A Proposal of Fuzzy Rule Partition and Its Application to Controller Design Based on Affine T-S Fuzzy Model

When designing a controller based on a fuzzy model composed of fuzzy rules, in most cases controllers are designed only based on the consequent parts of the fuzzy rules, equally meaning the information of the antecedent parts is merely ignored. This paper first partitions all of the rules into two groups based on the information of the antecedent parts, in which one contains certain rules around the origin, and the other is a group of rules away from the origin. While being able to make the former arbitrarily small, each rule of the latter leads to a favorable quadratic inequality, which will be useful in controller design by the help of the S-procedure. On the other hand, while the affine T-S fuzzy model is much more effective for describing the dynamics of the system concerned in comparison with the regular T-S fuzzy model, it encounters some difficulties when designing a controller based on the model because of the affine terms within. This paper makes clear that the difficulties can be overcame by using the quadratic inequalities based on the fuzzy rule partition. In addition, the effectiveness of the approach is demonstrated by applying it to the CSTR for an exothermic irreversible reaction. (c) 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.