• Bui Trung Thanh Hung Yen University of Technology and Education
Keywords: Robust controller; mixed H∞/H2 controller; particle swarm optimization; magnetic bearing systems; MIMO systems


This paper presents an algorithm for designing a robust and optimal controller for active magnetic bearing systems. The active magnetic bearing systems are widely applied for high speed machining due to no contact operation, low fiction, lubrication-free operation, and extended life. However, they are non-linear, unstable, multiple input and multiple output systems. Therefore, a robust and optimal controller is required. In this paper, we derive dynamic equation and analyze response of the open loop system. Based on the dynamic response of the system, we propose a suitable controller with robust and optimal criteria using particle swarm optimization. The simulation results show that the closed loop system attains good performance in compared with conventional PID controllers


Knospe C. R. (2007). Active Magnetic Bearings for Machining Applications. Control Engineering Practice, 15, 307-313.

Na U. J. (2005). Fault Tolerant Control of Magnetic Bearings with Force Invariance. Journal of Mechanical Science and Technology, 19(3), 731-742.

Na U. J. (2006). Fault Tolerant Homopolar Magnetic Bearings with Flux Invariant Control. Journal of Mechanical Science and Technology, 20(5), 643-651.

Jeng J. T. (2000). Nonlinear Adaptive Inverse Control for the Magnetic Bearing Systems. Journal of Magnetism and Magnetic Materials, 209, 186-188.

Lu B. et al. (2008). Linear Parameter-Varying Techniques for Control of a Magnetic Bearing System. Control Engineering Practice, 16, 1161-1172.

Cheng K. U. et al. (2009). A Self-tuning Fuzzy PID Type Controller Design for Unbalance Compensation in an Active Magnetic Bearing. Expert Systems with Applications, 36, 8560-8570.

Matsumura et al. (1996). Application of Gain Scheduled H Robust Controller to a Magnetic Bearing. IEEE Transaction on Control Systems Technology, 4(5), 484-493.

Jang M. J., Chen C. L. and Tsao Y. M. (2005). Sliding Mode Control for Active Magnetic Bearing Systems wirh Flexible Rotor. Journal of The Franklin Institute, 342, 401-419.

Hsu C. T. and Chen S. L. (2003). Nonlinear Control of a 3-pole Active Magnetic Bearing System. Automatica, 39, 291-298.

Bernstein, D.S. & Haddad, W.M. (1989). LQG control with a H∞ performance bound: A Riccati equation approach. IEEE Transactions on Automatic Control, Vol. 34(3), pp. 293-305.

Scherer, C.W. (1995). Multi-objective H2/H∞ control. IEEE Transaction on Automatic Control, Vol. 40(6), pp. 1054-1062.

Maria, R. & Sales, R.M. (1998). On the solution of coupled Riccati equations used in mixed H2 and H∞ control. Systems & Control Letters, Vol. 33(2), pp. 115-124.

Lee C. W. and Jeong H. S. (1996). Dynamic Modeling and Optimal Control of Coned-Shaped ABM Systems. Control Engineering Practice, 4(10), 1393-1403.

Hung J. Y., Albritton N. G. and Xia F. (2003). Nonlinear Control of a Magnetic Bearing System. Mechatronics, 13, 621-637.

Mizuno T. and Bleuler H. (1995). Self-Sensing Magnetic Bearing Control System Design Using the Geometric Approach. Control Engineering Practice, 3(7), 925-932.

Agarwal P. K. and Changd S. (2009). Fault-tolerant Control of Three-pole Active Magnetic Bearing. Expert Systems with Applications, 36, 12592-12604.

Kennedy, J. & Eberhart, R. (1995). Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942-1948.

Fleming. P.J. & Purshouse, R.C. (2002). Evolutionary algorithms in control systems engineering: A survey. Control Engineering Practice, Vol. 10(9), pp. 1223-1241.

Song, M.P. & Gu, G.C. (2004). Research on particle swarm optimization: A review. In: Proceedings of the third International Conference on Machine Learning and Cybernetics, pp. 2236-2241.

How to Cite
Bui Trung Thanh. (2016). ROBUST AND OPTIMAL MIXED H2/H¥ CONTROL FOR ACTIVE MAGNETIC BEARING SYSTEMS . UTEHY Journal of Science and Technology, 11, 16-22. Retrieved from