“Recent Advances in Static Output-Feedback Controller Design with Applications to Vibration Control of Large Structures”
Authors: Francisco Palacios-Quiñonero, Josep Rubio-Massegu, Josep M. Rossell and Hamid Reza Karimi,Affiliation: Universitat Politécnica de Catalunya and University of Agder
Reference: 2014, Vol 35, No 3, pp. 169-190.
Keywords: Static Output-feedback, Decentralized Control, Structural Vibration Control
Abstract: In this paper, we present a novel two-step strategy for static output-feedback controller design. In the first step, an optimal state-feedback controller is obtained by means of a linear matrix inequality (LMI) formulation. In the second step, a transformation of the LMI variables is used to derive a suitable LMI formulation for the static output-feedback controller. This design strategy can be applied to a wide range of practical problems, including vibration control of large structures, control of offshore wind turbines, control of automotive suspensions, vehicle driving assistance and disturbance rejection. Moreover, it allows designing decentralized and semi-decentralized static output-feedback controllers by setting a suitable zero-nonzero structure on the LMI variables. To illustrate the application of the proposed methodology, two centralized static velocity-feedback H-Infinity controllers and two fully decentralized static velocity-feedback H-Infinity controllers are designed for the seismic protection of a five-story building.
PDF (910 Kb)
DOI: 10.4173/mic.2014.3.4DOI forward links to this article:
| [1] Vasiliy Ye. Belozyorov (2016), doi:10.1016/j.laa.2016.04.001 |
| [2] Renan L. Pereira, Karl H. Kienitz and Fernando H. D. Guaracy (2017), doi:10.1109/MED.2017.7984186 |
| [3] J. Leventides, I. Meintanis and N. Karcanias (2017), doi:10.1016/j.ifacol.2017.08.2378 |
| [4] Janghoon Yang (2017), doi:10.1145/3175516.3175535 |
| [5] F. Palacios-Quiñonero, J. Rubió-Massegú, J.M. Rossell and H.R. Karimi (2018), doi:10.1016/j.engstruct.2018.05.075 |
| [6] Yazan M. Al-Rawashdeh, Sami El Ferik and Mohammed A. Abido (2019), doi:10.1109/IACS.2019.8809167 |
| [7] Y. Peretz and W. Wu (2019), doi:10.1080/00207721.2019.1691280 |
| [8] Janghoon Yang (2018), doi:10.1109/ICSTC.2018.8528637 |
| [9] Mohsen Kheirandishfard, Fariba Zohrizadch, Muhammad Adil and Ramtin Madani (2018), doi:10.1109/CDC.2018.8619762 |
| [10] Bachir Nail, Belkacem Bekhiti and Vicenc Puig (2020), doi:10.1016/j.jngse.2020.103697 |
[1] Amato, F., Cosentino, C., and Merola, A. (2010). Sufficient conditions for finite-time stability and stabilization of nonlinear quadratic systems, IEEE Transactions on Automatic Control. 55(2):430--434. doi:10.1109/TAC.2009.2036312
[2] Aouaouda, S., Chadli, M., and Karimi, H. (2014). Robust static output-feedback controller design against sensor failure for vehicle dynamics, IET Control Theory and Applications. 8(9):728--737. doi:10.1049/iet-cta.2013.0709
[3] Attia, S., Salhi, S., and Ksouri, M. (2012). Static switched output feedback stabilisation for linear discrete-time switched systems, International Journal of Innovative Computing, Information and Control. 8(5):3203--3213.
[4] Bakka, T. and Karimi, H. (2013). H-Infinity static output-feedback control design with constrained information for offshore wind turbine system, Journal of the Franklin Institute. 350(8):2244--2260. doi:10.1016/j.jfranklin.2013.05.028
[5] Bakka, T., Karimi, H., and Christiansen, S. (2014). Linear parameter-varying modelling and control of an offshore wind turbine with constrained information, IET Control Theory and Applications. 8(1):22--29. doi:10.1049/iet-cta.2013.0480
[6] Balas, G., Chiang, R., Packard, A., and Safonov, M. (2011). MATLAB Robust Control Toolbox 3, User's Guide. The MathWorks, Inc., Natick, USA.
[7] Ballesteros, P., Shu, X., Heins, W., and Bohn, C. (2013). Reduced-order two-parameter pLPV controller for the rejection of nonstationary harmonically related multisine disturbances, In Proceedings of the 2013 European Control Conference (ECC). Zurich, Switzerland, pages 1835--1842.
[8] Bara, G. and Boutayeb, M. (2005). Static output feedback stabilization with H-Infinity performance for linear discrete-time systems, IEEE Transactions on Automatic Control. 50(2):250--254. doi:10.1109/TAC.2004.841922
[9] Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, USA.
[10] Cao, Y.-Y., Lam, J., and Sun, Y.-X. (1998). Static output feedback stabilization: an ILMI approach, Automatica. 34(12):1641--1645. doi:10.1016/S0005-1098(98)80021-6
[11] Chen, A. and Wang, J. (2012). Delay-dependent L_2-L-Infinity control of linear systems with multiple time-varying state and input delays, Nonlinear Analysis: Real World Applications. 13(1):486--496. doi:10.1016/j.nonrwa.2011.08.006
[12] Chen, X.-B. and Stankovic, S. (2005). Decomposition and decentralized control of systems with multi-overlapping structure, Automatica. 41(10):1765--1772. doi:10.1016/j.automatica.2005.01.020
[13] Chen, Y., Zhang, W., and Gao, H. (2010). Finite frequency H-Infinity control for building under earthquake excitation, Mechatronics. 20(1):128--142. doi:10.1016/j.mechatronics.2009.11.001
[14] Chopra, A. (2007). Dynamics of Structures, Theory and Applications to Earthquake Engineering. Prentice Hall, Upper Saddle River, New Jersey, USA, 3rd edition, 2007.
[15] Crusius, C. and Trofino, A. (1999). Sufficient LMI conditions for output feedback control problems, IEEE Transactions on Automatic Control. 44(5):1053--1057. doi:10.1109/9.763227
[16] Dhawan, A. and Kar, H. (2011). An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems, Signal Processing. 91(4):1032--1035. doi:10.1016/j.sigpro.2010.07.014
[17] Dong, J. and Yang, G.-H. (2013). Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties, Automatica. 49(6):1821--1829. doi:10.1016/j.automatica.2013.02.047
[18] Du, H., Zhang, N., and Naghdy, F. (2011). Actuator saturation control of uncertain structures with input time delay, Journal of Sound and Vibration. 330(18--19):4399--4412. doi:10.1016/j.jsv.2011.04.025
[19] Feng, J.-E., Lam, J., Li, P., and Shu, Z. (2011). Decay rate constrained stabilization of positive systems using static output feedback, International Journal of Robust and Nonlinear Control. 21(1):44--54. doi:10.1002/rnc.1575
[20] Gadewadikar, J., Lewis, F., Xie, L., Kucera, V., and Abu-Khalaf, M. (2007). Parameterization of all stabilizing H-Infinity static state-feedback gains: application to output-feedback design, Automatica. 43(9):1597--1604. doi:10.1016/j.automatica.2007.02.005
[21] Ho, W.-H., Chen, S.-H., Chen, I.-T., Chou, J.-H., and Shu, C.-C. (2012). Design of stable and quadratic-optimal static output feedback controllers for TS-fuzzy-model-based control systems: an integrative computational approach, International Journal of Innovative Computing, Information and Control. 8(1):403--418.
[22] Hou, L., Zong, G., and Wu, Y. (2012). Finite-time control for switched delay systems via dynamic output feedback, International Journal of Innovative Computing, Information and Control. 8(7):4901--4913.
[23] Huang, L. and Mao, X. (2009). Robust delayed-state-feedback stabilization of uncertain stochastic systems, Automatica. 45(5):1332--1339. doi:10.1016/j.automatica.2009.01.004
[24] Karimi, H., Palacios-Quinonero, F., Rossell, J., and Rubio-Massegu, J. (2013). Sequential design of multioverlapping controllers for structural vibration control of tall buildings under seismic excitation, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 227(2):176--183. doi:10.1177/0959651812464026
[25] Kurata, N., Kobori, T., Takahashi, M., Niwa, N., and Midorikawa, H. (1999). Actual seismic response controlled building with semi-active damper system, Earthquake Engineering and Structural Dynamics. 28(11):1427--1447.
[26] Li, Z., Gao, H., and Karimi, H. (2014). Stability analysis and H-Infinity controller synthesis of discrete-time switched systems with time delay, Systems and Control Letters. 66:85 -- 93. doi:10.1016/j.sysconle.2013.12.010
[27] Liu, A., Yu, L., and Zhang, W. (2011). H-Infinity control for network-based systems with time-varying delay and packet disordering, Journal of the Franklin Institute. 348(5):917--932. doi:10.1016/j.jfranklin.2011.03.002
[28] Lunze, J. (1992). Feedback Control of Large-Scale Systems, Prentice Hall, Upper Saddle River, NJ, USA.
[29] Moerder, D. and Calise, A. (1985). Convergence of a numerical algorithm for calculating optimal output feedback gains, IEEE Transactions on Automatic Control. 30(9):900--903. doi:10.1109/TAC.1985.1104073
[30] Oishi, Y. and Fujioka, H. (2010). Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities, Automatica. 46(8):1327--1333. doi:10.1016/j.automatica.2010.05.006
[31] Oufroukh, N. and Mammar, S. (2014). Integrated driver co-pilote approach for vehicle lateral control, In Proceedings of the 2014 IEEE Intelligent Vehicles Symposium. Dearborn, USA, pages 1163--1168. doi:10.1109/IVS.2014.6856519
[32] Palacios-Quinonero, F., Karimi, H., Rubio-Massegu, J., and Rossell, J. (2013). Passive-damping design for vibration control of large structures, In Proceedings of the 10th International Conference on Control and Automation (IEEE ICCA 2013). Hangzhou, China, pages 33--38. doi:10.1109/ICCA.2013.6565018
[33] Palacios-Quinonero, F., Rodellar, J., and Rossell, J. (2010). Sequential design of multi-overlapping controllers for longitudinal multi-overlapping systems, Applied Mathematics and Computation. 217(3):1170--1183. doi:10.1016/j.amc.2010.01.130
[34] Palacios-Quinonero, F., Rossell, J., and Karimi, H. (2011). Semi-decentralized strategies in structural vibration control, Modeling, Identification and Control. 32(2):57--77. doi:10.4173/mic.2011.2.2
[35] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2012). Discrete-time multioverlapping controller design for structural vibration control of tall buildings under seismic excitation, Mathematical Problems in Engineering, 2012. 2012:1--20. doi:10.1155/2012/636878
[36] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2012). Discrete-time static output-feedback semi-decentralized H-Infinity controller design: an application to structural vibration control, In Proceedings of the 2012 American Control Conference. Montreal, Canada, pages 6126--6131, 2012. doi:10.1109/ACC.2012.6314816
[37] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2012). Optimal passive-damping design using a decentralized velocity-feedback H-Infinity approach, Modeling, Identification and Control, 2012. 33(3):87--97. doi:10.4173/mic.2012.3.1
[38] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2014). Discrete-time static output-feedback H-Infinity controller design for vehicle suspensions, In Proceedings of the 2014 International Conference on Mechatronics and Control (ICMC). Jinzhou, China, pages 2346--2351, 2014.
[39] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2014). Feasibility issues in static output-feedback controller design with application to structural vibration control, Journal of the Franklin Institute, 2014. 351(1):139--155. doi:10.1016/j.jfranklin.2013.08.011
[40] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2014). Optimal design of complex passive-damping systems for vibration control of large structures: an energy-to-peak approach, Abstract and Applied Analysis, 2014. 2014:1--9. doi:10.1155/2014/510236
[41] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2014). Static output-feedback controller design for structural vibration control: a two-step LMI approach, In Proceedings of the Sixth World Conference on Structural Control and Monitoring (6WCSCM). Barcelona, Spain, pages 1902--1913, 2014.
[42] Palacios-Quinonero, F., Rubio-Massegu, J., Rossell, J., and Karimi, H. (2014). Vibration control for adjacent structures using local state information, Mechatronics, 2014. 24(4):336--344. doi:10.1016/j.mechatronics.2013.08.001
[43] Prempain, E. and Postlethwaite, I. (2001). Static output feedback stabilisation with H-Infinity performance for a class of plants, Systems and Control Letters. 43(3):159--166. doi:10.1016/S0167-6911(01)00087-1
[44] Rossell, J., Palacios-Quinonero, F., and Rodellar, J. (2010). Semi-decentralized output feedback H-Infinity control strategy for large building structures, In Proceedings of the 5th World Conference on Structural Control and Monitoring (5WCSCM). Shinjuku, Japan.
[45] Rubio-Massegu, J., Palacios-Quinonero, F., and Rossell, J. (2012). Decentralized static output-feedback H-Infinity controller design for buildings under seismic excitation, Earthquake Engineering and Structural Dynamics. 41(7):1199--1205. doi:10.1002/eqe.1167
[46] Rubio-Massegu, J., Palacios-Quinonero, F., Rossell, J., and Karimi, H. (2013). Static output-feedback control for vehicle suspensions: a single-step linear matrix inequality approach, Mathematical Problems in Engineering, 2013. 2013:1--12. doi:10.1155/2013/907056
[47] Rubio-Massegu, J., Palacios-Quinonero, F., Rossell, J., and Karimi, H. (2014). Static output-feedback controller design for vehicle suspensions: an effective two-step computational approach, IET Control Theory and Applications. 8(15):1566--1574. doi:10.1049/iet-cta.2013.1129
[48] Rubio-Massegu, J., Rossell, J., Karimi, H., and Palacios-Quinonero, F. (2013). Static output-feedback control under information structure constraints, Automatica, 2013. 49(1):313--316. doi:10.1016/j.automatica.2012.10.012
[49] Shi, H.-B. and Qi, L. (2009). Static output feedback simultaneous stabilisation via coordinates transformations with free variables, IET Control Theory and Applications. 3(8):1051--1058. doi:10.1049/iet-cta.2008.0185
[50] Siljak, D. (1991). Decentralized Control of Complex Systems, Academic Press, New York, USA.
[51] Syrmos, V., Abdallah, C., Dorato, P., and Grigoriadis, K. (1997). Static output feedback - A survey, Automatica. 33(2):125--137. doi:10.1016/S0005-1098(96)00141-0
[52] Toscano, R. (2006). A simple method to find a robust output feedback controller by random search approach, ISA Transactions. 45(1):35--44. doi:10.1016/S0019-0578(07)60063-9
[53] Toscano, R. and Lyonnet, P. (2010). Robust static output feedback controller synthesis using Kharitonov's theorem and evolutionary algorithms, Information Sciences. 180(10):2023--2028. doi:10.1016/j.ins.2010.01.009
[54] Vasely, V., Rosinova, D., and Kucera, V. (2011). Robust static output feedback controller LMI based design via elimination, Journal of the Franklin Institute. 348(9):2468--2479. doi:10.1016/j.jfranklin.2011.04.020
[55] Wang, R., Jing, H., Yan, F., Karimi, H., and Chen, N. (2014). Optimization and finite-frequency H-Infinity control of active suspensions in in-wheel motor driven electric ground vehicles, Journal of the Franklin Institute. In press. doi:10.1016/j.jfranklin.2014.05.005
[56] Wang, Y., Lynch, J., and Law, K. (2009). Decentralized H-Infinity controller design for large-scale civil structures, Earthquake Engineering and Structural Dynamics. 38(3):377--401. doi:10.1002/eqe.862
[57] Wang, Z., Liu, Y., Wei, G., and Liu, X. (2010). A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances, Automatica. 46(3):543--548. doi:10.1016/j.automatica.2009.11.020
[58] Xiang, M., Xiang, Z., and Karimi, H. (2014). Stabilization of positive switched systems with time-varying delays under asynchronous switching, International Journal of Control, Automation and Systems, 2014. 12(5):939--947. doi:10.1007/s12555-013-0486-x
[59] Yang, R., Shi, P., Liu, G.-P., and Gao, H. (2011). Network-based feedback control for systems with mixed delays based on quantization and dropout compensation, Automatica. 47(12):2805--2809. doi:10.1016/j.automatica.2011.09.007
[60] Zecevic, A. and Siljak, D. (2004). Design of robust static output feedback for large-scale systems, IEEE Transactions on Automatic Control. 49(11):2040--2044. doi:10.1109/TAC.2004.837542
[61] Zecevic, A. and Siljak, D. (2010). Control of Complex Systems, Structural Constraints and Uncertainty. Springer. doi:10.1007/978-1-4419-1216-9
[62] Zhang, D. and Wang, X. (2012). Static output feedback control of networked control systems with packet dropout, International Journal of Systems Science. 43(4):665--672. doi:10.1080/00207721.2010.517873
[63] Zhang, Y., Shi, P., Nguang, S.K., Karimi, H., and Agarwal, R. (2014). Robust finite-time fuzzy H-Infinity control for uncertain time-delay systems with stochastic jumps, Journal of the Franklin Institute. 351(8):4211--4229. ewbloc doi:10.1016/j.jfranklin.2014.04.004
BibTeX:
@article{MIC-2014-3-4,
title={{Recent Advances in Static Output-Feedback Controller Design with Applications to Vibration Control of Large Structures}},
author={Palacios-Quiñonero, Francisco and Rubio-Massegu, Josep and Rossell, Josep M. and Karimi, Hamid Reza},
journal={Modeling, Identification and Control},
volume={35},
number={3},
pages={169--190},
year={2014},
doi={10.4173/mic.2014.3.4},
publisher={Norwegian Society of Automatic Control}
};