Active control vibration of circular and rectangular plate with Quantitative Feedback Theory (QFT) Method

Document Type: Research Paper

Authors

1 ahmad_azadi59@yahoo.com, corresponding Author, tel: +989120195909, Ph. D in mechanical engineering in control and vibration

2 kvntrb@kashanu.ac.ir, tel: 09134104534,

Abstract

Natural vibration analysis of plates represents an important issue in engineering applications. In this paper, a new and simplify method for vibration analysis of circular and rectangular plates is presented. The design of an effective robust controller, which consistently attenuates transverse vibration of the plate caused by an external disturbance force, is given. The dynamics of the plate is modeled as a distributed parameter system. We have studied the control vibration of the plate using quantitative feedback theory method by determining the transfer functions between various factors of control system. In this method we have developed the general distributed parameter system method for uncertainty problem for simply supported rectangular plate and clamped circular plate. The quantitative feedback method is one of the robust control methods which is capable to solve problems despite structural and non-structural uncertainty. Quantitative Feedback Theory introduces the new technique to design one-point feedback controllers for distributed parameter systems. The results demonstrate that the control law provided a significant reduction in the plate vibration. The numerical simulation of the designed controller demonstrates that the QFT controller can consistently attenuate the vibration compared to a passive system.

Keywords

Main Subjects


[1] Bailey T, Hubbard JE, Distributed piezoelectricpolymer active vibration control of a cantilever beam, J Guidance and Control 8 (1985) 605–611.
[2] Anderson EH, Hagood NW, Simultaneous piezoelectric sensing/actuation: analysis and application to controlled structures .J Sound Vib 174 (1994) 617–639.
[3] Zou HS, Piezoelectric Shells Distributed Sensing and Control of Continua, Dordrecht: Kluwer Academic Publishers (1993).
[4] Gaudenzi P, Carbonaro R, Benzi E, Control of beam vibrations by means of piezoelectric devices: theory and experiments .J Composite Structure 50 (2000) 373–379.
[5] Lam KY, Ng TY, Active control of composite plates with integrated piezoelectric sensors and actuators under various dynamic loading conditions. Smart Mater Struct 8 (1999) 223–237.
[6] Chandrashekhara K, Agarwal AN, Active vibration control of laminated composite plates using piezoelectric devices: a finite element approach. J Intel Mater System Struct 4 (1993) 496–508.
[7] Birman V, Adali S, Vibration damping using piezoelectric stiffener-actuators with application to orthotropic plates. Compos Struct 35 (1996) 251–261.
[8] J. C. Doyle, A. Let, State-space solutions to standard H2 and H∞ control problems, IEEE Trans. Auto. Cont. ,Vol., 34, No. 8, pp.331-847, (1989).
[9] J. C. Doyle, Al. Et, Survey of quantitative feedback theory (QFT), Inter. Jour. of Rob. and Non. Cont., Vol.11, Issue 10, pp.887-921, (2001).
[10] H. Houpis, S.J. Rasmussen, M.G. Sanz, Quantitative feedback theory: Fundamentals and applications, Published by CRC Press, (2006).
[11] Horowits I, Azor R, quantitative synthesis of feedback system with distributed uncertain plant, International Journal of control, 38 (2): 381-400, (1983).
[12] Horowitz I, Azor R, Uncertain partially noncausal distributed feedback systems, International Journal of Control, 40(5):989–1002, (1984).
[13] I. Horowitz, Quantitative feedback design theory, QFT Publication, 4470 Grinnell, Boulder, (1993).
[14] C. Chain, B. Wang, I. Horowitz, An alternative method for the design of MIMO system with large plant uncertainty, Control Theory and Adv. Tech., Vol.9, pp.955-969, (1993).
[15] C. Cheng, Y. Liao, T. Wang, Quantitative feedback design of uncertain multivariable control systems, Int. J. Con.,Vol.65, pp.237-553, (1996).
[16] C. Cheng, Y. Liao, T. Wang, Quantitative design of uncertain multivariable control system with an inner feedback loop, IEE Proc. Cont. The. and Appl., Vol.144, pp.195-201, (1997).
[17] M. Franchek, S. Jayasuria, Controller design for performance guarantees in uncertain reglating systems, Int. J. Cont., Vol. 61, No.1, pp.127-148, (1995).
[18] Longxiang Chen, Ji Pan, Active control of flexible cantilever plate with multiple time delays, Acta Mechanica Solida Sinica, Vol. 21, No. 3, June, (2008)
[19] K.T. Chen, S.H. Chang, C.H. Chou, Y.H. Liu, Active control by using optical sensors on the acoustic radiation from square plates, Applied Acoustics 69 (2008) 367–377.
[20] A. KACAR, O. KAYA, VIBRATION CONTROL OF LAMINATED PLATE BY SMART PATCHES, International Conference on Integrity, Reliability and Failure, Porto/Portugal, 20-24 July (2009).
[21] Giovanni Caruso, Sergio Galeani, Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators, Simulation Modeling Practice and Theory 11 (2003) 403–419.
[22] TianXiong Liu, HongXing Hua, Robust control of plate vibration via active constrained layer damping, Thin-Walled Structures 42 (2004) 427–448.
[23] M. Kozupa and J. Wiciak, Active Vibration Control of Rectangular Plate with Distributed Piezoelements Excited Acoustically and Mechanically, Acoustic and Biomedical Engineering, Vol. 118 (2010).
[24] Leissa AW. The free vibration of rectangular plates. Journal of Sound and Vibration 31 (1973) 257– 93.
[25] E. Ventsel, T. Krauthammer. Thin Plates and Shells Theory, Analysis, and Applications ISBN: 0- 8247 0575-0, (2011) 13-150.
[26] Reddy, J. N, Theory and Analysis of Elastic Plates, Taylor and Francis, Philadelphia (1999).
[27] Reddy, J. N, A general higher-order theory of plates with moderate thickness, Int. J. Non-Linear Mech, 25(6) (1990), 667-686.
[28] Garcia-Sanz M, Huarte A, Asenjo A. A quantitative robust control approach for distributed parameter systems, Int. J. Robust Nonlinear Control 17 (2007) 135–153.
[29] Garcia-Sanz M, Huarte A, Asenjo A. One-point feedback robust control for distributed parameter systems. Proceedings of 16th IFAC World Congress on Automatic Control, Prague, Czech Republic, (2005).
[30] Garcia-Sanz M, Huarte A, Asenjo A. QFT approach to control one-point feedback distributed parameter systems. Proceedings of 7th International Symposium on Quantitative Feedback Theory and Robust Frequency Methods, Lawrence, KS, U.S.A., (2005).
[31] Kelemen M, Kannai Y, Horowitz I. Improved method for designing linear distributed feedback systems. International Journal of Adaptive Control and Signal Processing 4 (1990) 249–257.
[32] Kelemen M, Kannai Y, Horowitz I. One-point feedback approach to distributed linear systems. International Journal of Control, 49(3) (1989) 969–980.
[33] Chait Y, Maccluer CR, Radcliffe CJ. A Nyquist stability criterion for distributed parameter systems. IEEE Transactions on Automatic Control 34(1) (1989) 90–92.
[34] Hedge MD, Nataraj PSV. The two-point feedback approach to linear distributed systems. Proceedings of the International Conference on Automation, Indore, India, (1995) 281–284.
[35] L. LENIOWSKA, Vibrations of circular plate interacting with an ideal compressible fluid, Archives of Acoustics, 24, 4, 435–449 (1999).
[36] I. MALECKI, Theory of waves and acoustic systems [in Polish], PWN, Warszawa (1964).
[37] L. MEIROVITCH, A theory for the optimal control of the far-field acoustic pressure radiating from submerged structures, Journal of the Acoustical Society of America, 93, 356–362 (1993).
[38] W. RDZANEK, Acoustic radiation of circular plate including the attenuation effect and influence of surroundings, Archives of Acoustics, 16, 3–4, 581– 590 (1991).
[39] L. LENIOWSKA, LENIOWSKI R., Active vibration control of a circular plate with clamped boundary condition, Molecular and Quantum Acoustics, 22, 145–156 (2001).
[40] L. LENIOWSKA, R. LENIOWSKI, Active attenuation of sound radiation from circular fluidloaded plate, Journal of Acoustic and Vibration, 6, 1, 35–41 (2001).
[41] L. LENIOWSKA, Active vibration control of the circular plate with simply-supported boundary condition, Molecular and Quantum Acoustics, 24, 109–124 (2003).