An Adaptive Vibration Control Procedure Based on Symbolic Solution of Diophantine Equation

• Autorzy: Leniowska L.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the adaptive control based on symbolic solution of Diophantine equation is used to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The plate is excited by a uniform force over the bottom surface generated by a loudspeaker. The axially-symmetrical vibrations of the plate are measured by the application of the strain sensors located along the plate radius, and two centrally placed piezoceramic discs are used to cancel the plate vibrations. The adaptive control scheme presented in this work has the ability to calculate the error sensor signals, to compute the control effort and to apply it to the actuator within one sampling period. For precise identification of system model the regularized RLS algorithm has been applied. Self-tuning controller of RST type, derived for the assumed system model of the 4th order is used to suppress the plate vibration. Some numerical examples illustrating the improvement gained by incorporating adaptive control are demonstrated.

Słowa kluczowe

EN

adaptive control; vibration cancellation; diophantine equations; self-tuning control; RLS algorithm

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2011
• Tom: Vol. 36, No. 4
• Strony: 901--912
• Opis fizyczny: Bibliogr. 13 poz., fot., wykr.

Twórcy

autor

Leniowska L.

• University of Rzeszów Rejtana 16, 35-310 Rzeszów, Poland,

Bibliografia

• 1. Appolinario J. (2009), QRD-RLS Adaptive Filtering, Springer-Verlag.
• 2. Bobal V., Böhm J., Prokop J., Fessl J. (2000), Practical Aspects of Self-Tuning Controllers: Algorithms and Implementation, VUTIUM Press, Brno.
• 3. Diniz P.S.R. (2008), Adaptive Filtering: Algorithms and Practical Implementation, 3rd Edition, Springer, New York.
• 4. Isserman R. (1982), Parameter adaptive control algorithms - a tutorial, Automatica, 18, 5, 513-528.
• 5. Latos M., Pawełczyk M. (2010), Adaptive algorithms for enhancement of speech subject to a high-level noise, Archives of Acoustics, 35, 2, 203-212.
• 6. Leniowska L., Kos P. (2009), Self-Tuning Control with Regularized RLS Algorithm for Vibration Cancellation of a Circular Plate, Archives of Acoustics, 34, 4, 613-624.
• 7. Leniowska L. (2008), Vibration control of a fluid-loaded circular plate via pole placement, Mechanics, 27, 1, 18-24.
• 8. Leniowska L. (2009), Modeling and Vibration Control of Planar Systems by the Use of Piezoelectric Actuators, Archives of Acoustics, 34, 4, 507-520.
• 9. Ljung L., Söderström T. (1983), Theory and Practice of Recursive Identification, MIT Press, Cambridge MA., 1983.
• 10. Machǎcek J., Bobal V. (2002), Adaptive PID controller with on-line identification, Journal of Electrical Engineering, 53, 233-240.
• 11. Peeters R., Hanzon B. (1998), Symbolic computation of Fisher information matrices, Part 2, Sylvester equations in controller companion form, Report M 98-02, Dept. Math., Universiteit Maastricht.
• 12. Söderström T., Stoica P. (1994), System Identification, Prentice Hall.
• 13. Tikhonov A., Arsenin V. (1997), Solutions of Ill-Posed Problems, Wiley, New York