Experimental results for almost global asymptotic and locally exponential stabilization of the natural equilibria of a 3D pendulum

Feedback controllers that guarantee asymptotic stabilization of either the hanging equilibrium or the inverted equilibrium of the 3D pendulum are presented and experimentally evaluated using the triaxial attitude control testbed (TACT). Asymptotic stabilization results obtained previously are shown to guarantee almost global response properties, but the local response properties near the equilibrium show non-exponential convergence. These feedback controllers are modified to guarantee almost global response properties and improved local response near the equilibrium. Experimental results illustrate the closed loop time responses for various feedback controllers