Artículos

 

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

 

Diseño de controladores difusos tipo–1 a través de La Síntesis Difusa de Lyapunov para sistemas mecánicos no suaves: el caso perturbado

 

Nohe Ramón Cazarez Castro¹, Luis Tupak Aguilar Bustos² and Oscar Castillo López³

 

¹ Facultad de Ciencias Químicas e Ingeniería, Universidad Autónoma de Baja California, Tijuana, México. Email: nohe@ieee.org

² Centro de Investigación y Desarrollo de Tecnología Digital, Instituto Politécnico Nacional Tijuana, México. Email: luis.aguilar@ieee.org

³ División de Estudios de Posgrado e Investigación, Instituto Tecnológico de Tijuana, Tijuana, México. Email: ocastillo@hafsamx.org

 

Article received on December 15, 2009
Accepted on March 23, 2010

 

Abstract

Fuzzy Lyapunov Synthesis is extended for the design of type–1 fuzzy logic controllers for an output regulation problem for a servomechanism with backlash. The problem in question 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. Provided the servomotor position is the only measurement available for feedback, the proposed extension is far from trivial because of nonminimum phase properties of the system. Performance issues of the fuzzy regulator constructed are illustrated in an experimental study.

Keywords: Fuzzy Control, Fuzzy Lyapunov Synthesis, Stability, Nonsmooth systems.

 

Resumen

La Síntesis Difusa de Lyapunov se extiende para el diseño de controladores difusos tipo–1 para un problema de regulación de salida de un servomecanismo con backlash. El problema en cuestión es el diseño de un controlador retroalimentado para obtener el sistema de lazo cerrado en el cual todas las trayectorias están acotadas y la carga del mecanismo se regula en una posición determinada a la vez que atenúa la influencia de perturbaciones externas. La posición del servomotor es la única medida disponible para retroalimentación, la propuesta está lejos de ser trivial debido a las propiedades de fase no mínima del sistema. El funcionamiento de los reguladores difusos construidos se muestran en un estudio experimental.

Palabras clave: Control Difuso, Síntesis Difusa de Lyapunov, Estabilidad, Sistemas no suaves.

 

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