Stability constraints of active magnetic bearing control systems

Direct Lyapunov stability method is employed to analyse the closed-loop stability of an electromagnetically suspended rotor system in which non-linearity and singular perturbation nature are embedded. Five explicit sets of stability constraints are proposed so that the state feedback loop is not over-designed. Under impact of modeling inaccuracy, due to neglected higher-order terms, stability conditions for equilibrium point, slow-mode manifold and boundary layer are studied. In addition, the singular perturbation order-reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller. The stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available. The proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness, rise time and overshoot is illustrated, in comparison to output feedback law and deadbeat control. The reported state feedback loop not only stabilizes the inherently unstable open-loop system, but also preserves the robustness with respect to the parasitic parameter variation and modeling error due to neglected higher-order terms of magnetic control force.

[1]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[2]  Hassan K. Khalil,et al.  Multirate and composite control of two-time-scale discrete-time systems , 1985 .

[3]  A. TUSTIN,et al.  Automatic Control Systems , 1950, Nature.

[4]  A. El Moudni,et al.  On analysis of discrete singularly perturbed non-linear systems: Application to the study of stability properties , 1997 .

[5]  Y.-C. Lin,et al.  Two-time-scale design of active suspension control using acceleration feedback , 1992, [Proceedings 1992] The First IEEE Conference on Control Applications.

[6]  L. Cao,et al.  REDUCED‐ORDER MODELS FOR FEEDBACK STABILIZATION OF LINEAR SYSTEMS WITH A SINGULAR PERTURBATION MODEL , 2005 .

[7]  Masayuki Fujita,et al.  mu -synthesis of an electromagnetic suspension system , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[8]  Huaping Liu,et al.  Stability analysis and synthesis of fuzzy singularly perturbed systems , 2005, IEEE Transactions on Fuzzy Systems.

[9]  Chao-Lin Kuo,et al.  Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System , 2005, J. Intell. Robotic Syst..

[10]  Feng Gao,et al.  Further results on active magnetic bearing control with input saturation , 2006, IEEE Transactions on Control Systems Technology.

[11]  Benjamin C. Kuo,et al.  Automatic control systems (7th ed.) , 1991 .

[13]  Nan-Chyuan Tsai,et al.  Digital sliding mode control for Maglev rotors , 2006, 2006 American Control Conference.

[14]  M. Mahmoud.  Order reduction and control of discrete systems , 1982 .

[15]  P. V. Kokotovic,et al.  On the control of dynamic systems with unknown operating point , 1997, 1997 European Control Conference (ECC).

[16]  Hassan K. Khalil.  Output feedback control of linear two-time-scale systems , 1987 .

[17]  Masayuki Fujita,et al.  Μ -synthesis of an Electromagnetic Suspension System , 1995, IEEE Trans. Autom. Control..

[18]  Magdi S. Mahmoud,et al.  Discrete two-time-scale systems , 1986 .