Abstract
Due to actuator time delay existing in an adaptive control of the active balancing system for a fast speed-varying Jeffcott rotor, if an unsynchronized control force (correction imbalance) is applied to the system, it may lead to degradation in control efficiency and instability of the control system. In order to avoid these shortcomings, a simple adaptive controller was designed for a strictly positive real rotor system with actuator time delay, then a Lyapunov-Krasovskii functional was constructed after an appropriate transform of this system model, the stability conditions of this adaptive control system with actuator time delay were derived. After adding a filter function, the active balancing system for the fast speed-varying Jeffcott rotor with actuator time delay can easily be converted to a strictly positive real system, and thus it can use the above adaptive controller satisfying the stability conditions. Finally, numerical simulations show that the adaptive controller proposed works very well to perform the active balancing for the fast speed-varying Jeffcott rotor with actuator time delay.
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References
Van de Vegte J. Continuous automatic balancing of rotating system [J]. Journal of Mechanical Engineering Science, 1964, 6(3): 264–269.
Gosiewski Z. Automatic balancing of flexible rotors, part 2: synthesis of system [J]. Journal of Sound and Vibration, 1987, 114(1): 103–119.
Lee C W, John Y D, Kim Y D. Automatic modal balancing of flexible rotors during operation: computer controlled balancing head [J]. Proc ImechE, 1990, 204(1): 19–25.
Knospe C R, Hope R W. Robustness of adaptive unbalance control of rotors with magnetic bearings [J]. Journal of Vibration and Control, 1996, 2(1): 33–52.
Zhou S, Shi J. Supervisory adaptive balancing of rigid rotors during acceleration [J]. Transactions of NAMRI/SME, 2000, 27: 425–430.
Zhou S, Shi J. Unbalance estimation for speed-varying rigid rotor using time-varying observer [J]. ASME Journal of Dynamic Systems, Measurement, and Control, 2001, 123: 637–644.
Zhou S, Shi J. Optimal one-plane active balancing of rigid rotor during acceleration [J]. Journal of Sound and Vibration, 2002, 249(1): 196–205.
Shin K K, Ni J. Adaptive control of multi-plane active balancing systems for speed-varying rotors [J]. ASME Journal of Dynamic Systems, Measurement, and Control, 2003, 125: 372–381.
Evesque S, Annaswamy A M, Niculescu S. Adaptive control of a class of time-delay system [J]. ASME Journal of Dynamic Systems, Measurement, and Control, 2003, 125: 186–193.
Niculescu S, Annaswamy A M. An adaptive Smith-controller for time-delay system with relative degree n* ≤ 2 [J]. System & Control Letters, 2003, 49: 347–358.
Niculescu S. Delay effects on stability, a robust control approach, in: lecture notes in control and information sciences [M]. Heidelberg: Springer, 2001: 269.
Astrom K J, Wittenmark B. Adaptive controlp [M]. New York: Addison Wesley, 1995.
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Hu, B., Fang, Zc. Adaptive control of active balancing system for a fast speed-varying Jeffcott rotor with actuator time delay. J. Shanghai Jiaotong Univ. (Sci.) 13, 297–303 (2008). https://doi.org/10.1007/s12204-008-0297-z
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DOI: https://doi.org/10.1007/s12204-008-0297-z