**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Multivariable Control of Smart Timoshenko Beam Structures Using POF Technique

**Authors:**
T.C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko theory,
Euler-Bernoulli
theory,
Periodic output feedback control,
Finite Element Method,
State space model,
Vibration control,
Multivariable system,
Linear
Matrix Inequality

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1328874

**References:**

[1] O. J. Aldraihem, R. C. Wetherhold, and T. Singh, "Distributed control of laminated beams : Timoshenko Vs. Euler-Bernoulli Theory," J. of Intelligent Materials Systems and Structures, vol. 8, pp. 149-157, 1997.

[2] H. Abramovich, "Deflection control of laminated composite beam with piezoceramic layers-Closed form solutions," Composite Structures, vol. 43, no. 3, pp. 217-131, 1998.

[3] O. J. Aldraihem, and K. A. Ahmed, "Smart beams with extension and thickness-shear piezoelectric actuators," Smart Materials and Structures, vol. 9, no. 1, pp. 1-9, 2000.

[4] A. K. Ahmed, and J. A. Osama, "Deflection analysis of beams with extension and shear piezoelectric patches using discontinuity functions" Smart Materials and Structures, vol. 10, no. 1, pp. 212-220, 2001.

[5] L. E. Azulay, and H. Abramovich, "Piezoelectric actuation and sensing mechanisms-Closed form solutions," Composite Structures J., vol. 64, pp. 443-453, 2004.

[6] T. Baily, and J. E. Hubbard Jr., "Distributed piezoelectric polymer active vibration control of a cantilever beam," J. of Guidance, Control and Dynamics, vol. 8, no.5, pp. 605-611, 1985.

[7] A. Benjeddou, M. A. Trindade, and R. Ohayon, "New shear actuated smart structure beam finite element," AIAA J., vol. 37, pp. 378-383, 1999.

[8] E. F. Crawley, and J. De Luis, "Use of piezoelectric actuators as elements of intelligent structures," AIAA J., vol. 25, pp. 1373-1385, 1987.

[9] K. Chandrashekhara, and S. Varadarajan, "Adaptive shape control of composite beams with piezoelectric actuators," J. of Intelligent Materials Systems and Structures, vol. 8, pp. 112-124, 1997.

[10] B. Culshaw, "Smart Structures : A concept or a reality," J. of Systems and Control Engg., vol. 26, no. 206, pp. 1-8, 1992.

[11] C. R. Cooper, "Shear coefficient in Timoshenko beam theory," ASME J. of Applied Mechanics, vol. 33, pp. 335-340, 1966.

[12] S. B. Choi, C. Cheong, and S. Kini, "Control of flexible structures by distributed piezo-film actuators and sensors," J. of Intelligent Materials and Structures, vol. 16, pp. 430-435, 1995.

[13] A. B. Chammas, and C. T. Leondes, "Pole placement by piecewise constant output feedback," Int. J. Contr., vol. 29, pp. 31-38, 1979.

[14] A. B. Chammas, and C. T. Leondes, "On the design of LTI systems by periodic output feedback, Part-I, Discrete Time pole assignment," Int. J. Ctrl., vol. 27, pp. 885-894, 1978.

[15] Chammas, A. B. and C. T. Leondes, "On the design of LTI systems by periodic output feedback, Part-II, Output feedback controllability," Int. J. Ctrl., vol. 27, pp. 895-903, 1978.

[16] C. Doschner, and M. Enzmann, "On model based controller design for smart structure," Smart Mechanical Systems Adaptronics SAE International USA, pp. 157-166, 1998.

[17] P. Donthireddy, and K. Chandrashekhara, "Modeling and shape control of composite beam with embedded piezoelectric actuators," Comp. Structures, vol. 35, no. 2, pp. 237-244, 1996.

[18] J. L. Fanson, and T. K. Caughey, "Positive position feedback control for structures," AIAA J., vol. 18, no. 4, pp. 717-723, 1990.

[19] J. C. Geromel, C. C. De Souza, and R. E. Skeleton, "LMI Numerical solution for output feedback stabilization," Proc. American Contr. Conf., pp. 40-44, 1994.

[20] P. Gahnet, A. Nemirovski, A. J. Laub, and M. Chilali, "LMI Tool box for Matlab", The Math works Inc., Natick MA, 1995.

[21] S. Hanagud, M. W. Obal, and A. J. Callise, "Optimal vibration control by the use of piezoceramic sensors and actuators," J. of Guidance, Control and Dyn., vol. 15, no. 5, pp. 1199-1206, 1992.

[22] W. Hwang, and H. C. Park, "Finite element modeling of piezoelectric sensors and actuators", AIAA J., vol. 31, no. 5, pp. 930-937, 1993.

[23] J. B. Kosmataka, and Z. Friedman, "An improved two-node Timoshenko beam finite element", Computers and Struct., vol. 47, no. 3, pp. 473- 481, 1993.

[24] W. S. Levine, and M. Athans, "On the determination of the optimal constant output feedback gains for linear multivariable systems," IEEE Trans. Auto. Contr., vol. AC-15, pp. 44-48, 1970.

[25] T. C. Manjunath, and B. Bandyopadhyay, "Modeling and fast output sampling feedback control of a smart Timoshenko cantilever beam," International Journal of Smart Structures and Systems, vol. 1, no. 3, ISSN 1738-1584, pp. 283-308, Sep. 2005.

[26] T. C. Manjunath, and B. Bandyopadhyay, "Vibration control of a smart flexible cantilever beam using periodic output feedback," Asian Journal of Control, vol. 6, no. 1, pp. 74 - 87, Mar. 2004.

[27] T. C. Manjunath, and B. Bandyopadhyay, "Fault tolerant control of flexible smart structures using robust decentralized periodic output sampling feedback technique," International Journal of Smart Materi. and Struct., vol. 14, no. 4, pp. 624-636, Aug. 2005.

[28] T. C. Manjunath, and B. Bandyopadhyay, R. Gupta, and M. Umapathy, "Multivariable control of a smart structure using periodic output feedback control technique," Proc. of the Seventh International Conference on Control, Automation, Robotics and Computer Vision, ICARCV 2002, Singapore, Paper No. 2002P1283, pp. 1481-1486, Dec. 2-5, 2002.

[29] Manjunath, T.C., Bandyopadhyay, B. and Janardhanan, S., "Multivariable control of a smart structure using periodic output feedback control technique," Proc. 3rd International Conference on System Identification and Control Problems, SICPRO 2004, Institute of Control Sciences, Moscow, Russia, Paper No. 23016, pp. 1300-1312, Jan. 28 -30, 2004.

[30] S. Raja, G. Prathap, and P. K. Sinha, P.K., "Active vibration control of composite sandwich beams with piezoelectric extension-bending and shear actuators," Smart Materials and Structures, vol. 11, no. 1, pp. 63- 71, 2002.

[31] S. Rao, and M. Sunar, "Piezoelectricity and its uses in disturbance sensing and control of flexible structures : A survey," Applied Mechanics Rev., vol. 47, no. 2, pp. 113-119, 1994.

[32] C. T. Sun, and X. D. Zhang, "Use of thickness-shear mode in adaptive sandwich structures," Smart Materials and Structures J., vol. 3, no. 4, pp. 202-206, 1995.

[33] V. L. Syrmos, P. Abdallah, P. Dorato, and K. Grigoriadis, "Static output feedback : A survey," Automatica, vol. 33, no. 2, pp. 125-137, 1997.

[34] P. Seshu, "Textbook of Finite Element Analysis," 1st Ed. Prentice Hall of India, New Delhi, 2004.

[35] J. Thomas, and B. A. H. Abbas, "Finite Element Methods for dynamic analysis of Timoshenko beam," J. of Sound and Vibration, vol. 41, pp. 291-299, 1975.

[36] M. Umapathy, and B. Bandyopadhyay, "Control of flexible beam through smart structure concept using periodic output feedback," System Science Journal, vol. 26, no. 1, pp. 23-46, 2000.

[37] H. Werner, and K. Furuta, "Simultaneous stabilization based on output measurements," Kybernetika, vol. 31, no. 4, pp. 395-411, 1995.

[38] H. Werner, H., "Robust multivariable control of a turbo-generator by periodic output feedback," Proc. American Contr. Conf., New Mexico, pp. 1979-1983, 1997.

[39] Y. C. Yan, J. Lam, and Y. X. Sun, "Static output feedback stabilization: An LMI approach," Automatica, vol. 34, no. 12, pp. 1641-1645, 1998.

[40] X. D. Zhang, and C. T. Sun, "Formulation of an adaptive sandwich beam," Smart Mater. and Struct., vol. 5, no.6, pp. 814-823, 1996.

[41] T. C. Manjunath, and B. Bandyopadhyay, "Modeling and fast output sampling feedback control of a smart Timoshenko cantilever beam", Smart Structures and Systems, vol. 1, no. 3, pp. 283-308, Sept. 2005.