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)

  • $\begingroup$ It's not a big problem but general convention is to use phi for roll, and theta for pitch angles. $\endgroup$ Jun 20 '17 at 17:04

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.

  • $\begingroup$ Oh, you are right. But how can you say it will be an unstable equilibrium? $\endgroup$
    – Manish
    Jun 20 '17 at 14:59
  • 1
    $\begingroup$ If that equality is satisfied for a certain $\theta$ but $\dot{\theta} \ne 0$ the system will continue to rotate away from that equilibrium point. $\endgroup$
    – ryan0270
    Jun 20 '17 at 15:31

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