I want to design a linear controller for a quadcopter which is 6dof nonlinear.

I have non-linear equations. But in order to design a linear controller, I need to find a linear state-space model of the vehicle.

I skimmed bunch of articles and thesis without any result. Most of them have some approximations for separate parts of the model to linearize.

I need the state-space as a form like below,


I couldn't find the $A$ and $B$ matrices. I made the small angle and hover condition approximations so that equations become simpler yet they are still non-linear.

Non-simplified equations are as follow, enter image description here

  • $\begingroup$ If you want to determine the A and B matrices, take a look at 1. If you want to see your 6 dof quadcopter in the air and fly autonomously use a "timed behaviortree". $\endgroup$ Jan 29, 2017 at 6:06
  • $\begingroup$ For ? The question seems to be incomplete. $\endgroup$ Jan 29, 2017 at 10:17
  • 1
    $\begingroup$ Your system is still nonlinear. You may take a look at Full linear control of a quadrotor UAV, LQ vs H $\endgroup$
    – CroCo
    Jan 29, 2017 at 10:31
  • $\begingroup$ @GürkanÇetin For u silmeyi unutmuşum :).[Turkish] I have forgotten to delete the "For".[English] $\endgroup$
    – freezer
    Jan 29, 2017 at 21:48
  • $\begingroup$ @GürkanÇetin how can I contact with you if possible? I am not sure if we start a chat here. $\endgroup$
    – freezer
    Jan 29, 2017 at 21:49

1 Answer 1


enter image description here State-space equations for your case.


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