Multivariable circle criterion: stable fuzzy control of a milling process

Finding for a complex control plant an analytical model that is detailed enough for controller design is often hard or even impossible. In such cases the regulation of the system can be performed by knowledge-based fuzzy control. Under the assumption that there exists a locally valid linear description for the plant the stability problem of the nonlinear fuzzy control-loop can be addressed with the multivariable circle criterion, e.g. in linear-matrix-inequality format. The application of that stability criterion is demonstrated for fuzzy control of a nonlinear parameter-varying milling process and approved in both simulations and real-time application.