This paper faces two of the main drawbacks in networked control systems: bandwidth constraints and timevarying delays. The bandwidth limitations are solved by using multirate control techniques. The resultant multirate controller must ensure closed-loop stability in the presence of time-varying delays. Some stability conditions and a state feedback controller design are formulated in terms of linear matrix inequalities. The theoretical proposal is validated in two different experimental environments: a crane-based test-bed over Ethernet, and a maglev based platform over Profibus. © 2012 Ángel Cuenca et al. The authors A. Cuenca, R. Piza, and J. Salt are grateful to the Spanish Ministry of Education research Grants DPI2011-28507-C02-01 and DPI2009-14744-C03-03, and Generalitat Valenciana Grant GV/2010/018. A. Sala is grateful to the financial support of Spanish Ministry of Economy research Grant DPI2011-27845-C02-01, and Generalitat Valenciana Grant PROMETEO/2008/088. Cuenca Lacruz, ÁM.; Pizá, R.; Salt Llobregat, JJ.; Sala Piqueras, A. (2012). Linear matrix inequalities in multirate control over networks. Mathematical Problems in Engineering. 2012(768212):1-22. doi:10.1155/2012/768212 Tipsuwan, Y., & Chow, M.-Y. (2003). Control methodologies in networked control systems. Control Engineering Practice, 11(10), 1099-1111. doi:10.1016/s0967-0661(03)00036-4 Halevi, Y., & Ray, A. (1988). Integrated Communication and Control Systems: Part I—Analysis. Journal of Dynamic Systems, Measurement, and Control, 110(4), 367-373. doi:10.1115/1.3152698 Yang, T. C. (2006). Networked control system: a brief survey. IEE Proceedings - Control Theory and Applications, 153(4), 403-412. doi:10.1049/ip-cta:20050178 Cuenca, Á., Salt, J., Sala, A., & Piza, R. (2011). A Delay-Dependent Dual-Rate PID Controller Over an Ethernet Network. IEEE Transactions on Industrial Informatics, 7(1), 18-29. doi:10.1109/tii.2010.2085007 Tipsuwan, Y., & Chow, M.-Y. (2004). On the Gain Scheduling for Networked PI Controller Over IP Network. IEEE/ASME Transactions on Mechatronics, 9(3), 491-498. doi:10.1109/tmech.2004.834645 Hu, J., Wang, Z., Gao, H., & Stergioulas, L. K. (2012). Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities. IEEE Transactions on Industrial Electronics, 59(7), 3008-3015. doi:10.1109/tie.2011.2168791 Wing Shing Wong, & Brockett, R. W. (1999). Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback. IEEE Transactions on Automatic Control, 44(5), 1049-1053. doi:10.1109/9.763226 Casanova, V., Salt, J., Cuenca, A., & Piza, R. (2009). Networked Control Systems: control structures with bandwidth limitations. International Journal of Systems, Control and Communications, 1(3), 267. doi:10.1504/ijscc.2009.024556 Cuenca, A., García, P., Albertos, P., & Salt, J. (2011). A Non-Uniform Predictor-Observer for a Networked Control System. International Journal of Control, Automation and Systems, 9(6), 1194-1202. doi:10.1007/s12555-011-0621-5 Tian, Y.-C., & Levy, D. (2008). Compensation for control packet dropout in networked control systems. Information Sciences, 178(5), 1263-1278. doi:10.1016/j.ins.2007.10.012 Wang, Z., Shen, B., Shu, H., & Wei, G. (2012). Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements. IEEE Transactions on Automatic Control, 57(6), 1431-1444. doi:10.1109/tac.2011.2176362 Wang, Z., Shen, B., & Liu, X. (2012). H∞ filtering with randomly occurring sensor saturations and missing measurements. Automatica, 48(3), 556-562. doi:10.1016/j.automatica.2012.01.008 Ma, L., Wang, Z., Bo, Y., & Guo, Z. (2011). Finite-horizonℋ2/ℋ∞control for a class of nonlinear Markovian jump systems with probabilistic sensor failures. International Journal of Control, 84(11), 1847-1857. doi:10.1080/00207179.2011.627379 Li, J.-N., Cai, M., Wang, Y.-L., & Zhang, Q.-L. (2009). H∞ control of networked control systems with packet disordering. IET Control Theory & Applications, 3(11), 1463-1475. doi:10.1049/iet-cta.2008.0416 Time synchronization in a local area network. (2004). IEEE Control Systems, 24(2), 61-69. doi:10.1109/mcs.2004.1275432 Sala, A., Cuenca, Á., & Salt, J. (2009). A retunable PID multi-rate controller for a networked control system. Information Sciences, 179(14), 2390-2402. doi:10.1016/j.ins.2009.02.017 Sala, A. (2005). Computer control under time-varying sampling period: An LMI gridding approach. Automatica, 41(12), 2077-2082. doi:10.1016/j.automatica.2005.05.017 Salt, J., & Albertos, P. (2005). Model-based multirate controllers design. IEEE Transactions on Control Systems Technology, 13(6), 988-997. doi:10.1109/tcst.2005.857410 Cuenca, Á., Salt, J., & Albertos, P. (2006). Implementation of algebraic controllers for non-conventional sampled-data systems. Real-Time Systems, 35(1), 59-89. doi:10.1007/s11241-006-9001-2 Lall, S., & Dullerud, G. (2001). An LMI solution to the robust synthesis problem for multi-rate sampled-data systems. Automatica, 37(12), 1909-1922. doi:10.1016/s0005-1098(01)00167-4 Shi, Y., Fang, H., & Yan, M. (2009). Kalman filter-based adaptive control for networked systems with unknown parameters and randomly missing outputs. International Journal of Robust and Nonlinear Control, 19(18), 1976-1992. doi:10.1002/rnc.1390 Li, D., Shah, S. L., & Chen, T. (2002). Analysis of dual-rate inferential control systems. Automatica, 38(6), 1053-1059. doi:10.1016/s0005-1098(01)00295-3 Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory. doi:10.1137/1.9781611970777 Yun-Bo Zhao, Guo-Ping Liu, & Rees, D. (2009). Modeling and Stabilization of Continuous-Time Packet-Based Networked Control Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(6), 1646-1652. doi:10.1109/tsmcb.2009.2027714 Yang Shi, & Bo Yu. (2009). Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains. IEEE Transactions on Automatic Control, 54(7), 1668-1674. doi:10.1109/tac.2009.2020638 Shi, Y., & Yu, B. (2011). Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica, 47(4), 754-760. doi:10.1016/j.automatica.2011.01.022 Van Loan, C. (1978). Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control, 23(3), 395-404. doi:10.1109/tac.1978.1101743 Khargonekar, P., Poolla, K., & Tannenbaum, A. (1985). Robust control of linear time-invariant plants using periodic compensation. IEEE Transactions on Automatic Control, 30(11), 1088-1096. doi:10.1109/tac.1985.1103841 Marti, P., Yepez, J., Velasco, M., Villa, R., & Fuertes, J. M. (2004). Managing Quality-of-Control in Network-Based Control Systems by Controller and Message Scheduling Co-Design. IEEE Transactions on Industrial Electronics, 51(6), 1159-1167. doi:10.1109/tie.2004.837873 Tipsuwan, Y., & Chow, M.-Y. (2004). Gain Scheduler Middleware: A Methodology to Enable Existing Controllers for Networked Control and Teleoperation—Part I: Networked Control. IEEE Transactions on Industrial Electronics, 51(6), 1218-1227. doi:10.1109/tie.2004.837866 Apkarian, P., & Adams, R. J. (1998). Advanced gain-scheduling techniques for uncertain systems. IEEE Transactions on Control Systems Technology, 6(1), 21-32. doi:10.1109/87.654874 Montestruque, L. A., & Antsaklis, P. (2004). Stability of Model-Based Networked Control Systems With Time-Varying Transmission Times. IEEE Transactions on Automatic Control, 49(9), 1562-1572. doi:10.1109/tac.2004.834107 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. doi:10.1080/10556789908805766

Salt, J., Casanova, V., Cuenca, A., & Pizá, R. (2008). Sistemas de Control Basados en Red Modelado y Diseño de Estructuras de Control. Revista Iberoamericana de Automática e Informática Industrial RIAI, 5(3), 5-20. doi:10.1016/s1697-7912(08)70157-2

Salt, J., Casanova, V., Cuenca, A., Part-Pizá, R. (2008). Network-based control systems designed and designed for control structures. Ibero-American magazine for Automatic and Industrial Informatics RIAI, 5 (3), 5-20. doi:10.1016/s1697-7912 (08) 70157-2

Linear matrix inequalities in multirate control over networks

Abstract