Regulación no lineal de la salida para sistemas descriptores en tiempo discreto
Resumen
El presente trabajo propone un regulador no lineal en tiempo discreto para sistemas no lineales tipo descriptor. El diseño está dividido en dos partes: 1) un estabilizador no lineal calculado por medio del método directo de Lyapunov y modelos convexos, 2) un regulador lineal calculado a través de las llamadas ecuaciones de Francis-Isidori-Byrnes para modelos descriptores; las condiciones de diseño de ambas partes están en términos de desigualdades matriciales lineales. A diferencia de la teoría de regulación tradicional, se propone un exosistema desconocido, es decir, que las trayectorias se generan de forma arbitraria por algún otro sistema o usuario, un observador de alta ganancia estima dichas señales para utilizarlas, posteriormente, en el diseño del regulador.
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Belov, A. A., Andrianova, O. G., y Kurdyukov, A. P. (2018). Control of discrete-time descriptor systems. Cham: Springer International Publishing, 39.
Bernal, M., Marquez, R., Estrada-Manzo, V., y Castillo-Toledo, B. (2012). Nonlinear output regulation via Takagi-Sugeno fuzzy mappings: A fullinformation LMI approach. En 2012 IEEE International Conference on Fuzzy Systems, pp. 1–7. IEEE.
Bernal, M., Sala, A., Lendek, Z., y Guerra, T. M. (2022). Analysis and Synthesis of Nonlinear Control Systems: A Convex Optimisation Approach, volumen 408. Springer Nature
Boyd, S., Ghaoui, L. E., Feron, E., y Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, volumen 15. SIAM: Studies In Applied Mathematics, Philadelphia, USA.
Campbell, S. (1982). Singular systems of. Differential Equations II Pitman, New York.
Duan, G.-R. (2010). Analysis and design of descriptor linear systems, volumen 23. Springer Science & Business Media.
Estrada-Manzo, V., Guerra, T. M., Lendek, Z., y Pudlo, P. (2014). Discretetime Takagi-Sugeno descriptor models: controller design. En 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 2277–2281.
Estrada-Manzo, V., Lendek, Z., Guerra, T. M., y Pudlo, P. (2015). Controller design for discrete-time descriptor models: a systematic LMI approach. IEEE Transactions on Fuzzy Systems, 23(5):1608–1621.
Francis, B. (1977). The linear multivariable regulator problem. SIAM Journal of Control and Optimization, 15:486–505.
Gahinet, P., Nemirovskii, A., Laub, A. J., y Chilali, M. (1994). The LMI control toolbox. En Proceedings of 1994 33rd IEEE conference on decision and control, volumen 3, pp. 2038–2041. IEEE.
Galor, O. (2007). Discrete dynamical systems. Springer Science & Business Media.
Guerra, T. M. y Vermeiren, L. (2004). LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi-Sugeno’s form. Automatica, 40(5):823–829.
Hernandez-Cortes, T., Amador-Macias, M., Tapia-Herrera, R., y Meda-Campana, J. (2024). Output regulation for descriptor systems with high-gain observer used as exosystem for unmodeled references. IEEE Latin America Transactions, 22(2):156–65
Hernandez-Cortes, T., Amador-Macias, M., Tapia-Herrera, R., y Meda-Campaña, J. A. (2023). On the output regulation for an underactuated inverse pendulum when the exosystem is a high-gain observer. IEEE Access, 11:10792–10800.
Isidori, A. (1995). Nonlinear Control Systems. Springer, London, 3 edición.
Isidori, A. y Byrnes, C. I. (1990). Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 35(2):131–140.
Kumar, A. y Daoutidis, P. (1998). Control of nonlinear differential algebraic equation systems: an overview. Nonlinear model based process control, pp. 311–344.
Lin, W. y Dai, L. (1996). Solutions to the output regulation problem of linear singular systems. Automatica, 32(12):1713–1718.
Liu, X. y Zhang, Q. (2003). Approaches to quadratic stability conditions and H∞; control designs for T-S fuzzy systems. IEEE Transactions on Fuzzy Systems, 11(6):830–839.
Mahmoud, M. S. y Singh, M. G. (2012). Discrete systems: analysis, control and optimization. Springer Science & Business Media.
Ohtake, H., Tanaka, K., y Wang, H. O. (2001). Fuzzy modeling via sector nonlinearity concept. En Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference, volumen 1, pp. 127–132.
Oliveira, M. y Skelton, R. (2001). Stability tests for constrained linear systems. En Perspectives in robust control, volumen 268 de Lecture Notes in Control and Information Sciences, pp. 241–257. Springer-Verlag, Berlin.
Poblete, Luis A and Hernández-Cortés, Tonatiuh and Estrada-Manzo, Víctor and others (2022). On the nonlinear output regulation for systems described by takagi-sugeno fuzzy descriptor models with a steady-state mapping as an lmi optimization problem. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 9(18):85–91.
Saad, M., Shirazi, R. A., y Liaquat, M. (2018). Output regulation of n-link robotic manipulator using feedback linearizable systems under the approach of cascade high gain observers. En Proceedings of the 6th International Conference on Control, Mechatronics and Automation, pp. 16–20.
Takagi, T. y Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 15(1):116–132.
Tanaka, K. y Wang, H. (2001). Fuzzy Control Systems Design and Analysis: A linear matrix inequality approach. John Wiley & Sons, New York.
Tuan, H., Apkarian, P., Narikiyo, T., y Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Transactions on Fuzzy Systems, 9(2):324–332.
Wang, H., Tanaka, K., y Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4(1):14–23.
Wells, D. A. (1967). Lagrangian dynamics: With a treatment of Euler’s equations of motion, Hamilton’s equations and Hamilton’s principle. McGraw-Hill.
Derechos de autor 2024 Raúl Santillan, Nery Ortiz, Víctor Estrada-Manzo, Tonatiuh Hernández-Cortés, Jaime González-Sierra
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.