A practical robust nonlinear controller for maglev levitation system

Abstract

In order to explore the precise dynamic response of the maglev train and verify the validity of proposed controller, a maglev guideway-electromagnet-air spring-cabin coupled model is developed in the first step. Based on the coupled model, the stresses of the modules are analyzed, and it is pointed out that the inherent nonlinearity, the inner coupling, misalignments between the sensors and actuators, and external disturbances are the main issues that should be considered for the maglev engineering. Furthermore, a feedback linearization controller based on the mathematical model of a maglev module is derived, in which the nonlinearity, coupling and misalignments are taken into account. Then, to attenuate the effect of external disturbances, a disturbance observer is proposed and the dynamics of the estimation error is analyzed using the input-to-state stability theory. It shows that the error is negligible under a low-frequency disturbance. However, at the high-frequency range, the error is unacceptable and the disturbances can not be compensated in time, which lead to over designed fluctuations of levitation gap, even a clash between the upper surface of electromagnet and lower surface of guideway. To solve this problem, a novel nonlinear acceleration feedback is put forward to enhancing the attenuation ability of fast varying disturbances. Finally, numerical comparisons show that the proposed controller outperforms the traditional feedback linearization controller and maintains good robustness under disturbances.

Keywords

dynamic / robust / nonlinear / decoupling / separation / levitation system / maglev

References

[1] LeeH W, KimK C, LeeJ. Review of maglev train technologies [J]. IEEE Transactions on Magnetic, 2006, 42(7): 1917-1925

[2] YanL-guang. Development and application of the maglev transportation system [J]. IEEE Transactions on Applied Superconductivity, 2008, 18(2): 92-99

[3] LinF J, TengL T, ShiehP H. Intelligent adaptive backstepping control system for magnetic levitation apparatus [J]. IEEE Transactions on Magnetic, 2007, 43(5): 2009-2018

[4] ZhouD-f, HansenC H, LiJie. Suppression of maglev vehicle-girder self-excited vibration using a virtual tuned mass damper [J]. Journal of Sound and Vibration, 2011, 330(5): 883-901

[5] WaiR J, LeeJ D. Robust levitation control for linear maglev rail system using fuzzy neural network [J]. IEEE Transaction on Control Systems Technology, 2009, 17(1): 4-14

[6] YangZ-j, TsubakiharaH, KanaeS, WadaK, SuC-yi. A novel robust nonlinear motion controller with disturbance observer [J]. IEEE Transactions Control Systems Technology, 2008, 16(1): 137-147

[7] WaiR J, LeeJ D. Adaptive fuzzy-neural-network control for maglev transportation system [J]. IEEE Transactions on Neural Networks, 2008, 19(1): 54-70

[8] ZengY-h, LiuS-j, Jia-qiangE. Neuron PI control for semi-active suspension system of tracked vehicle [J]. Journal of Central South University of Technology, 2011, 18(2): 444-450

[9] ZhangL-l, ZhangZ-z, HuangL-hong. Double Hopf bifurcation of time-delayed feedback control for maglev system [J]. Nonlinear Dynamic, 2012, 69(3): 961-967

[10] ZhouH-b, YingH, DuanJ-an. Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems [J]. Journal of Central South University of Technology, 2011, 18(3): 760-766

[11] ZhouD-f, LiJ, HansenC HSuppression of maglev track-induced self-excited vibration using an adaptive cancellation algorithm [J], 2011, 44–47: 586-590

[12] YangJ, ZolotasA, ChenW-h, MichailK, LiS-hua. Robust control of nonlinear maglev suspension system with mismatched uncertainties via DOBC approach [J]. ISA Transactions, 2011, 50(3): 389-396

[13] ZhangL-l, CampbellS A, HuangL-hong. Nonlinear analysis of a maglev system with time-delayed feedback control [J]. Physica D, 2011, 240(21): 1761-1770

[14] ShenG, MeisingerR, ShuG-wei. Modeling of a high-speed maglev train with vertical and lateral control [J]. International Journal of Vehicle Mechanics and Mobility, 2008, 46(1): 643-651

[15] KwonS D, LeeJ S, MoonJ W, KimM Y. Dynamic interaction analysis of urban transit maglev vehicle and guideway suspension bridge subjected to gusty wind [J]. Engineering Structures, 2008, 30(12): 3445-3456

[16] CuiP, LiJ, LiuD-sheng. The carrying capacity for the electromagnetic suspension low-speed maglev train on the horizontal curve [J]. Science in China, 2010, 53(4): 1082-1087

[17] ZhangG, LiJie. Calculation of electromagnetic force of low-speed maglev on a vertical curve [J]. Proceeding of the CSEE, 2012, 32(3): 150-156

[18] RahideH, ShaheedM H. Constrained output feedback model predictive control for nonlinear system [J]. Control Engineering Practice, 2012, 20(3): 431-443

[19] DoughertyC. A practical multiple model adaptive strategy for multivariable model predictive control [J]. Control Engineering Practice, 2003, 11(2): 649-664

[20] RaoA. Experimental studies on multiple-model predictive control for automated regulation of dynamic variable [J]. IEEE Transaction on Biomedical Engineering, 2003, 50(2): 277-288

[21] ZhangJ, DaiS, LiJ-m, WangNing. Fuzzy RBF neural network in the application of magnetic levitation system [C]. The 6th International Forum on Strategic Technology, 2011PiscatawayIEEE Press990-994

[22] LiY-g, ChangW-sen. Cascade control of an EMS maglev vehicle’s levitation control system [J]. ACTA Automatica Sinica, 1999, 25(2): 247-251

[23] GuzmanH. Current loops in a magnetic levitation system [J]. International Journal of Innovative Computing, Information and Control, 2009, 5(5): 1275-1283

[24] YoonT-s, WangF-g, Parks-K, KwakG-P, AhnH-kyun. Linearization of T-S fuzzy systems and robust H∞ control [J]. Journal of Central South University of Technology, 2011, 18(1): 140-145

[25] TrisantoA, YasserM, HaggagA, LuJ-ming. Application of neural networks to MRAC for the nonlinear magnetic levitation system [J]. JSME International Journal, 2006, 49(4): 1073-1083

[26] TrisantoA, PhuahJ, LuJ-m, YahagiY. The use of NNs in MRAC to control nonlinear magnetic levitation system [J]. IEEE international symposium on circuits and system, 2005, 5(2): 3051-3054

[27] LefebrvreT, BruyninckxH, SchutterJ. Online statistical model recognition and state estimation for autonomous compliant motion [J]. IEEE Transactions on Systems, Man and Cybernetics, 2005, 35: 16-29

[28] CortesaoR. On Kalman active observers [J]. Journal of Intelligent and Robotic System, 2007, 48(2): 131-155

[29] ChenW-h, BalanceD J, GawthorpP J. A nonlinear disturbance observer for robotic manipulators [J]. IEEE Transaction on Industrial Electronics, 2000, 47(4): 932-938

[30] ButlerH. Acceleration feedback in a lithographic tool [J]. Control Engineering Practice, 2012, 20(4): 453-464