创建要在ode45中使用的函数

Question

So this is part of a larger project but I am stuck on number two of this section. I rewrote the system to get it in the required form:

dx(1)/dt = x(2)

dx(2)/dt = (-(M+m)/mL))x(4) + 1/(mL)u

dx(3)/dt = x(4)

dx(4)/dt = -(mg/M)x(1) + (1/M)u

After substituting the variables given in the problem I wrote the funcion:

function dx = fun(t,x)
dx = zeros(4,1);
dx(1) = x(2);
dx(2) = -((2+.1)/(.1*.5)).*x(4);
dx(3) = x(4);
dx(4) = -((.1*9.81)/2).*x(1);
end

I am confused on how to implement u(t) = 0 and how to create the theta function.

Any help even if its just pointing me in the right direction would be amazing. Thank you in advance :)

Answer 1

It's easy. You implement theta as another state. This is possible since you know the derivative, which does not even depend on the other states. To be more precise, you should add two more states here. One for theta and one for theta_dot .

dx(5) = x(6)  % Theta'
dx(6) = -0.1  % Theta''

And by the way, you can also pass additional variables to your differential equation. You just add more arguments to it

function dx = diffeq(t,x,parameters)
  ...
end

and create a new function handle where you execute the ODE solver

[T,X] = ode45(@(t,x)diffeq(t,x,parameters),t_span,X0, ode_options);

This is just a hint since you're using magic numbers in your differential equation function.