Control of Flexible Rotors

The goal of this chapter is to discuss the problems that rotor flexibility and hardware limitations introduce in the design of AMB controllers and to present some solution strategies for these problems. Rotor flexibility means that the rotor can have relatively high gain at higher frequencies and this introduces complications in designing controllers with physically realizable bandwidths. Further, non-collocation of actuators and sensors along with finite bandwidth of actuation, sensing, and control mechanisms can mean that a passivity type of approach to controller design is not feasible. These issues and others will be explored here through a series of examples. Control solutions are presented for a flexible rotor ranging from the simplest PID approach through to a fairly sophisticated μ−synthesis solution. The performances of these controllers are compared in terms of complexity, forced response performance, and sensitivity to model parameters. The literature relating to control of AMBs and, especially, those supporting flexible rotors is vast: certainly the largest segment of AMB literature is devoted to control. The bibliography for this chapter attempts to provide a survey of this literature but is by no means complete: a comprehensive survey would contain hundreds of references. Over 80 references are provided: a mix of background material on the general control problem and papers directed specifically at AMB control.

[1]  M. N. Sahinkaya,et al.  Vibration control of multi-mode rotor-bearing systems , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  Carl R. Knospe,et al.  Experiments in the control of unbalance response using magnetic bearings , 1995 .

[3]  Markus Ahrens,et al.  Cross Feedback Control of a Magnetic Bearing System: Controller Design Considering Gyroscopic Effects , 1996 .

[4]  Roland Siegwart,et al.  Control Concepts for Active Magnetic Bearings , 1991 .

[5]  Paul E. Allaire,et al.  Effect of Control Algorithms on Magnetic Journal Bearing Properties , 1986 .

[6]  J. Bay.  Fundamentals of Linear State Space Systems , 1998 .

[7]  James Patrick Lyons,et al.  Integration of Magnetic Bearings in the Design of Advanced Gas Turbine Engines , 1994 .

[8]  Helmut Habermann,et al.  The Active Magnetic Bearing Enables Optimum Damping of Flexible Rotor , 1984 .

[9]  Kenzo Nonami,et al.  Robust Control of Flexible Rotor-Magnetic Bearing Systems Using Discrete Time Sliding Mode Control , 1994 .

[10]  Raoul Herzog,et al.  Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings , 1996, IEEE Trans. Control. Syst. Technol..

[11]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[12]  J. Cruz,et al.  RELATIONSHIP BETWEEN SENSITIVITY AND STABILITY OF MULTIVARIABLE FEEDBACK SYSTEMS. , 1981 .

[13]  M. Balas.  Active control of flexible systems , 1978 .

[14]  Stefano Carabelli,et al.  Active magnetic bearing control loop modeling for a finite element rotordynamics code , 1994 .

[15]  Carl R. Knospe,et al.  Robustness of Adaptive Rotor Vibration Control to Structured Uncertainty , 1997 .

[16]  John C. Doyle,et al.  Guaranteed margins for LQG regulators , 1978 .

[17]  Lloyd E. Barrett,et al.  Practical applications of singular value decomposition in rotordynamics , 2005 .

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

[19]  H. Habermann,et al.  An active magnetic bearing system , 1980 .

[20]  Joga Dharma Setiawan,et al.  Synchronous Sensor Runout and Unbalance Compensation in Active Magnetic Bearings Using Bias Current Excitation , 2002 .

[21]  Carl R. Knospe,et al.  Robustness of Adaptive Unbalance Control of Rotors with Magnetic Bearings , 1996 .

[22]  Antero Arkkio,et al.  Active Magnetic Bearings , 2007 .

[23]  Abdelfatah M. Mohamed,et al.  Modeling and robust control of self-sensing magnetic bearings with unbalance compensation , 1997, Proceedings of the 1997 IEEE International Conference on Control Applications.

[24]  Jürgen Ackermann,et al.  Sampled-Data Control Systems , 1985 .

[25]  Roland Siegwart,et al.  Application of digital signal processors for industrial magnetic bearings , 1994, IEEE Trans. Control. Syst. Technol..

[26]  Carl R. Knospe,et al.  Gain-scheduled control of a magnetic bearing with low bias flux , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[27]  J. R. Salm.  Active Electromagnetic Suspension of an Elastic Rotor: Modelling, Control, and Experimental Results , 1988 .

[28]  J. Cruz,et al.  A new approach to the sensitivity problem in multivariable feedback system design , 1964 .

[29]  Giancarlo Genta,et al.  Dynamics of Rotating Systems , 2005 .

[30]  Hannes Bleuler.  Decentralized control of magnetic rotor bearing systems , 1984 .

[31]  Fen Wu,et al.  A generalized LPV system analysis and control synthesis framework , 2001 .

[32]  T. N. Shiau,et al.  Vibration and Control of a Flexible Rotor in Magnetic Bearings Using Hybrid Method and H∞ Control Theory , 1997 .

[33]  B. Shafai,et al.  Magnetic bearing control systems and adaptive forced balancing , 1994, IEEE Control Systems.

[34]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[35]  Rainer Nordmann,et al.  Implementation results of µ-synthesis control for an energy storage flywheel test rig , 2000 .

[36]  V. A. Spector,et al.  Modeling and Design Implications of Noncollocated Control in Flexible Systems , 1990 .

[37]  V. Cheng,et al.  Limitations on the closed-loop transfer function due to right-half plane transmission zeros of the plant , 1980 .

[38]  Florian Lösch.  Identification and automated controller design for active magnetic bearing systems , 2002 .

[39]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[40]  Yohji Okada,et al.  Vibration Analysis and Active Control of Flexible-Shell-Structured Rotor Supported by Magnetic Bearings , 1994 .

[41]  Jianjun Shi,et al.  Active Balancing and Vibration Control of Rotating Machinery: A Survey , 2001 .

[42]  Kenzo Nonami,et al.  LMI approach to gain scheduled H/sub /spl infin// control beyond PID control for gyroscopic rotor-magnetic bearing system , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[43]  Roger L. Fittro,et al.  The μ Approach to Control of Active Magnetic Bearings , 2002 .

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

[45]  Chris R. Fuller,et al.  The Effect of Actuator and Sensor Placement on the Active Control of Rotor Unbalance , 2003 .

[46]  Hidekazu Nishimura,et al.  Robust Control of Magnetic Levitation Systems by Means of H ∞ Control/μ-Synthesis , 1994 .

[47]  Lloyd E. Barrett,et al.  Optimization of Bearing Locations for Rotor Systems With Magnetic Bearings , 1995 .

[48]  G. Zames,et al.  On H ∞ -optimal sensitivity theory for SISO feedback systems , 1984 .

[49]  Kamal Youcef-Toumi,et al.  Modeling, design, and control integration: a necessary step in mechatronics , 1996 .

[50]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[51]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[52]  G. Zames,et al.  Feedback, minimax sensitivity, and optimal robustness , 1983 .

[53]  J. Freudenberg,et al.  Limitations of feedback properties imposed by open-loop right half plane poles , 1991 .

[54]  Stefano Carabelli,et al.  Rotor on active magnetic suspension, part I : Theoretical considerations , 1998 .

[55]  H. Ulbrich,et al.  Active Control of Vibrations in the Case of Asymmetrical High-Speed Rotors by Using Magnetic Bearings , 1985 .

[56]  F. Matsumura,et al.  System modeling and control design of a horizontal-shaft magnetic-bearing system , 1986 .

[57]  J. C. Pradetto,et al.  Rotor dynamic behaviour of a high-speed oil-free motor compressor with a rigid coupling supported on four radial magnetic bearings , 1994 .

[58]  John C. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[59]  Kamal Youcef-Toumi,et al.  Dynamic Analysis and Control of High Speed and High Precision Active Magnetic Bearings , 1992 .

[60]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[61]  E. H. Maslen,et al.  A Stability Model for Flexible Rotors With Magnetic Bearings , 1992 .

[62]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[63]  Graham C. Goodwin,et al.  Fundamental limits in sensitivity minimization: multiple-input-multiple-output (MIMO) plants , 2001, IEEE Trans. Autom. Control..

[64]  Reza Langari,et al.  Robust fuzzy control of a magnetic bearing system subject to harmonic disturbances , 1997, IEEE Trans. Control. Syst. Technol..

[65]  D. L. Trumper,et al.  Linearizing control of magnetic suspension systems , 1997, IEEE Trans. Control. Syst. Technol..

[66]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[67]  Brian T. Murphy,et al.  Analysis and Testing of a Magnetic Bearing Energy Storage Flywheel With Gain-Scheduled, MIMO Control , 2000 .

[68]  M. Spirig,et al.  Three Practical Examples of Magnetic Bearing Control Design Using a Modern Tool , 2002 .

[69]  George T. Gillies,et al.  Digital controller for a magnetic suspension system , 1986 .