Stabilization of Unstable Equilibrium Postures of a Two-Link Pendulum Using a Flywheel

摘要

The planar double-link pendulum has three unstable equilibrium postures. We want to design control laws to stabilize each unstable posture. A flywheel equips the first link. This flywheel is actuated by an electrical drive. The control signal (voltage) is applied to the drive, and our double-link pendulum is an underactu-ated system. We show that this system is controllable. The number of unstable modes, one or two, depends on the posture. Then, the control laws are designed to suppress the unstable modes, using the linear models of the motion near each unstable equilibrium posture. These control laws are nonlinear, since the saturation of the voltage is taken into account explicitly. Numerical investigations of the nonlinear models with the designed control laws are presented in each case.