Using circle criteria for verifying asymptotic stability in PI-like fuzzy control systems: application to the milling process

A fuzzy controller that is suitable for regulating the milling process and ensuring absolute stability with a finite domain (i.e. local asymptotic stability) is presented. The stability analysis is performed on the basis of two versions of the circle criterion: (i) the extended circle criterion reducing the problem to the scalar case; and (ii) the multiple-input multiple-output circle criterion, here stated using a linear matrix inequality in order to profit from the advantages of convex optimisation. In order to verify the robust stability of the fuzzy control system, the plant gain is considered to be uncertain, and the allowed range for this uncertainty is maximised. Simulations based on the linearised plant model demonstrate how the improvement of robust stability affects the dynamics of the control loop. The robust stability improvement turns out to also yield a better fuzzy controller performance. A real-time application proves both stability and dynamic performance in an industrial environment.