zbMATH — the first resource for mathematics

A practical solution to implement nonlinear output regulation via dynamic mappings. (English) Zbl 1449.93098
Summary: This paper presents a novel error-feedback practical solution for real-time implementation of nonlinear output regulation. Sufficient and necessary conditions for both state- and error-feedback output regulation have been established for linear and nonlinear systems several decades ago. In their most general form, these solutions require solving a set of nonlinear partial differential equations, which may be hard or even impossible to solve analytically. In recent years, a methodology for dynamic calculation of the mappings required for state-feedback regulation has been put forward; following the latter, an error-feedback extension is hereby provided which, when combined with design conditions in the form of linear matrix inequalities, becomes suitable for real-time setups. Real-time results are presented for a nonlinear twin rotor MIMO system. Issues concerning the implementation as well as the solutions adopted, are discussed.
93C10 Nonlinear systems in control theory
93C95 Application models in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
Full Text: DOI
[1] Ahmed, Q.; Bhatti, A. I.; Iqbal, S., Robust decoupling control design for twin rotor system using Hadamard weights., In: Control Applications, (CCA) and Intelligent Control, (ISIC), 2009 IEEE, pp. 1009-1014
[2] Bernal, M.; Marquez, R.; Estrada, V.; Castillo, B., An element-wise linear matrix inequality approach for output regulation problems., In: World Automation Congress (WAC) 2012, Puerto Vallarta 2012, pp. 1-6
[3] Bernal, M.; Marquez, R.; Estrada-Manzo, V.; Castillo-Toledo, B., Nonlinear output regulation via Takagi-Sugeno fuzzy mappings: A full-information LMI approach., In: IEEE International Conference on Fuzzy Systems 2012, pp. 1-7
[4] Boyd, S.; Ghaoui, L. E.; Feron, E.; Belakrishnan, V., Linear Matrix Inequalities in System and Control Theory., SIAM, Studies In Applied Mathematics 15, Philadelphia 1994
[5] Byrnes, C. I.; Isidori, A., Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation., IEEE Trans. Automat. Control 48 (2003), 10, 1712-1723
[6] Byrnes, C. I.; Isidori, A., Nonlinear internal models for output regulation., IEEE Trans. Automat. Control 49 (2004), 12, 2244-2247
[7] Byrnes, C. I.; Priscoli, F. D.; Isidori, A., Output regulation of uncertain nonlinear systems., Springer Science and Business Media, 2012
[8] Davison, E., The robust control of a servomechanism problem for linear time-invariant multivariable systems., IEEE Trans. Automat. Control 21 (1976), 1, 25-34
[9] Duan, G. R.; Yu, H. H., LMIs in Control Systems: Analysis, Design and Applications., CRC Press, 2013
[10] Ltd, Feedback instruments; Manual, East Sussex. TRMS 33-949S User, Twin Rotor MIMO System Control Experiments, 1998.
[11] Francis, B. A., The linear multivariable regulator problem., SIAM J. Control Optim. 15 (1077), 486-505
[12] Francis, B. A.; Wonham, W. M., The internal model principle for linear multivariable regulators., J. Appl. Math. Optim. 2 (1975), 170-194
[13] Glauser, M.; Lin, Z.; Allaire, P. E., Modeling and control of a partial body weight support system: an output regulation approach., IEEE Trans. Control Systems Technol. 18 (2010), 2, 480-490
[14] Henriques, J.; Gil, P.; Cardoso, A.; Carvalho, P.; Dourado, A., Adaptive neural output regulation control of a solar power plant., Control Engrg. Practice 18 (2010), 10, 1183-1196
[15] Isidori, A., Nonlinear Control Systems. Third edition., Springer, London 1995
[16] Isidori, A.; Byrnes, C. I., Output regulation of nonlinear systems., IEEE Trans. Automat. Control 35 (1990) 2, 131-140
[17] Jensen, T. N.; Wisniewski, R.; DePersis, C.; Kallesøe, C. S., Output regulation of large-scale hydraulic networks with minimal steady state power consumption., Control Engrg. Practice 22 (2014), 103-113
[18] Khalil, H., Nonlinear Systems. Third edition., Prentice Hall, New Jersey 2002
[19] Kim, W.; Kim, H.; Chung, C. C.; Tomizuka, M., Adaptive output regulation for the rejection of a periodic disturbance with an unknown frequency., IEEE Trans. Control Systems Technol. 19 (2011), 5, 1296-1304
[20] Lewis, F. L.; Dawson, D. M.; Abdallah, C. T., Robot Manipulator Control: Theory and Practice., CRC Press, 2003
[21] Mahony, R.; Mareels, I.; Bastin, G.; Campion, G., Static-state feedback laws for output regulation of non-linear systems., Control Engingrg. Practice 4 (1966), 7, 1009-1014
[22] Marconi, L.; Praly, L., Uniform practical nonlinear output regulation., IEEE Trans. Automat. Control 53 (2008), 5, 1184-1202
[23] Meda, J. A.; Castillo, B., Synchronization of chaotic systems from a fuzzy regulation approach., Fuzzy Sets Systems 160 (2009), 19, 2860-2875
[24] Meda, J. A.; Gomez, J. C.; Castillo, B., Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models., IEEE Trans. Fuzzy Systems 20 (2012), 2, 235-247
[25] Nejjari, F.; Rotondo, D.; Puig, V.; Innocenti, M., LPV modelling and control of a Twin Rotor MIMO system., In: 19th Mediterranean Conference on Control and Automation (MED), IEEE 2011, pp. 1082-1087
[26] Pandey, S. K.; Laxmi, V., Optimal control of twin rotor MIMO system using LQR technique., Comput. Intell. Data Mining 31 (2015), 11-21
[27] Pavlov, A.; Janssen, B.; Wouw, N. Van de; Nijmeijer, H., Experimental Output Regulation for a Nonlinear Benchmark System., IEEE Trans. Control Systems Technol. 15 (2007), 4, 786-793
[28] Pratap, B.; Purwar, S., Neural network observer for twin rotor mimo system: an lmi based approach., In: The 2010 International Conference on Modelling, Identification and Control (ICMIC), IEEE 2010, pp. 539-544
[29] Robles, R.; Bernal, M., Comments on Exact output regulation for nonlinear systems described by Takagi-Sugeno fuzzy models., IEEE Trans. Fuzzy Systems 23 (2015), 1, 230-233
[30] Tanaka, K.; Wang, H. O., Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach., John Wiley and Sons, New York 2001
[31] Tao, C.-W.; Taur, J.-S.; Chang, Y.-H.; Chang, C.-W., A novel fuzzy-sliding and fuzzy-integral-sliding controller for the twin-rotor multi-input-multi-output system., IEEE Trans. Fuzzy Systems 18 (2010), 5, 893-905
[32] Tapia, A.; Márquez, R.; Bernal, M.; Cortez, J., Sliding subspace design based on linear matrix inequalities., Kybernetika 50 (2014), 3, 633-641
[33] Tarn, T. J.; Sanposh, P.; Cheng, D.; Zhang, M., Output Regulation for Nonlinear Systems: Some Recent Theoretical and Experimental Results., IEEE Trans. Control Systems Technol. 13 (2005), 605-610
[34] Umemura, Y.; Sakamoto, N., Optimal servo design for lock-up slip control for torque converter nonlinear output regulation approach., IEEE Trans. Control Systems Technol. 23 (2015), 4, 1587-1593
[35] Yoon, S. Y.; Di, L.; Lin, Z., Unbalance compensation for AMB systems with input delay: An output regulation approach., Control Engrg. Practice 46 (2016), 166-175
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.