I am trying to develop a controller for a quadrotor using dynamic feedback linearization technique, but I am not sure I am doing thigs correctly. I know that for designing such controller I have to keep derivating until I see the input and it appears in a nonsingular way.

In my case, if I do this for example just for the $z$ coordinate I obtain that if I derivate two times I see the input in the expression of the second derivative, so after derivating two times I have:

$\ddot{z} = -cos(\theta )cos(\varphi )\frac{T}{m}+g$

where we can see that the thrust $T$ appears. Now we can derive a control law using a dynamic controller of the form :

$J(\xi ,\zeta )^{-1}(-l(\xi ,\zeta)+v)$

where $\zeta = \begin{pmatrix} T\\ \dot{T} \end{pmatrix}$, and I have understand well, we have do design such controller such that $\ddot{z} = v$ .

Now, if I apply this to the quadrotor, I obtain:

$T = \frac{m(g-\ddot{z}))}{cos(\theta )cos(\gamma )}$

where $\ddot{z} = \ddot{z_{d}} -K_{d}(\dot{z_{d}} - \dot{z}) - K_{p}(z_{d}-z)$ and with $z_{d}$ as desired value for the $z$.

The problem is that it looks too much as a PID controller to me, so I don't see the difference between the two types of controller.

[EDIT] moreover, what are the benefits of using feedback linearization and what is the difference between this tecnhnique and using backstepping or PID controllers?

Can somebody please help me? Thank's in advance.

  • $\begingroup$ What do you mean by "the two types of controller"? You mean feedback linearization (or input-output linearization) and PID? Namely feedback linearization alone isn't a full control law yet, but only your equation for $T$ with $\ddot{z}$ set equal to some to be determined new virtual input. $\endgroup$ – fibonatic Oct 14 '19 at 0:26
  • $\begingroup$ yes, by two controllers i meant feedback linearization and PID, but if I can' t derive a controller with feedback linearization I have some doubts on why is it used to control a quadrotor. I have understood that it is used beacause the quadrotor equations of motion are non-linear, but why is it present and is it not just used just backstepping? So what is the point of using feedback linearization and what are its benefits? I have a bit of confusion on this topic. $\endgroup$ – J.D. Oct 14 '19 at 3:55

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