this link may be help you

https://www.mathworks.com/matlabcentral/fileexchange/51076-displacement-control-of-a-quadcopter?s_tid=srchtitle

Gabriele Scordamaglia Please mention the dimensions of A,B,C and D matrices. Then I will help you.

Reference is "what you want". I don't know which model/control did you use but you need to provide a signal representing the expected behavior of your system. E.g. x, y and heading coordinates, a trivial example: x = cos(t), y = sin(t), theta ~ omega*t+pi/2 is a circular trajectory.

We wrote some papers about trajectory planning for a skid-steer robot which needs to track a trajectory, from a conceptual point of view your problem is not much different.

At each sampling step we evaluate the coordinates the robot must should have, then the difference with actual robot coordinates is given to the controller.

Don't forget you usually work with a linearized model, thus you should take into account the relevant nominal state.

Abbas Miry Hi, I opened that file but I can't understand what it does and how to eventually give a "customized" trajectory (i.e. a circumference).

Jagannath Samantaray A is 12x12, B is 12x4, C is 12x12 (identity matrix) and D is just zero.

Vito Antonio Nardi hi, I'm using a state feedback LQR control (as you can see from the K matrix in negative feedback). If I put a step as a input, all the state variables goes to zero, which I think is right because the quadcopter is in hovering condition. What I don't understand is how to give the input to make it follow a circumference (i.e.) or any other pre-established path.

P.S. possiamo parlare in italiano se per te va bene

Il problema è che se scriviamo in italiano qualcun altro che leggesse la domanda non potrebbe beneficiarne, eventualmente scrivimi in privato.

I see it's a state feedback but I don't know the model, I can assume it's 3D coordinates + 3D velocities + 3 axis angles + 3 axis angles rotational velocities, anyway this makes not so much difference.

I can assume the four inputs are the speeds of the four rotors.

You have a nominal velocity for the four rotors which is allows the quadrotor to fly at an equilibrium point, let's call it U0.

Then you should apply a U0+dU control action in order to control system state E to the desired value E0, with dU = K(E0-E).

Basically LQR allowed you to create a controller which controls to zero the state of a system, now you should be smart in using it in the right way.

Your problem is "how to generate the reference E?".

It should be a 12x1 signal, assuming states are ordered as I wrote before, 3D speeds should be 0, same for pitch, roll, and the three angular velocities.

You must then define proper values of x,y,z and yaw coordinates.

For a circular trajectory on a plane:

*x = Rcos(omega*t)

*y = Rsin(omega*t)

*z = h

*yaw = omega*t + pi/2

with omega the angular velocity, R the radius of the trajectory and h the altitude.

Vito Antonio Nardi the idea about giving a 12x1 input and only defining x,y,z and yaw was the same as mine, but I can't understand how to implement it in Simulink because the system only takes 4 inputs, which are not the rotors speed, but an upward force on the z axis and roll, pitch and yaw rate.

What I can't understand is how to "translate" my x,y,z,yaw desired into something that the system can understand.