Designing Type-1 Fuzzy Logic Controllers via Fuzzy Lyapunov Synthesis for Nonsmooth Mechanical Systems: The Perturbed Case

Abstract— In this paper Fuzzy Lyapunov Synthesis is extended to the design of Type-1 Fuzzy Logic Controllers for nonsmooth mechanical systems. The output regulation problem for a servomechanism with nonlinear backlash is proposed as a case of study. The problem at hand is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. The servomotor position is the only measurement available for feedback; the proposed extension is far from trivial because of the nonminimum phase properties of the system. Performance issues of the Type-1 Fuzzy Logic Regulators that were designed are illustrated in a simulation study.