Implementação de lei de comutação restrita para controle de sistemas lineares comutado
Palavras-chave:
sistemas lineares comutados, lei de comutação restrita, função quadrática de lyapunov, desigualdade de matriz linearResumo
Uma classe especial de sistemas lineares comutados com lei de comutação restrita a entrada de estado lógico pode ser empregada para modelar uma ampla gama de diferentes sistemas. O presente artigo apresenta um novo método de análise de estabilidade e design de controlador para esta classe de sistemas híbridos. Os métodos propostos são baseados na função quadrática de Lyapunov. A análise de estabilidade e o projeto desses sistemas resultaram na solução de um problema de otimização convexa do tipo Desigualdade de Matriz Linear. Os resultados da simulação no conversor dc-dc buck confirmam a eficácia do método proposto.
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Referências
Beccuti, A., Mariethoz, S., Cliquennois, S., Wang, S., Morari, M. (2009). “Explicit model predictive control of DC-DC switched mode power supplies with extended Kalman filtering” IEEE Trans. Ind. Electron., Vol. 56, No. 3, pp. 1864–1874.
Bemporad, A., Borrelli, F., Morari, M. (2002). “Model predictive control based on linear programming—The explicit solution,” IEEE Trans. Autom. Control, Vol. 47, pp. 1974–1985.
Bemporad, A., Morari, M. (1999). “Control of systems integrating logic, dynamics, and constraints,” Automatica, Vol. 35, No. 3, pp. 407– 427.
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Philadelphia, The SIAM press.
Ge, S.S., Sun, Z. (2008). “Switched Controllability via Bumpless Transfer Input and Constrained Switching,” IEEE Trans. On Automatic Control, Vol. 53, No. 7.
Greco, L. (2005). “Stability and Stabilization Issues in Switched Systems,” PHD thesis, Bioingegneria, Robotica e Sistemi di Automazione Industriale - Ciclo XVII.
Hejri, M., Mokhtari, H. (2009). “Global hybrid modeling and control of a buck converter: A novel concept,” International Journal of Circuit Theory and Applications, Vol 37, pp 968–986.
Hejri, M., Mokhtari, H. (2010). “Hybrid predictive control of a DC–DC boost converter in both continuous and discontinuous current modes of operation,” Optimal Control Applications and Methods.
Johansson, M. (2002). Piecewise Linear Control Systems-A Computational Approach, New York: Springer-Verla, Vol, 284.
Lin, H., Panos, J. (2009). Antsaklis, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results,” IEEE Trans. Automatic Control, Vol. 54, No. 2.
Pettersson, S., Lennartson, B. (2001). “Stabilization of hybrid systems using a min projection strategy,” in Proc. Amer. Control Conf, pp. 223– 228.
Pettersson, S., Lennartson, B. (2002). “Hybrid system stability and robustness verification using linear matrix inequalities,” Inter. J. Control, Vol. 75,N. 16-17, pp. 1335–1355.
Rantzer, A., Johansson, M. (2000). “Piecewise linear quadratic optimal control,” IEEE Trans. Automat Control, Vol. 45, No. 4, pp. 629–637.
Rodrigues, L. (2002). "Dynamic Output Feedback Controller Synthesis for Piecewise Affine Systems," PhD Thesis, Stanford university.
Rodrigues, L., How, J.P. (2003). “Observer-based control of piecewise-affine systems,” Internat. J. Control, Vol. 76, pp. 459–477.
Sen, M., A. Ibeas, A.(2008) “Stability Results for Switched Linear Systems with Constant Discrete Delays,” Mathematical Problems in Engineering, vol. 2008.
Shorten, R., Wirth, F., Mason, O., Wulff, K., King, K. (2007). “Stability Criteria for Switched and Hybrid Systems,” SIAM REVIEW, Vol. 49, No. 4, pp. 545–592.
Sulistyaningsih, D., & Aziz, A. (2018). Development of Learning Design for Mathematics Manipulatives Learning based on E-learning and Character Building. International Electronic Journal of Mathematics Education, 14(1), 197-205.
Sun, Z., Shuzhi S.G. (2004). Switched Linear Systems: Control and Design, Springer-Verlag Publication.
Uhlig, F. (1979). “A recurring theorem about pairs of quadratic forms and extensions: A survey,” Linear Algebra and Applications, Vol. 25, pp 219-237.
Yakubovich, V.A. (1977). “The S procedure in non-linear control theory,” Vestnik Leningrad Univ. Math, Vol. 4, pp 73-93.
Bemporad, A., Borrelli, F., Morari, M. (2002). “Model predictive control based on linear programming—The explicit solution,” IEEE Trans. Autom. Control, Vol. 47, pp. 1974–1985.
Bemporad, A., Morari, M. (1999). “Control of systems integrating logic, dynamics, and constraints,” Automatica, Vol. 35, No. 3, pp. 407– 427.
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Philadelphia, The SIAM press.
Ge, S.S., Sun, Z. (2008). “Switched Controllability via Bumpless Transfer Input and Constrained Switching,” IEEE Trans. On Automatic Control, Vol. 53, No. 7.
Greco, L. (2005). “Stability and Stabilization Issues in Switched Systems,” PHD thesis, Bioingegneria, Robotica e Sistemi di Automazione Industriale - Ciclo XVII.
Hejri, M., Mokhtari, H. (2009). “Global hybrid modeling and control of a buck converter: A novel concept,” International Journal of Circuit Theory and Applications, Vol 37, pp 968–986.
Hejri, M., Mokhtari, H. (2010). “Hybrid predictive control of a DC–DC boost converter in both continuous and discontinuous current modes of operation,” Optimal Control Applications and Methods.
Johansson, M. (2002). Piecewise Linear Control Systems-A Computational Approach, New York: Springer-Verla, Vol, 284.
Lin, H., Panos, J. (2009). Antsaklis, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results,” IEEE Trans. Automatic Control, Vol. 54, No. 2.
Pettersson, S., Lennartson, B. (2001). “Stabilization of hybrid systems using a min projection strategy,” in Proc. Amer. Control Conf, pp. 223– 228.
Pettersson, S., Lennartson, B. (2002). “Hybrid system stability and robustness verification using linear matrix inequalities,” Inter. J. Control, Vol. 75,N. 16-17, pp. 1335–1355.
Rantzer, A., Johansson, M. (2000). “Piecewise linear quadratic optimal control,” IEEE Trans. Automat Control, Vol. 45, No. 4, pp. 629–637.
Rodrigues, L. (2002). "Dynamic Output Feedback Controller Synthesis for Piecewise Affine Systems," PhD Thesis, Stanford university.
Rodrigues, L., How, J.P. (2003). “Observer-based control of piecewise-affine systems,” Internat. J. Control, Vol. 76, pp. 459–477.
Sen, M., A. Ibeas, A.(2008) “Stability Results for Switched Linear Systems with Constant Discrete Delays,” Mathematical Problems in Engineering, vol. 2008.
Shorten, R., Wirth, F., Mason, O., Wulff, K., King, K. (2007). “Stability Criteria for Switched and Hybrid Systems,” SIAM REVIEW, Vol. 49, No. 4, pp. 545–592.
Sulistyaningsih, D., & Aziz, A. (2018). Development of Learning Design for Mathematics Manipulatives Learning based on E-learning and Character Building. International Electronic Journal of Mathematics Education, 14(1), 197-205.
Sun, Z., Shuzhi S.G. (2004). Switched Linear Systems: Control and Design, Springer-Verlag Publication.
Uhlig, F. (1979). “A recurring theorem about pairs of quadratic forms and extensions: A survey,” Linear Algebra and Applications, Vol. 25, pp 219-237.
Yakubovich, V.A. (1977). “The S procedure in non-linear control theory,” Vestnik Leningrad Univ. Math, Vol. 4, pp 73-93.
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Publicado
2018-08-30
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Kashisaz, S., & Manna, M. (2018). Implementação de lei de comutação restrita para controle de sistemas lineares comutado. Amazonia Investiga, 7(15), 367–385. Recuperado de https://amazoniainvestiga.info/index.php/amazonia/article/view/468
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