Nonlinear Optimal Internal Forces Control and Application to Swing-Up and Stabilization of Pendulum

Internal forces are brought by the connection of a multilink mechanism as integrated effects of constraint forces at joints, centrifugal/Coriolis forces, and external forces. In this paper, in order to enhance a performance in the stabilization of the total system, the internal forces are considered to be reduced by the nonlinear regulation based on a State-Dependent Riccati Equation (SDRE), where the internal forces are derived by a projection method. The dynamics of individual components and the relations of the constraint motions yield the dynamic model of whole system. Considering a criterion function of which integrands consist of the conventional quadratic forms with the state-dependent weighting matrices, a nonlinear optimal control law for the criterion function, named nonlinear state-dependent controller, is determined by solving the SDRE in real time. As the results of the proposed control, system’s mechanical components would not receive large internal forces and the control performance has been improved. The proposed method is effectively demonstrated by an experiment of a global stabilization control of the 1-link Furuta pendulum at the upright position.