Passivity based control of the double inverted pendulum driven by a linear induction motor

In this paper, we propose a nonlinear passivity based controller for a double inverted pendulum system, consisting of a two-link pendulum mounted on a pad which is moved by a linear induction motor so that the double pendulum points straight-up. The proposed controller not only can drive the double pendulum from its "natural stable hanging position" to its "unstable upright inverted position" while linear the induction motor\´s displacement is brought to zero but also can guarantee that the motor with very unique end-effect can achieve servo motion tracking with high performance. Also, computer simulations are provided to demonstrate the effectiveness of the hereby presented controller design.