Solving Boundary Value with bvp4c Matlab - matlab

Question

i'm trying to solve a boundary value problem of an system q' = f(q(t), a(t)) with an input a using bvp4c in Matlab. Where q = [q1, q2, q1_dot, q2_dot]'
My Matlab Code does not work properly. Does anyone know how to solve this?
img: System Equation of the One Pendulum
a is a input function.
the initial state: q1(0) = pi, q2(0) = 0, q1_dot(0) = 0, q2_dot(0) = 0.
the end state: q1(te) = 0, q2(te) = 0, q1_dot(te) = 0, q2_dot(te) = 0.
input initial state: a(0) = 0, and the end state: a(te) = 0.
i've in total 10 boundaries. one_pendulum_bc can take only 5 and not more and fewer.
function one_pendulum
options = []; % place holder
solinit = bvpinit(linspace(0,1,1000),[pi, 0, 0, 0],0);
sol = bvp4c(#one_pendulum_ode,#one_pendulum_bc,solinit,options);
t = sol.x;
plot(t, sol.y(1,:))
figure(2)
plot(t, sol.y(2,:))
figure(3)
plot(t, sol.y(3,:))
figure(4)
plot(t, sol.y(4,:))
% --------------------------------------------------------------------------
function dydx = one_pendulum_ode(x,y,a)
% Parameter of the One-Pendulum
m1 = 0.3583; % weight of the pendulum [kg]
J1 = 0.03799; % moment of inertia [Nms^2]
a1 = 0.43; % center of gravity [m]
d1 = 0.006588; % coefficient of friction [Nms]
g = 9.81; % gravity [m/s^2]
dydx = [ y(3)
y(4)
(a*a1*m1*cos(y(1)) + a1*g*m1*sin(y(1)) - d1*y(3))/(J1 + a1^2 *m1)
a ];
% --------------------------------------------------------------------------
function res = one_pendulum_bc(ya,yb,a)
res = [ya(1) - pi
ya(2)
ya(4)
yb(1)
yb(3)];
img: The result should look like this

Answer 1

i just solved it with a model function.
function one_pendulum
options = bvpset('stats', 'on', 'NMax', 3000);
T = 2.5;
sol0 = [
-5.3649
119.5379
-187.3080
91.6670];
solinit = bvpinit(linspace(0, T, T/0.002),[pi, 0, 0, 0], sol0);
sol = bvp4c(#one_pendulum_ode,#one_pendulum_bc,solinit,options, T);
t = sol.x;
ax1 = subplot(2,2,1);
ax2 = subplot(2,2,2);
ax3 = subplot(2,2,3);
ax4 = subplot(2,2,4);
plot(ax1, t, sol.y(1,:))
title(ax1, 'phi');
plot(ax2, t, sol.y(2,:))
title(ax2, 'x');
plot(ax3, t, sol.y(3,:))
title(ax3, 'phi_d');
plot(ax4, t, sol.y(4,:))
title(ax4, 'x_d');
length = size(t)
k = sol.parameters
for i=1:length(2)
k5 = -(k(1) * sin(pi) + k(2) * sin(2*pi) + k(3) * sin(3*pi) + k(4) * sin(4*pi))/sin(5*pi);
x = t(i);
acc(i)=k(1) * sin(pi*x/T) + k(2) * sin(2*pi*x/T) + k(3) * sin(3*pi*x/T) + k(4) * sin(4*pi*x/T) + k5* sin(5*pi*x/T);
end
figure(2)
plot(t,acc)
% --------------------------------------------------------------------------
function dydx = one_pendulum_ode(x,y,k,T)
% Parameter of the One-Pendulum
m1 = 0.3583; % weight of the pendulum [kg]
J1 = 0.03799; % moment of inertia [Nms^2]
a1 = 0.43; % center of gravity [m]
d1 = 0.006588; % coefficient of friction [Nms]
g = 9.81; % gravity [m/s^2]
% Ansatzfunktion
k5 = -(k(1) * sin(pi) + k(2) * sin(2*pi) + k(3) * sin(3*pi) + k(4) * sin(4*pi))/sin(5*pi);
a = k(1) * sin(pi*x/T) + k(2) * sin(2*pi*x/T) + k(3) * sin(3*pi*x/T) + k(4) * sin(4*pi*x/T) + k5* sin(5*pi*x/T);
dydx = [ y(3)
y(4)
(a*a1*m1*cos(y(1)) + a1*g*m1*sin(y(1)) - d1*y(3))/(J1 + a1^2 *m1)
a ];
% --------------------------------------------------------------------------
function res = one_pendulum_bc(ya,yb,k,T)
res = [ya(1) - pi
ya(2)
ya(3)
ya(4)
yb(1)
yb(2)
yb(3)
yb(4)];