Linear Algebra Based Swing-Up Control of the Pendubot

The swing up control problem for the Pendubot refers to swinging up both of the two links to the top equilibrium point and balance them at that point. The balancing controller is usually designed based on the linearized model at the desired equilibrium. Therefore, the challenging task is to design a swing up controller that can bring the Pendubot within a neighborhood of the desired equilibrium in which it can be stabilized by the linear balancing controller. This paper presents a novel linear algebra based methodology for the swing up control of the Pendubot. By controlling the actuated link to converge to the top position while the unactuated one oscillates near that position, the Pendubot is eventually stabilized by the balancing controller once the switching condition is satisfied. Simulation and experimental results are provided and discussed, demonstrating the good performance of the proposed approach.