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

摘要

There are many publications on the stabilization of an inverted pendulum because it is a typical unstable system and is well used as an example to verify many control theories. However, few approaches consider the inverted pendulum as an 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 all of whose parameters are unknown. The control system provides two kinds of adaptive controllers, and stabilization of the inverted pendulum is achieved by separating the system into two parts, the pendulum and the rotary arm. The rotational angle of the pendulum is stabilized by a tracking-type VSS adaptive control method, and the rotary arm is simultaneously stabilized by an STC (self-tuning control) system that assures the boundary reference angle of the pendulum. It is then not sufficient to construct an STC system using only the adjustable parameters of the VSS adaptive control system. Therefore, all basic parameters are recursively estimated in order to realize the STC system by using the least squares parameter adaptive law, and this is achieved by superimposing the perturbation signal on the stable adaptive control input over a limited short interval. Furthermore, the STC system designs an LQ controller by developing an efficient QR method for real-time operation. Finally, the validity of the proposed system is demonstrated by numerical simulations and practical experimental results. 【Keywords】 inverted pendulum; VSS adaptive con-trol; self-tuning control; least-squares adaptive law;Lyapunov function