Abstract
In this paper, the MFC sensor and actuators are applied to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The mathematical model of the plate was obtained on the base of registration of a system response on a fixed excitation. For the estimation of the system’s behaviour the ARX identification method was used to derive the linear model in the form of a transfer function of the order nine. The obtained model is then used to develop the linear feedback control algorithm for the cancellation of vibration by using the MFC star-shaped actuator (SIMO system). The MFC elements location is dealt with in this study with the use of a laser scanning vibrometer. The control schemes presented have the ability to compute the control effort and to apply it to the actuator within one sampling period. This control scheme is then illustrated through some numerical examples with simulations modelling the designed controller. The paper also describes the experimental results of the designed control system. Finally, the results obtained for the considered plate show that in the chosen frequency limit the designed structure of a closed-loop system with MFC elements provides a substantial vibration suppression.Keywords:
MFC elements, active methods, parametric identification, ARX model, plate vibration suppression.References
1. BRUANT I, GALLIMARD L, NIKOUKAR S, (2010), Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm, Journal of Sound and Vibration, Volume 329, Issue 10, p. 1615–1635.
2. HAC A., LIU L., (1993), Sensor and Actuator Location in Motion Control of Flexible Structures, Journal of Sound and Vibration, 167 (2), pp.239-261.
3. KOS P, LENIOWSKA L, MAZAN D, SIERŻĘGA M.(2013) Active noise and vibration control of circular plate with the use of MFC elements, Advances of Acoustics, University of Rzeszow Publishing House, Rzeszow 2013 ISBN 83-914391-0-9 (in Polish).
4. LENIOWSKA L. (2006) The use of active methods in the suppression of vibration in circular plates, University of Rzeszow Publishing House, Rzeszow 2006, ISBN 978-83-7338-194-0 (in Polish).
5. LENIOWSKA L (2008)., Influence of Damping and Fluid Loading on the Plate Vibration Control Archives of Acoustics, 33, 4, 531–540 (2008).
6. LENIOWSKA L.,(2008) Vibration control of a fluid-loaded circular plate via pole placement, Mechanics, 2008, vol. 27 No.1, pp. 18-24.
7. LENIOWSKA L. (2009), Modelling and Vibration Control of Planar Systems by the Use of Piezoelectric Actuators Archives of Acoustics, vol. 34, no 4, pp. 507-520;
8. Matlab 2014a Documentation – Mathworks - http://www.mathworks.com/help/matlab/.
9. MAZAN D., LENIOWSKA L, MFC sensors and actuators in active noise and vibration control of flexible structure, Procc. of Forum Acusticum, Cracow 2014, ISSN 2221-3767
10. MAZUR, K., PAWEŁCZYK M. (2011), Feed-forward compensation for nonlinearity of vibrating plateas the sound source for active noise control, Mechanics and Control, 2011, 30, 3, 146–150.
11. PATEL I. (2011)., Ceramic Based Intelligent Piezoelectric Energy Harvesting Device, InTech China 2011 pp.133-150.
12. RAMESH KUMAR K., NARAYANAN S.,(2008) Active vibration control of beams with optimal placement of piezoelectric sensors/actuator pairs, Smart Materials and Structures, 17
13. SONG, H.J., CHOI, Y.T., WERELEY, N.M., PUREKAR, A.S., (2010), Energy Harvesting Devices using Macro-Fiber Composite Materials, Journal of Intelligent Material Systems and Structures, 21:647–658.
14. SӦDERSTRӦM T., STOICA P.,(1989) System identification, Prentice Hall Int., London 1989.
15. WILKIE, W. K., BRYANT, G. R., HIGH, J. W. et al., NASA- Langley Research Center Macro-Fiber Composite Actuator (LaRC-MFC): Technical Overview, 2004.
16. http://embedded-solutions.pl/.
2. HAC A., LIU L., (1993), Sensor and Actuator Location in Motion Control of Flexible Structures, Journal of Sound and Vibration, 167 (2), pp.239-261.
3. KOS P, LENIOWSKA L, MAZAN D, SIERŻĘGA M.(2013) Active noise and vibration control of circular plate with the use of MFC elements, Advances of Acoustics, University of Rzeszow Publishing House, Rzeszow 2013 ISBN 83-914391-0-9 (in Polish).
4. LENIOWSKA L. (2006) The use of active methods in the suppression of vibration in circular plates, University of Rzeszow Publishing House, Rzeszow 2006, ISBN 978-83-7338-194-0 (in Polish).
5. LENIOWSKA L (2008)., Influence of Damping and Fluid Loading on the Plate Vibration Control Archives of Acoustics, 33, 4, 531–540 (2008).
6. LENIOWSKA L.,(2008) Vibration control of a fluid-loaded circular plate via pole placement, Mechanics, 2008, vol. 27 No.1, pp. 18-24.
7. LENIOWSKA L. (2009), Modelling and Vibration Control of Planar Systems by the Use of Piezoelectric Actuators Archives of Acoustics, vol. 34, no 4, pp. 507-520;
8. Matlab 2014a Documentation – Mathworks - http://www.mathworks.com/help/matlab/.
9. MAZAN D., LENIOWSKA L, MFC sensors and actuators in active noise and vibration control of flexible structure, Procc. of Forum Acusticum, Cracow 2014, ISSN 2221-3767
10. MAZUR, K., PAWEŁCZYK M. (2011), Feed-forward compensation for nonlinearity of vibrating plateas the sound source for active noise control, Mechanics and Control, 2011, 30, 3, 146–150.
11. PATEL I. (2011)., Ceramic Based Intelligent Piezoelectric Energy Harvesting Device, InTech China 2011 pp.133-150.
12. RAMESH KUMAR K., NARAYANAN S.,(2008) Active vibration control of beams with optimal placement of piezoelectric sensors/actuator pairs, Smart Materials and Structures, 17
13. SONG, H.J., CHOI, Y.T., WERELEY, N.M., PUREKAR, A.S., (2010), Energy Harvesting Devices using Macro-Fiber Composite Materials, Journal of Intelligent Material Systems and Structures, 21:647–658.
14. SӦDERSTRӦM T., STOICA P.,(1989) System identification, Prentice Hall Int., London 1989.
15. WILKIE, W. K., BRYANT, G. R., HIGH, J. W. et al., NASA- Langley Research Center Macro-Fiber Composite Actuator (LaRC-MFC): Technical Overview, 2004.
16. http://embedded-solutions.pl/.
