Design of Hybrid Controller using Qualitative Simulation Internal Modeling for Inverted Pendulum

Abstract

Multiple model methods for nonlinear dynamical system control are appealing because local models can be simple and obvious, and global dynamics can be studied in terms of transitions between small operating zones. In this study, we propose that using qualitative models strengthens the multiple model method even more by enabling each local model to explain a huge class of effective nonlinear dynamical systems. Furthermore, reasoning using qualitative models reveals weak necessary conditions sufficient to verify qualitative features like stability analysis. The authors show the method by creating a global controller for the free pendulum. In addition, local controllers are specified and validated by comparing their patterns to basic general qualitative models. Our proposed procedure establishes qualitative limitations on controller designs that are sufficient to ensure the necessary local attributes and to establish feasible transitions between local areas for the existing problems. As a result, the continuous phase picture may be reduced to a simple transitional graph. The degrees of freedom in the system that are not bound by the qualitative description are still accessible to the designer for optimization for any other purpose. An example of a pendulum plant illustrates the effectiveness of the proposed method.