Nonlinear Control of the Gyroscopic Pendulum

I watched it for some minutes, somewhat in fear, but more in wonder.. .. it seemed massy and heavy, tapering from the edge into a solid and broad structure above. It was appended to a weighty rod of brass, and the whole hissed as it swung through the air. Abstract In this paper we consider the nonlinear control of the Gyroscopic Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating mass at the end. We study the problem of swingup and balance of the pendulum, where the control input is the coupling torque produced by the angular acceleration of the end-mass. We show that the system is locally feedback linearizable by a local diieomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we compare two diierent energy based controllers; one based on passivity of the Lagrangian dynamics of the system and the other based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Both simulations and experimental results are presented.