A light weight rotary double pendulum: maximizing the domain of attraction

The usual application of feedback stabilization is based on linearization and the assumption of linear controllability. Least squares optimal control is often used to determine a set of feedback gains that will stabilize the system. In addition to the commonly acknowledged challenges arising when this methodology is applied to open-loop unstable systems with significant nonlinearities, there are also significant problems which are not given prominence in the literature. These include the role of high gain feedback in exciting vibrations in unmodeled modes and the possibility of lightly damped oscillatory modes accentuating the effect of the nonlinearities. In this paper we report some experimental results relating to these points and suggest some techniques for dealing with them.