Function Handle and RK4 problem.

I'm trying to implement a variable (tau) inside the function func1 in which i need first to obtain the values from the output [ yout(:,1) or pendulum position] and update the variable each loop, and i dont know how to implement like that.

clear all
clc
%% Constants
m=1;
l=2;
g=9.81;
%% Time step
h=0.01;                                            
tfinal = 30;
N=ceil(tfinal/h);                                    
%% IC
x1CI=pi/2;
x2CI=0;

t=zeros(N,1);

yout = zeros(N,2);

y0 = [x1CI x2CI]'

yout(1,:)=y0;

%% Function Handle

system = @(t,y)func1(t,y,m,l,g); 

%% Integrator

for i=1:N
                                              %  dt,dx,t,x
    [ t(i+1), yout(i+1,:) ] = integrator_rk4(h,system,t(i),yout(i,:)');

end

%% Figure

figure
plot(t, yout(:,1))
grid

%% Functions
function dy = func1(t,y,m,l,g)
% y = [x1 x2]' = [y(1) y(2)]


dy=zeros(2,1); 
%dy e dy^2 

dy(1)= y(2);

dy(2)= ((-g*sin(y(1)))/l);%+Tau=0.01*yout(:,1)

end

function [tout, xout] = integrator_rk4(dt,dx,t,x)

tout = t + dt;

dt_half = 0.5*dt;
k1 = dx(t,x);
k2 = dx(t+dt_half,x+dt_half*k1);
k3 = dx(t+dt_half,x+dt_half*k2);
k4 = dx(tout,x+dt*k3);

xout = x + dt*(k1+2*k2+2*k3+k4)/6;
end

[James Tursa]

Can you provide more detail about what tau is supposed to be in your code?

[Marcio]

this is just a example of a simple pendulum i'm trying to learn , i have another program i'm working on (reaction wheel pendulum, almost the same program with more complex dynamics) where my tau is the torque provided by the DC motor, and i wish to apply a control to bring the pendulum to the inverted position. So briefly explained i need the outputs so i can feedback the system with the torque provided by a DC motor.

[J. Alex Lee]

here's what I'm seeing from your code: you want the derivative definition in func1() to know not just about the current value of y, but the whole time history of y.

here's what i'm hearing from your comment: you want to write a different system of equations that adjusts the dynamics accounting for an additional quantity (torque).

So is the torque supposed to react only instantaneously to soem current state, or is there some integral aspect of the controller?

[Marcio]

there's no integral aspect of the controller, he'll react to states, the problem is that i cant figure out how to use the outputs like dy(2) (acelleration) on tau in the function of the reaction wheel (real system), i need the aceleration on tau and he show up in one equation before the acelleration equation, so i need somehow obtain the values outside the func1 and inside the loop, and update him in the func1, i can't obtain the values of tau also if he's only inside the func1...