{"title":"Stabilization of a Three-Pole Active Magnetic Bearing by Hybrid Control Method in Static Mode","authors":"Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi","volume":116,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":1456,"pagesEnd":1467,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10005095","abstract":"The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.","references":"[1]\tR. Fierro, A. K. Das, V. Kumar, and J. P. Ostrowski, \"Hybrid control of formations of robots,\" in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, 2001, pp. 157-162.\r\n[2]\tA. Karimoddini, H. Lin, B. M. Chen, and T. H. Lee, \"A bumpless hybrid supervisory control algorithm for the formation of unmanned helicopters,\" Mechatronics, vol. 23, pp. 677-688, 9\/\/ 2013.\r\n[3]\tX. Lin-Shi, F. Morel, A. M. Llor, B. Allard, and J.-M. Retif, \"Implementation of hybrid control for motor drives,\" Industrial Electronics, IEEE Transactions on, vol. 54, pp. 1946-1952, 2007.\r\n[4]\tB. Han, X. Luo, Q. Liu, B. Zhou, and X. Chen, \"Hybrid control for SLIP-based robots running on unknown rough terrain,\" Robotica, vol. 32, pp. 1065-1080, 2014.\r\n[5]\tX. Liu and P. Stechlinski, \"Hybrid control of impulsive systems with distributed delays,\" Nonlinear Analysis: Hybrid Systems, vol. 11, pp. 57-70, 1\/\/ 2014.\r\n[6]\tC. Yuan and F. Wu, \"Analysis and synthesis of linear hybrid systems with state-triggered jumps,\" Nonlinear Analysis: Hybrid Systems, vol. 14, pp. 47-60, 11\/\/ 2014.\r\n[7]\tS. M. Darbandi, M. Behzad, H. Salarieh, and H. Mehdigholi, \"Linear Output Feedback Control of a Three-Pole Magnetic Bearing,\" pp. 1323-1330, 2013.\r\n[8]\tC.-T. Hsu and S.-L. Chen, \"Exact linearization of a voltage-controlled 3-pole active magnetic bearing system,\" Control Systems Technology, IEEE Transactions on, vol. 10, pp. 618-625, 2002.\r\n[9]\tS.-L. Chen, S.-H. Chen, and S.-T. Yan, \"Stabilization of a current-controlled three-pole magnetic rotor-bearing system by integral sliding mode control,\" in Networking, Sensing and Control, 2004 IEEE International Conference on, 2004, pp. 949-954.\r\n[10]\tS.-L. Chen and C.-C. Weng, \"Robust control of a voltage-controlled three-pole active magnetic bearing system,\" Mechatronics, IEEE\/ASME Transactions on, vol. 15, pp. 381-388, 2010.\r\n[11]\tS.-L. Chen, S.-H. Chen, and S.-T. Yan, \"Experimental validation of a current-controlled three-pole magnetic rotor-bearing system,\" Magnetics, IEEE Transactions on, vol. 41, pp. 99-112, 2005.\r\n[12]\tS. M. Darbandi, M. Behzad, H. Salarieh, and H. Mehdigholi, \"Harmonic disturbance attenuation in a three-pole active magnetic bearing test rig using a modified notch filter,\" Journal of Vibration and Control, p. 1077546315586494, 2015.\r\n[13]\tS.-L. Chen and C.-T. Hsu, \"Optimal design of a three-pole active magnetic bearing,\" Magnetics, IEEE Transactions on, vol. 38, pp. 3458-3466, 2002.\r\n[14]\tS. Bouaziz, N. Belhadj Messaoud, J.-Y. Choley, M. Maatar, and M. Haddar, \"Transient response of a rotor-AMBs system connected by a flexible mechanical coupling,\" Mechatronics, vol. 23, pp. 573-580, 9\/\/ 2013.\r\n[15]\tG. Schweitzer, H. Bleuler, E. H. Maslen, M. Cole, P. Keogh, R. Larsonneur, et al., Magnetic bearings: theory, design, and application to rotating machinery: Springer, 2009.\r\n[16]\tL. Rodrigues and S. Boyd, \"Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization,\" Systems & Control Letters, vol. 54, pp. 835-853, 2005.\r\n[17]\tL. Rodrigues and J. P. How, \"Observer-based control of piecewise-affine systems,\" International Journal of Control, vol. 76, pp. 459-477, 2003.\r\n[18]\tA. Hassibi, J. How, and S. Boyd, \"A path-following method for solving BMI problems in control,\" in American Control Conference, 1999. Proceedings of the 1999, 1999, pp. 1385-1389.\r\n[19]\tD. E. Kirk, Optimal control theory: an introduction: Courier Corporation, 2012.\r\n[20]\tZ. Sun, J. Zhao, Z. Shi, and S. Yu, \"Soft sensing of magnetic bearing system based on support vector regression and extended Kalman filter,\" Mechatronics, vol. 24, pp. 186-197, 4\/\/ 2014.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 116, 2016"}