Robust nonlinear position-flux zero-bias control for uncertain AMB system

This paper presents a robust nonlinear control law that combines a parametric uncertainty of the single one-degree-of-freedom active magnetic bearing (AMB) system with disturbance. The robust nonlinear feedback tool such as control Lyapunov function (CLF) and robust stability techniques are developed. The control objective is to globally stabilise the mass position of an AMB with flux feedback. The flux-based control model for an AMB system is derived due to voltage switching strategy with voltage saturation. This strategy enables the flux control under a zero-bias or low-bias flux operation. In the zero-bias control, only one electromagnet in each axis of the AMB is active at any given time, depending on the rotor displacement. The proposed robust nonlinear CLF with a zero-bias for an uncertain AMB system can achieve a dynamic performance superior to that of a linear controller with the zero-bias or with the classical bias operations.

[1]  Hannes Bleuler,et al.  New concepts for cost-effective magnetic bearing control , 1994, Autom..

[2]  Eduardo Sontag A Lyapunov-Like Characterization of Asymptotic Controllability , 1983, SIAM Journal on Control and Optimization.

[3]  J. L. Massera Contributions to Stability Theory , 1956 .

[4]  P. Kokotovic,et al.  Global robustness of nonlinear systems to state measurement disturbances , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[5]  J. Willems Dissipative dynamical systems part I: General theory , 1972 .

[6]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[7]  Rafal P. Jastrzebski,et al.  Cascaded Position-Flux Controller for an AMB System Operating at Zero Bias , 2014 .

[8]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[9]  Zdzisław Gosiewski,et al.  Robust control of active magnetic suspension: Analytical and experimental results , 2008 .

[10]  A. Mystkowski Robust control and modal analysis of flexible rotor magnetic bearings system , 2010 .

[11]  Zdzisław Gosiewski,et al.  The Robust Control of Magnetic Bearings for Rotating Machinery , 2006 .

[12]  A. Mystkowski,et al.  m-Synthesis control of flexible modes of AMB rotor , 2009 .

[13]  A. Isidori,et al.  H∞ control via measurement feedback for general nonlinear systems , 1995, IEEE Trans. Autom. Control..

[14]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[15]  P. S. Bauer Dissipative Dynamical Systems: I. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[16]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[17]  Arkadiusz Mystkowski Mu‐Synthesis for Magnetic Bearings of Flywheel , 2009 .

[18]  Panagiotis Tsiotras,et al.  Low-bias control of AMB subject to voltage saturation: state-feedback and observer designs , 2005, IEEE Transactions on Control Systems Technology.

[19]  The Robust Control of Magnetic Suspension with Rapidly Changing of Rotor Speed , 2009 .

[20]  Z. Artstein Stabilization with relaxed controls , 1983 .

[21]  A. E. Hartavi,et al.  Variable Bias Current in Magnetic Bearings for Energy Optimization , 2007, IEEE Transactions on Magnetics.

[22]  Z. Gosiewski,et al.  One-DoF robust control of shaft supported magnetically , 2006 .

[23]  Mi-Ching Tsai,et al.  Robust and Optimal Control , 2014 .

[24]  Panagiotis Tsiotras,et al.  Control of zero-bias magnetic bearings using control Lyapunov functions , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[25]  G. Schweitzer,et al.  Magnetic bearings : theory, design, and application to rotating machinery , 2009 .

[26]  T. Kaczorek Pointwise completeness and pointwise degeneracy of standard and positive hybrid linear systems described by the general model , 2010 .

[27]  Panagiotis Tsiotras,et al.  Zero- and low-bias control designs for active magnetic bearings , 2003, IEEE Trans. Control. Syst. Technol..

[28]  John Tsinias Stabilizations of affine in control nonlinear systems , 1988 .

[29]  Carl R. Knospe The nonlinear control benchmark experiment , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).