u) > 1 )
u = sign(u);
end
xprime = zeros(6,1);
xprime(1) = f1;
xprime(2) = f2;
xprime(3) = f3;
xprime(4) = f4;
xprime(5) = f5 -x(2)*cos(x(6))*(1/hs + 2*g/x(3)^2)*L*u;
xprime(6) = f6 + L*u/x(3);
When I go to my main function file I can easily plot my states by using the command
plot(t,x(:,1)
plot(t,x(:,2)
.
.
.
plot(t,x(:,n))
and so on for n states. Since u is a function of these states I could plot u, i.e, u = blahblah(x(:,1),x(:,2),...,x(:,3)) and use the command plot(t,u)
However, my control input in this case is really long and complex and rewriting my control input in terms of my numerical answers x(:,n) seems time-consuming. Is there an easier way to plot my control input without having to rewrite the whole thing in my main function file? Any help is appreciated. Thanks.
