VSS Robust Adaptive Control Including a Self-Tuning Controller for a Rotary Inverted Pendulum

Abstract

So many papers with respect to the stabilization of the inverted pendulum are reported, because it is typically unstable system and is well used as example to verify many control theories. However, few approaches consider the inverted pendulum as unknown parameter system. This paper proposes a new VSS (Variable Structure System) robust adaptive control system including a self-tuning controller for a rotary inverted pendulum whose whole parameters are unknown. The control system prepares two kinds of adaptive controllers, and the stabilization of inverted pendulum is achieved by separating the system to two parts of the pendulum and the rotary arm. The rotational angle of the pendulum is stabilized by tracking type's VSS adaptive control method, and the rotary arm is simultaneously stabilized by STC (self-tuning control) system that assures the boundary reference angle of the pendulum. It is then not sufficient to construct STC system by using only adjustable parameter of VSS adaptive control system. Therefore, whole basic parameters are recursively estimated in order to realize STC system by using least squares parameter adaptive law, and it is achieved by superposing the perturbation signal to the stable adaptive control input on limited short interval. Furthermore, STC system designs LQ controller by developing an efficient QR method for real time operation.
Finally, the validity of the proposed system is demonstrated through some numerical simulations and practical experimental result.