A STABLE HIERARCHICAL FUZZY CONTROL DESIGN FOR CERTAIN NON-LINEAR SYSTEMS BASED ON INPUT–OUTPUT PASSIVITY THEORY

C. Xu∗ and Y.C. Shin∗∗

Keywords

Fuzzy control, adaptive systems, non-linear control, stability

Abstract

In this paper, a hierarchical fuzzy control algorithm is designed with the auto-tuning ability for certain non-linear systems. The resultant closed-loop system remains stable not only for an open-loop stable system but also for a certain open-loop unstable system, whose augmentation is passive stable. The design of the fuzzy control scheme is straightforward, which is based on human knowledge in terms of linguistic rules instead of mathematical models. The stability of the resultant closed-loop system is mathematically proven in both continuous and discrete domains. The proposed hierarchical fuzzy control scheme can be used to control both single variable systems and multivariable systems. In the simulation example, the control performance of the hierarchical fuzzy controller is compared with an input-state linearization non-linear controller for an unstable non-linear magnetic bearing system and a non- linear adaptive controller for a multivariable chemical pressure tank system. Much better system performances are achieved with the hierarchical fuzzy controller to stabilize the system in the presence of unknown external disturbances and model parameter variations.

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