What's wrong in controlling Roll+Roll rate in a quad-copter instead of using 2 separate loops for each?

Question

I am curious to know why we can't apply control algorithm like PID on the weighted signal of Roll and Roll rate in a quad-copter instead of using two loops to control them independently. Fundamentally PID will make the input signal to approach $0$. In the case of (Roll + Roll-Rate), which would be $ w_1\theta + w_2\dot\theta$, the sum becomes $0$ when individually both tend to $0$; since we have an exponentially decaying curve.

So why do people generally use sequential loops to control each of them separately? (Roll is just for example)

Answer 1

That only works when the desire roll angle is 0. What happens if you are trying to turn and have a desired roll angle of 1deg? Even changing your sum to match the angle error, $w_1 (\theta - \theta_d) + w_2 \dot{\theta}$ you are still not guaranteed to reach $\theta=\theta_d$; you're only driving towards $w_1 (\theta - \theta_d) = -w_2 \dot{\theta}$. For most situations this will not be a stable equilibrium so then you'll oscillate back the other direction.