# How to find state-space representation of quadcopter?

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,

$$\dot{x}=Ax(t)+Bu(t)$$

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,

• 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". – Manuel Rodriguez Jan 29 '17 at 6:06
• For ? The question seems to be incomplete. – Gürkan Çetin Jan 29 '17 at 10:17
• Your system is still nonlinear. You may take a look at Full linear control of a quadrotor UAV, LQ vs H – CroCo Jan 29 '17 at 10:31
• @GürkanÇetin For u silmeyi unutmuşum :).[Turkish] I have forgotten to delete the "For".[English] – freezer Jan 29 '17 at 21:48
• @GürkanÇetin how can I contact with you if possible? I am not sure if we start a chat here. – freezer Jan 29 '17 at 21:49