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

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

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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.

Inspec keywords: milling; PI control; asymptotic stability; stability criteria; robust control; MIMO systems; fuzzy control; optimisation; absolute stability; linear matrix inequalities

Other keywords: extended circle criterion; robust stability improvement; control loop dynamics; milling process; multiple-input multiple-output circle criterion; PI-like fuzzy control systems; circle criteria; real-time application; linear matrix inequality; linearised plant model; finite domain; absolute stability; convex optimisation; local asymptotic stability; uncertain plant gain; industrial environment; asymptotic stability criteria; scalar case

Subjects: Optimisation techniques; Stability in control theory; Machining; Optimisation; Control technology and theory (production); Fuzzy control; Multivariable control systems; Control applications in machining processes and machine tools

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