The SAM chips have ARM cores, so you should look compiliing with arm-none-eabi-gcc and flashing/debugging with openocd instead.
OpenOCD is a program that communicates with debugging probes for a number of processor/microcontroller architectures, analogous to avrdude for AVR. You will have to figure out how to configure openocd to talk to your board. A quick ...
I am assuming that the desired application would be to control a quadrotor drone or similar platform.
The scalar representations of distance shown in the paper above can be represented in 2 ways (that I see). You could extend from the 2d plane to the 3d plane using the same vector norm function as before. This would mean that the mathematical operations ...
As you pointed out, $y=f\left(u\right)$ is a static map, hence it does not represent in any way the temporal evolution of a dynamical system.
With this in mind, resorting to an observer is fundamentally a wrong approach. An observer, in fact, provides you with an estimate of the temporal evolution of the dynamical system under subject; however, here $f\left(\...
Consider the traditional control diagram below.
If you set $C=(2\zeta\omega_ns+\omega_n^2)/(0.13s+1)$, then you'll get the following closed-loop system transfer function:
This can be achieved through zero-pole cancelation, which is doable since $G$ has a zero in LHP.
Steps one should take to eventually write a flight controller software:
Learn the mathematics and physics laws behind the airplanes, helicopters, multi-rotors, etc.
Electronics is a huge field and learning the robotics related stuff would be enough.
Learn how computers work.
The electronics behind a computer. How does ...