La regulación no lineal de la salida para sistemas descritos por modelos descriptores tipo Takagi-Sugeno con variedad estacionaria como un problema LMI de optimización

Palabras clave: Diseño de regulador no lineal, sistema descriptor, desigualdad matricial lineal, modelo Takagi-Sugeno

Resumen

Este artículo presenta una solución numérica al problema de regulación no lineal de salida para sistemas descriptores. La ley de control es no lineal y consiste en un estabilizador combinado con un mapeo lineal en estado estacionario así como una entrada de estado estacionario no lineal; todos ellos se calculan mediante desigualdades matriciales lineales. Se utilizan un ejemplo numérico y un sistema mecánico para ilustrar la viabilidad del enfoque propuesto.

Descargas

La descarga de datos todavía no está disponible.

Citas

Arceo, J. C., V´azquez, D., Estrada-Manzo, V., M´arquez, R., Bernal, M., 2016. Nonlinear convex control of the furuta pendulum based on its descriptor model. In: 2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE). IEEE, pp. 1–6.

Armenta, C., A´ lvarez, J.,Ma´rquez, R., Bernal,M., 2019. A practical solution to implement nonlinear output regulation via dynamic mappings. Kybernetika 55 (2), 385–401.

Bernal, M., Marquez, R., Estrada-Manzo, V., Castillo-Toledo, B., 2012a. An element-wise linear matrix inequality approach for output regulation problems. In: World Automation Congress 2012. IEEE, pp. 1–6.

Bernal, M., Marquez, R., Estrada-Manzo, V., Castillo-Toledo, B., 2012b.

Nonlinear output regulation via Takagi-Sugeno fuzzy mappings: A fullinformation LMI approach. In: 2012 IEEE International Conference on Fuzzy Systems. IEEE, pp. 1–7.

Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia, PA.

Castillo-Toledo, B., Di Gennaro, S., Jurado, F., June 2012. Trajectory tracking for a quadrotor via fuzzy regulation. In: World Automation Congress (WAC), 2012. pp. 1–6.

Chen, S., 2005. Output regulation of nonlinear singularly perturbed systems based on t-s fuzzy model. Journal of Control Theory and Applications 3 (4), 399–403.

Chiu, C.-S., Chiang, T.-S., Aug 2009. Robust output regulation of t–s fuzzy systems with multiple time-varying state and input delays. Fuzzy Systems, IEEE Transactions on 17 (4), 962–975. DOI: 10.1109/TFUZZ.2009.2017013

Duan, G.-R., 2010. Analysis and design of descriptor linear systems. Vol. 23. Springer Science & Business Media.

Fantoni, I., Lozano, R., Sinha, S., 2002. Non-linear control for underactuated mechanical systems. Appl. Mech. Rev. 55 (4), B67–B68.

Francis, B. A., 1977. The linear multivariable regulator problem. SIAM J. Cont. Optimiz. 15, 486–505.

Francis, B. A., Wonham, W. M., 1976. The internal model principle of control theory. Automatica 12, 457–465.

Gahinet, P., Nemirovskii, A., Laub, A. J., Chilali, M., 1994. The LMI control toolbox. In: Proceedings of 1994 33rd IEEE Conference on Decision and Control. Vol. 3. IEEE, pp. 2038–2041.

Hern´andez-Cort´es, T., Meda Campa˜na, J. A., P´aramo Carranza, L. A., G´omez Mancilla, J. C., 2015. A simplified output regulator for a class of takagi-sugeno fuzzy models. Mathematical Problems in Engineering.

Isidori, A., 1995. Nonlinear Control Systems. Springer, Berlin.

Isidori, A., Byrnes, C. I., 1990. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control 35 (2), 131–140.

Karamanos, K., Aguilar-Ibanez, C., Meda-Campana, J. A., Suarez-Castanon, M. S., Rubio, J. d. J., Cruz-Cortes, N., 2018. On the output regulation problem: The generalized second-order underactuated linear system case. Mathematical Problems in Engineering 2018, 3820935. URL: https://doi.org/10.1155/2018/3820935, DOI: 10.1155/2018/3820935

Lee, H. J., Park, J. B., Joo, Y. H., June 2003. Comments on output tracking and regulation on nonlinear system based on Takagi-Sugeno fuzzy model. IEEE Transactions on Systems, Man, and Cybertics-Part B:Cybernetics 33 (3), 521–523.

Lewis, F. L., Dawson, D. M., Abdallah, C. T., 2003. Robot manipulator control: theory and practice. CRC Press.

Lian, K.-Y., Liou, J.-J., 2006. Output tracking control for fuzzy systems via output feedback design. Fuzzy Systems, IEEE Transactions on 14 (5), 628–639. DOI: 10.1109/TFUZZ.2006.876725

Lin, W., Dai, L., 1996. Solutions to the output regulation problem of linear singular systems. Automatica 32 (12), 1713–1718.

Luenberger, D. G., 1979. Non-linear descriptor systems. Journal of Economic Dynamics and Control 1 (3), 219–242.

Ma, X.-J., qi Sun, Z., Feb 2000. Output tracking and regulation of nonlinear system based on takagi-sugeno fuzzy model. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 30 (1), 47–59. DOI: 10.1109/3477.826946

Meda-Campa˜na, J. A., Castillo-Toledo, B., Chen, G., 2009. Synchronization of chaotic systems from a fuzzy regulation approach. Fuzzy Sets and Systems 160.

Ohtake, H., Tanaka, K., Wang, H. O., 2003. Fuzzy modeling via sector nonlinearity concept. Integrated Computer-Aided Engineering 10 (4), 333–341.

Sturm, J. F., 1999. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization methods and software 11 (1-4), 625–653.

Tanaka, K., Sugeno, M., 1992. Stability analysis and design of fuzzy control systems. Fuzzy sets Syst. 45 (2), 135–156.

Tanaka, K., Wang, H. O., 2001. Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach. John Wiley and Sons, Inc.

Taniguchi, T., Tanaka, K., Wang, H. O., 2000. Fuzzy descriptor systems and nonlinear model following control. IEEE Transactions on Fuzzy Systems 8 (4), 442–452. DOI: 10.1109/91.868950

Taniguchi, T., Tanaka, K., Yamafuji, K., Wang, H. O., 1999. Fuzzy descriptor systems: stability analysis and design via lmis. In: Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251). Vol. 3. pp. 1827–

vol.3. DOI: 10.1109/ACC.1999.786165

Tapia-Herrera, R., Meda-Campa˜na, J. A., Alc´antara-Montes, S., Hern´andez-Cort´es, T., 2013. Tuning of a TS fuzzy output regulator using the steepest descent aproach and anfis. Mathematical Problems in Engineering 2013, 14.

Wang, H. O., Tanaka, K., Griffin, M., 1995. Parallel distributed compensation of nonlinear systems by takagi-sugeno fuzzy model. In: Proceedings of 1995 IEEE International Conference on Fuzzy Systems. Vol. 2. IEEE, pp. 531–538.

X.-Jun, M., Z.-Qi, S., February 2000. Output tracking and regulation on nonlinear system based on Takagi-Sugeno fuzzy model. IEEE Transactions on Systems, Man, and Cybertics-Part B:Cybernetics 30 (1), 47–59.

Xie, X., Yue, D., Ma, T., Zhu, X., 2014. Further studies on control synthesis of discrete-time TS fuzzy systems via augmented multi-indexed matrix approach. IEEE Transactions on Cybernetics 44 (12), 2784–2791.

Publicado
2022-01-05
Cómo citar
Poblete, L. A., Hernández-Cortés , T., & Estrada-Manzo, V. (2022). La regulación no lineal de la salida para sistemas descritos por modelos descriptores tipo Takagi-Sugeno con variedad estacionaria como un problema LMI de optimización. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 9(18), 85-91. https://doi.org/10.29057/icbi.v9i18.7649