[adciv]

We covered this in non-linear control theory. Take a model of your system, in this case angle vs. the force required to hold the arm in place and then invert it.

Mathematically, we describe it as this (provided I remember it correctly):
You have some system for which y = f(x) where x is you control signal.
There is another system for which g(f(x)) = x.
You can treat your system as a linear system if you use g(x) as your control signal.