Study on subspace control based on modal analysis (2nd report, swing-up control of double-parallel inverted pendulum system by using nonlinear resonance)

The purpose of this study is to establish a dynamic control procedure that utilizes the kinetic properties of a control subject as much as possible. The subspace control method detailed in the first report is one method that could satisfy this criterion. In subspace control, the state equation of a system is represented by modal coordinates, and certain modes that need to be controlled are selected and controlled This control method allows for the simplification of control subjects and for increased flexibility. In this report, subspace control is applied to the swinging-up and stabilization of a double parallel inverted pendulum system. More specifically, there is a process that the system is working to stabilize a pendulum while during the up-swing of another pendulum. Due to the interference between the two, it is difficult to control the system in the process. In order to reduce the influence of the interference, a new swing up technique that employs a nonlinear resonance is proposed. This technique causes the nonlinear resonance of a pendulum by moving a cart vibrationally. The effectiveness of the proposed control method is verified by numerical simulation and experiment.