Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Controller Design for Euler-Bernoulli Smart Structures Using Robust Decentralized POF via Reduced Order Modeling

Authors: T.C. Manjunath, B. Bandyopadhyay

Abstract:

This paper features the proposed modeling and design of a Robust Decentralized Periodic Output Feedback (RDPOF) control technique for the active vibration control of smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Euler-Bernoulli beam theory and the Finite Element Method (FEM) technique by dividing the beam into 4 finite elements and placing the piezoelectric sensor / actuator at two finite element locations (positions 2 and 4) as collocated pairs, i.e., as surface mounted sensor / actuator, thus giving rise to a multivariable model of the smart structure plant with two inputs and two outputs. Five such multivariable models are obtained by varying the dimensions (aspect ratios) of the aluminum beam, thus giving rise to a multimodel of the smart structure system. Using model order reduction technique, the reduced order model of the higher order system is obtained based on dominant eigen value retention and the method of Davison. RDPOF controllers are designed for the above 5 multivariable-multimodel plant. The closed loop responses with the RDPOF feedback gain and the magnitudes of the control input are observed and the performance of the proposed multimodel smart structure system with the controller is evaluated for vibration control.

Keywords: Smart structure, Euler-Bernoulli beam theory, Periodic output feedback control, Finite Element Method, State space model, SISO, Embedded sensors and actuators, Vibration control, Reduced order model

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071738

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1672

References:


[1] M. Aoki, "Control of large scale dynamic systems by aggregation," IEEE Trans. Auto. Contr., vol. AC-13, pp. 246 - 253, 1968.
[2] 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, pp, 605 - 611, 1985.
[3] E. F. Crawley, and J. De Luis, "Use of piezoelectric actuators as elements of intelligent structures," AIAA J, vol. 25, pp. 1373 - 1385, 1987.
[4] A. B. Chammas, and C. T. Leondes, "Pole placement by piecewise constant output feedback," Int. J. Contr., vol. 29, pp. 31 - 38, 1979.
[5] 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.
[6] A. B. Chammas, 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.
[7] B. Culshaw, "Smart Structures : A concept or a reality," J. of Systems and Control Engg., vol. 26, no. 206, pp. 1 - 8, 1992.
[8] 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.
[9] E. J. Davison, "A method for simplifying linear dynamical systems," IEEE Trans. Auto. Contr., vol. AC-11, pp. 93 - 101, 1966.
[10] J. L. Fanson, and T. K. Caughey, "Positive position feedback control for structures," AIAA J., vol. 18, no. 4, pp. 717 - 723, 1990.
[11] P. Gahnet, A. Nemirovski, A. J. Laub, and M. Chilali, "LMI Tool box for Matlab", The Math works Inc., Natick MA, 1995.
[12] W. Hwang, and H. C. Park, "Finite element modeling of piezoelectric sensors and actuators", AIAA J., vol. 31, no. 5, pp. 930 - 937, 1993.
[13] 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.
[14] S. S. Lamba, and S. Vittal Rao, "On the suboptimal control via the simplified model of Davison," IEEE Trans. Auto. Contr., vol. AC-19, pp. 448 - 450, 1974.
[15] 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.
[16] J. Mark Balas, "Feedback control of flexible structures," IEEE Trans. Automat. Contr., vol. AC-23, pp. 673 - 679, 1978.
[17] T. C. Manjunath, and B. Bandyopadhyay, "Vibration control of a smart flexible cantilever beam using periodic output feedback control technique," Proc. Fourth Asian Control Conference ASCC-2002, paper no. 1679, pp. 1302 - 1307, Sept. 25-27, 2002.
[18] 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.
[19] 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 Mater. and Struct., vol. 14, no. 4, pp. 624 - 636, Aug. 2005.
[20] 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.
[21] M. S. Mahmoud, and G. M. Singh, "Large scale systems modeling," Pergamon Press, Oxford, 1981.
[22] 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.
[23] V. L. Syrmos, P. Abdallah, P. Dorato, and K. Grigoriadis, "Static output feedback : A survey," Automatica, vol. 33, no. 2, pp. 125 - 137, 1997.
[24] P. Seshu, "Textbook of Finite Element Analysis," 1st Ed. Prentice Hall of India, New Delhi, 2004.
[25] 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.
[26] H. Werner, and K. Furuta, "Simultaneous stabilization based on output measurements," Kybernetika, vol. 31, no. 4, pp. 395 - 411, 1995.
[27] H. Werner, "Robust multivariable control of a turbo-generator by periodic output feedback," vol. 31, no. 4, pp. 395 - 411, 1997.
[28] 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.