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.
DESCARGAR ARTÍCULO EN FORMATO PDF
References
1. Aguilar, L.T., Orlov, Y., Cadiou, J.C. & Merzouki, R. (2007). Nonlinear H∞ –output regulation of a nonminimum phase servomechanism with backlash. Journal of Dynamic Systems, Measurement and Control, 129(4), 544–549. [ Links ]
2. Castillo, 0., Lozano, A. & Melin, P. (2004). Hierarchical genetic algorithms for fuzzy system optimization in intelligent control. IEEE Annual Meeting of the National Association of Fuzzy Information, Banff, Canada, 292–297. [ Links ]
]]>3. Castillo, O. & Melin, P. (2008). Type–2 Fuzzy Logic: Theory and Applications. New York: Springer–Verlag. [ Links ]
4. Castillo, O., Aguilar, L.T., Cazarez, N. & Cardenas, S. (2008). Systematic design of a stable type–2 fuzzy logic controller. Journal of Applied Soft Computing, 8(3), 1274–1279. [ Links ]
5. Cazarez–Castro, N. R., Aguilar, L.T. , Castillo, O. & Cardenas, S. (2008). Fuzzy Control for Output Regulation of a Servomechanism with Backlash. In Castillo O., Melin, P., Kacprzyk J., Pedrycz W. (Eds.), Soft Computing for Hybrid Intelligent Systems (19–28). Berlin: Springer–Verlag. [ Links ]
6. Cazarez–Castro, N.R., Aguilar, L.T. & Castillo, O. (2008). Hybrid Genetic–Fuzzy Optimization of a Type–2 Fuzzy Logic Controller. Eighth International Conference on Hybrid Intelligent Systems, Barcelona, España, 216–221. [ Links ]
7. Cazarez–Castro, N.R., Aguilar, L.T., Castillo, O. & Rodriguez, A. (2008). Optimizing Type–1 and Type–2 Fuzzy Logic Systems with Genetic Algorithms. Research in Computing Science, 39, 131–153. [ Links ]
]]>8. Cazarez–Castro, N.R., Aguilar, L.T. & Castillo, O. (2008). Genetic optimization of a type–2 fuzzy controller for output regulation of a servomechanism with backlash. 5th International Conference on Electrical Engineering, Computing Science and Automatic Control, Ciudad de Mexico, Mexico, 268–273. [ Links ]
9. Cazarez–Castro, N.R., Aguilar, L.T. & Castillo, O. (2009). Designing type–1 fuzzy logic controllers via fuzzy Lyapunov synthesis for nonsmooth mechanical systems. Congreso Anual 2009 de la Asociacion de Mexico de Control Automatico, Zacatecas, Mexico, cd–rom. [ Links ]
10. Grefenstette, J.J. (1986). Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man, and Cybernetics, 16(1), 122–128. [ Links ]
11. Isidori, A. (1995). Nonlinear Control Systems. New York: Springer–Verlag. [ Links ]
12. Isidori, A. (2000). A tool for semi–global stabilization of uncertain non–minimum–phase nonlinear systems via output feedback. IEEE Transactions on Automatic Control, 45(10), 1817–1827. [ Links ]
]]>13. Khalil, H. K. (2002). Nonlinear Systems. New Jersey: Prentice Hall. [ Links ]
14. Lagerberg, A. & Egardt, B. (2003). Estimation of backlash with application to automotive powertrains. 42nd Conference on Decision and Control, 5, Maui, USA, 4521–4526. [ Links ]
15. Lee, M.A. & Takagi, H. (1993). Integrating design stage of fuzzy systems using genetic algorithms. Second IEEE International Conference On Fuzzy Systems, San Francisco, USA, 612–617. [ Links ]
16. Mamdani, E.H. (1976). Advances in the linguistic synthesis of fuzzy controllers. International Journal of Man– Machine Studies, 8(6), 669–678. [ Links ]
17. Mamdani, E.H. & Assilian, S. (1975). An experiment in linguistic synthesis with fuzzy logic controller. International Journal of Man–Machine Studies, 7(1), 1–13. [ Links ]
]]>18. Margaliot, M. & Langholz, G. (1998). Adaptive fuzzy controller design via fuzzy Lyapunov synthesis. The 1998 IEEE International Conference on Fuzzy Systems, 1, Archorage, AK, USA, 354–359. [ Links ]
19. Melin, P. & Castillo, O. (2001). Intelligent control of complex electrochemical systems with a neuro–fuzzy–genetic approach. IEEE Transactions on Industrial Electronics., 48(5), 951–955. [ Links ]
20. Mendel, J.M. (2007). Computing with words: Zadeh, Turing, Popper and Occam. IEEE Computational Intelligence Magazine, 2(4), 10–17. [ Links ]
21. Merzouki, R., Cadiou, J.C. & M'Sirdi, N.K. (2004). Compensation of friction and backlash effects in an electrical actuator. Journal of System And Control Engineering, 218(2), 75–84. [ Links ]
22. Nordin, M. P., Bodin, P. & Gutman, P. (2001). New Models and Identification Methods for Backlash and Gear Play. In Tao G., Lewis F.L. (Eds.), Adaptive Control of Nonsmooth Dynamic Systems (1–30). Berlin: Springer–Verlag. [ Links ]
]]>23. Zadeh, L.A. (1996). Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems, 4(2), 103–111. [ Links ]
]]>