Modeling and stabilization control of an underactuated double rotating pendulums system

Dynamical modeling, controllability condition and stabilization control design are presented for an underactuated double rotating pendulums system. Based on Lagrange equations, a dynamic model is derived by selecting the rotating angles of actuated arm and two pendulums as general coordinates of the system. Several important properties of the dynamics are also summarized. The dynamics are linearized around the unstable equilibrium to yield the controllability condition that the system is uncontrollable at the unstable equilibrium once the two pendulums are identical. According to the linearized model, a linear full state feedback controller is developed to stabilize the system at the unstable equilibrium. Finally, simulation results demonstrate the effectiveness of the prompted controller.