On bifurcation control of an underactuated mechanical device

D. M. ALONSO; E. E. PAOLINI; J. L. MOIOLA

Eindhoven

Congreso; Fifth Euromech Nonlinear Dynamics Conference; 2005

Eindhoven University of Technology

This paper deals with a (partial) global bifurcation analysis of a controlled underactuated mechanical system. The mechanical device is an inertia wheel pendulum consisting of a pendulum with a rotating disk at the end. The underlying constraint for swinging-up and stabilizing the pendulum at the inverted position is that the torque supplied to the disk from a small DC motor is not sufficient to dominate the effect of the gravity on the pendulum. The considered controller has a restricted magnitude output but ensures local stability of the upward position. After an analytical local bifurcation study, a numerical bifurcation analysis is performed to characterize the dynamical behavior over a larger domain. A partial two-parameter bifurcation diagram revealing a rich dynamical scenario helps to identify regions in the parameter space where the expected dynamical behavior is achieved. For example, selecting appropriately control gain values one can avoid complex behaviors and eventually achieve simultaneous stabilization of the upright position together with a large basin of attraction. The methodology presented here can be helpful to obtain new insights on the system dynamics to design more efficient controllers for mechanical systems.