Achieving an Equilibrium Position of Pendubot Via Swing-Up and Stabilizing Model Predictive Control

In this paper, a complex control strategy to swing-up and balance the under-actuated pendubot system in one of its unstable equilibrium positions is presented. The initial swing-up maneuver is performed using an energy-based approach. For the purposes of stabilizing the system in its mid unstable equilibrium position a model predictive controller based on optimal control law with integral action is proposed. Satisfaction of constraints is ensured by introducing perturbations in the LQ control law acting as corrections when input amplitude/rate bounds are to be exceeded. The stability issue is addressed via additional constraints imposed on the terminal set. The emphasis of the paper is on the experimental realization of the pendubot swing-up followed by its balancing, which reveals the accuracy of the proposed control scheme.