# Control each axis separately - quadcopter

I would like to know why axis can be controlled independently in a quadcopter. I mean, I was told that you can control $$x$$ and $$y$$ independently but I couldn't find a demonstration

Edit: the testbench that is used when you want to see how the response of a quadcopter would be is a one arm quadcopter (i.e, just 2 propellers like this:

That testbench can be used because you can control how the response of the $$x$$ axis is and then use the $$y$$ axis. And, when you put both axis together, each axis response would be as they were in the testbench

How can we demonstrate that?

Or, the question would be: why you can use a one-arm testbench for a quadcopter?

• Do you mean translation of the entire quadcopter along the $x$ and $y$ axes? Dec 4, 2019 at 10:17
• Ah, you meant rotation around $x$ and $y$, that makes more sense. Dec 5, 2019 at 11:56

With that testbench you are only testing the tracking performance of the rotation around a given axis. The dynamics of each of those rotations is dominated by the inertia around that axis, also known as moment of inertia. The moment of inertia contribution of point masses around a given axis can defined as $$I=\sum_i m_i\,r_i^2$$, with $$m_i$$ and $$r_i$$ the mass and (shortest) distance to the rotation axis of each point mass respectively. The removed arms of the quadcopter would contribute to this inertia. However, its contribution will be very small, since the mass of those arms would be very close the axis of rotation and thus $$r_i$$ would be very small.