15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
EXTENDED CIRCLE CRITERION: STABLE FUZZY CONTROL OF A MILLING PROCESS
R. E. Haber Guerra1, G. Schmitt-Braess2, R. H. Haber3, A. Alique1, S. Ros1
1 Instituto de Automática Industrial (CSIC). km. 22800 N-III, La Poveda. 28500.
Madrid. SPAIN. email:rhaber@iai.csic.es
2 Universität Erlangen-Nürnberg. Lehrstuhl für Regelungstechnik. Cauerstraße 7
D-91058 Erlangen. GERMANY. gabriele.schmitt-braess@rzmail.uni-erlangen.de
3 Departamento de Control Automático. Universidad de Oriente. CUBA

In this work, the Extended Circle Criterion and fuzzy approaches are combined to develop a practical tech-nique for checking stability of Fuzzy Control Systems (FCS). The controller is designed on the basis of skilled operator criteria and engineering knowledge about the process. Afterwards, stability is verified by means of the so-called Extended Circle Criterion, under the assumption that the static characteristic of the controller is sector-bounded (nonlinear portion) and the process (linear portion) can be rendered Strictly Positive Real (SPR). The method is tested in a FCS applied to the milling process. Theoretical and experimental results show that the closed loop system is stable. Moreover, suitable scaling factors of the controller for a robustly stable perform-ance are provided
Keywords: Fuzzy control, nonlinear systems, absolute stability, knowledge-based systems, machining
Session slot T-Mo-M04: Fuzzy control theory/Area code 3e : Fuzzy and Neural Systems