Try classical controller

[IvanKenevich]

Design PID and compare with state space

[IvanKenevich]

[IvanKenevich]

Need to find Ps from equations of motion (linearize). Cs are designed with classical controller design methods. R_theta2 = 0 always.

This seems like a better method than trying to extract theta_2 transfer function using ss2tf().

[IvanKenevich]

$P_{\theta_2}$ appears plausible to find. Use derived kinematics of inverted pendulum on a cart to skip that math and see if you can go straight to transfer function of $\theta_2/\dot{\theta}_1$.

[IvanKenevich]

From the math, it turns out

$\displaystyle\frac{\theta_2}{\dot{\theta}_1} = $

$\displaystyle\frac{L1 m l{2}s^3}{(J{2zz-cg}+m l{2}^2)s^2 + b2 s - mg l{2}}$