Modeling and FOS Feedback Based Control of SISO Intelligent Structures with Embedded Shear Sensors and Actuators
Active vibration control is an important problem in
structures. The objective of active vibration control is to reduce the vibrations of a system by automatic modification of the system-s
structural response. In this paper, the modeling and design of a fast
output sampling feedback controller for a smart flexible beam system embedded with shear sensors and actuators for SISO system using
Timoshenko beam theory is proposed. FEM theory, Timoshenko beam theory and the state space techniques are used to model the
aluminum cantilever beam. For the SISO case, the beam is divided into 5 finite elements and the control actuator is placed at finite
element position 1, whereas the sensor is varied from position 2 to 5, i.e., from the nearby fixed end to the free end. Controllers are
designed using FOS method and the performance of the designed FOS controller is evaluated for vibration control for 4 SISO models
of the same plant. The effect of placing the sensor at different locations on the beam is observed and the performance of the
controller is evaluated for vibration control. Some of the limitations of the Euler-Bernoulli theory such as the neglection of shear and
axial displacement are being considered here, thus giving rise to an accurate beam model. Embedded shear sensors and actuators have
been considered in this paper instead of the surface mounted sensors
and actuators for vibration suppression because of lot of advantages. In controlling the vibration modes, the first three dominant modes of
vibration of the system are considered.
[1] S.M. Yang, and Y.J. Lee, "Optimization of non-collocated sensor /
actuator location and feedback gain in control systems," Smart materials and Structures, vol. 8, pp. 157-166, 1993.
[2] E. Crawley, and J. Luis, "Use Of Piezoelectric Actuators As Elements
Of Intelligent Structures," AIAA Journal, vol.25, no. 10, pp. 1373-1385, 1987.
[3] S. Hanagud, M.W. Obal, and A.J. Callise, "Optimal Vibration Control
By The Use Of Piezoelectric Sensors And Actuators," Journal of Guidance Control and Dynamics, vol. 15, no. 5, pp. 1199 - 1206, 1992.
[4] B. Bona, M. Indri, and A. Tornamble, "Flexible Piezoelectric Structures-Approximate Motion Equations and Control Algorithms," IEEE Transactions on Automatic Control, vol. 42, no. 1, pp. 94- 101, 1997.
[5] J.E. Hubbard Jr., and T. Baily, "Distributed Piezoelectric Polymer
Active Vibration Control Of A Cantilever Beam," Journal Guidance Dynamics and Control, vol. 8, no. 5, pp. 605 - 611, 1985.
[6] 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.
[7] Yong-Yan Cao, J. Lam, and Y.X. Sun, "Static Output Feedback Stabilization: An LMI Approach", Automatica, vol. 34, no. 12, pp.
1641-1645, 1998.
[8] P. Donthireddy, and K. Chandrashekhara, "Modeling and Shape Control of Composite Beam with Embedded Piezoelectric Actuators", Composite Structures, vol. 35, no. 2, pp. 237- 244, 1996.
[9] C.T. Sun, and X.D. Zhang, "Use of Thickness-Shear Mode in Adaptive Sandwich Structures", Smart Materials and Structures, vol.
4, no. 3, pp. 202 - 206, 1995.
[10] W. Hwang, and H.C. Park, "Finite Element Modeling of Piezoelectric
Sensors and Actuators", AIAA Journal, vol. 31, no. 5, pp. 930-937,1993.
[11] C. Doschner, and M. Enzmann, "On Model based Controller Design
for Smart Structure", Smart Mechanical Systems Adaptronics SAE
International USA, pp. 157-166, , 1998.
[12] 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.
[13] O.J. Aldraihem, R.C. Wetherhold, and T. Singh, "Distributed Control
of Laminated Beams: Timoshenko vs. Euler-Bernoulli Theory",
Journal of Intelligent Materials Systems and Structures, vol. 8, pp. 149-157, 1997.
[14] H. Abramovich, "Deflection Control of Laminated Composite Beam
with Piezoceramic Layers-Closed Form Solution", Composite Structures, vol. 43, no. 3, pp. 217-231, 1998.
[15] X.D. Zhang, and C.T. Sun, "Formulation of an Adaptive Sandwich
Beam", Smart Materials and Structures, vol. 5, no. 6, pp. 814-823, 1996.
[16] S. Raja, G. Prathap, and P.K. Sinha, "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,
[17] A. Benjeddou, M.A. Trindade, and R. Ohayon, "New Shear Actuated
Smart Structure Beam Finite Element", AIAA Journal, vol. 37, pp.
378 - 383, 1998.
[18] O.J. Aldraihem, and A.A. Khdeir, "Smart Beams with Extension and Thickness-Shear Piezoelectric Actuators", Smart Materials and Structures, vol. 9, no. 1, pp. 1- 9, 2000.
[19] V.L. Syrmos, P. Abdallah, P. Dorato, and K. Grigoriadis, "Static Output Feedback A Survey", Automatica, vol. 33, no. 2, pp. 125-137,1997.
[20] H. Werner, and K. Furuta, "Simultaneous Stabilization Based on
Output Measurements", Kybernetika, vol. 31, no. 4, pp. 395 - 411,1995
[21] Herbert Werner, 1998, "Multimodal Robust Control by Fast Output Sampling-An LMI Approach," Automatica, Vol. 34, No. 12, pp. 1625-1630.
[22] B. Culshaw, "Smart Structure A Concept or A Reality," Journal of
Systems and Control Engg., vol. 26, no. 206, pp. 1-8, 1992.
[23] 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.
[24] 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.
[25] T. C. Manjunath, and B. Bandyopadhyay, "Control of vibrations in
flexible smart structures using FOS feedback technique," Int. Journal of Computational Intelligence, vol. 3, no. 2, pp. 127-141, Apr. 2006.
[26] 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.
[27] L. E. Azulay, and H. Abramovich, "Piezoelectric actuation and sensing mechanisms-Closed form solutions," Composite Structures J., vol. 64, pp. 443 - 453, 2004.
[28] 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.
[29] J.S.M. Moita, I.F.P. Coreia, C.M.M. Soares, and C.A.M. Soares, "Active Control of Adaptive Laminated Structures With Bonded Piezoelectric Sensors and Actuators," in Computers and Structures, 82, 1349 - 1358, 2004.
[30] J.A. Zapfe, and G.A. Lesieutre, "A Discrete Layer Beam Finite Element for The Dynamic Analysis of Composite Sandwiched Beams With Integral Damping Layers," in Computers and Structures, vol. 70, pp. 647 - 666, 1999.
[31] J. Lee, "Free Vibration Analysis of Delaminated Composite Beams,"
in Computers and Structures, vol. 74, pp. 121 - 129, 2000.
[32] R.C. Louis, C.S. Edward, and M. Brian, "Induced Shear Piezoelectric Actuators for Rotor Blade Trailing Edge Flaps," in Smart Materials
and Structures, vol. 11, pp. 24 - 35, 2002.
[33] H. Abramovich, and A. Lishvits, "Free Vibrations of Non-symmetric Cross-ply Laminated Composite Beams," in Journal of Sound and Vibration, vol. 176, no. 5, pp. 597 - 612, 1994.
[34] J.L. Fanson, and et al., "Positive position feedback control for structures," AIAA J., vol. 18, no. 4, pp. 717 - 723, 1992.
[35] P. Seshu, "Textbook of Finite Element Analysis," 1st Ed. Prentice Hall of India, New Delhi, 2004.
[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] 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.
[1] S.M. Yang, and Y.J. Lee, "Optimization of non-collocated sensor /
actuator location and feedback gain in control systems," Smart materials and Structures, vol. 8, pp. 157-166, 1993.
[2] E. Crawley, and J. Luis, "Use Of Piezoelectric Actuators As Elements
Of Intelligent Structures," AIAA Journal, vol.25, no. 10, pp. 1373-1385, 1987.
[3] S. Hanagud, M.W. Obal, and A.J. Callise, "Optimal Vibration Control
By The Use Of Piezoelectric Sensors And Actuators," Journal of Guidance Control and Dynamics, vol. 15, no. 5, pp. 1199 - 1206, 1992.
[4] B. Bona, M. Indri, and A. Tornamble, "Flexible Piezoelectric Structures-Approximate Motion Equations and Control Algorithms," IEEE Transactions on Automatic Control, vol. 42, no. 1, pp. 94- 101, 1997.
[5] J.E. Hubbard Jr., and T. Baily, "Distributed Piezoelectric Polymer
Active Vibration Control Of A Cantilever Beam," Journal Guidance Dynamics and Control, vol. 8, no. 5, pp. 605 - 611, 1985.
[6] 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.
[7] Yong-Yan Cao, J. Lam, and Y.X. Sun, "Static Output Feedback Stabilization: An LMI Approach", Automatica, vol. 34, no. 12, pp.
1641-1645, 1998.
[8] P. Donthireddy, and K. Chandrashekhara, "Modeling and Shape Control of Composite Beam with Embedded Piezoelectric Actuators", Composite Structures, vol. 35, no. 2, pp. 237- 244, 1996.
[9] C.T. Sun, and X.D. Zhang, "Use of Thickness-Shear Mode in Adaptive Sandwich Structures", Smart Materials and Structures, vol.
4, no. 3, pp. 202 - 206, 1995.
[10] W. Hwang, and H.C. Park, "Finite Element Modeling of Piezoelectric
Sensors and Actuators", AIAA Journal, vol. 31, no. 5, pp. 930-937,1993.
[11] C. Doschner, and M. Enzmann, "On Model based Controller Design
for Smart Structure", Smart Mechanical Systems Adaptronics SAE
International USA, pp. 157-166, , 1998.
[12] 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.
[13] O.J. Aldraihem, R.C. Wetherhold, and T. Singh, "Distributed Control
of Laminated Beams: Timoshenko vs. Euler-Bernoulli Theory",
Journal of Intelligent Materials Systems and Structures, vol. 8, pp. 149-157, 1997.
[14] H. Abramovich, "Deflection Control of Laminated Composite Beam
with Piezoceramic Layers-Closed Form Solution", Composite Structures, vol. 43, no. 3, pp. 217-231, 1998.
[15] X.D. Zhang, and C.T. Sun, "Formulation of an Adaptive Sandwich
Beam", Smart Materials and Structures, vol. 5, no. 6, pp. 814-823, 1996.
[16] S. Raja, G. Prathap, and P.K. Sinha, "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,
[17] A. Benjeddou, M.A. Trindade, and R. Ohayon, "New Shear Actuated
Smart Structure Beam Finite Element", AIAA Journal, vol. 37, pp.
378 - 383, 1998.
[18] O.J. Aldraihem, and A.A. Khdeir, "Smart Beams with Extension and Thickness-Shear Piezoelectric Actuators", Smart Materials and Structures, vol. 9, no. 1, pp. 1- 9, 2000.
[19] V.L. Syrmos, P. Abdallah, P. Dorato, and K. Grigoriadis, "Static Output Feedback A Survey", Automatica, vol. 33, no. 2, pp. 125-137,1997.
[20] H. Werner, and K. Furuta, "Simultaneous Stabilization Based on
Output Measurements", Kybernetika, vol. 31, no. 4, pp. 395 - 411,1995
[21] Herbert Werner, 1998, "Multimodal Robust Control by Fast Output Sampling-An LMI Approach," Automatica, Vol. 34, No. 12, pp. 1625-1630.
[22] B. Culshaw, "Smart Structure A Concept or A Reality," Journal of
Systems and Control Engg., vol. 26, no. 206, pp. 1-8, 1992.
[23] 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.
[24] 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.
[25] T. C. Manjunath, and B. Bandyopadhyay, "Control of vibrations in
flexible smart structures using FOS feedback technique," Int. Journal of Computational Intelligence, vol. 3, no. 2, pp. 127-141, Apr. 2006.
[26] 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.
[27] L. E. Azulay, and H. Abramovich, "Piezoelectric actuation and sensing mechanisms-Closed form solutions," Composite Structures J., vol. 64, pp. 443 - 453, 2004.
[28] 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.
[29] J.S.M. Moita, I.F.P. Coreia, C.M.M. Soares, and C.A.M. Soares, "Active Control of Adaptive Laminated Structures With Bonded Piezoelectric Sensors and Actuators," in Computers and Structures, 82, 1349 - 1358, 2004.
[30] J.A. Zapfe, and G.A. Lesieutre, "A Discrete Layer Beam Finite Element for The Dynamic Analysis of Composite Sandwiched Beams With Integral Damping Layers," in Computers and Structures, vol. 70, pp. 647 - 666, 1999.
[31] J. Lee, "Free Vibration Analysis of Delaminated Composite Beams,"
in Computers and Structures, vol. 74, pp. 121 - 129, 2000.
[32] R.C. Louis, C.S. Edward, and M. Brian, "Induced Shear Piezoelectric Actuators for Rotor Blade Trailing Edge Flaps," in Smart Materials
and Structures, vol. 11, pp. 24 - 35, 2002.
[33] H. Abramovich, and A. Lishvits, "Free Vibrations of Non-symmetric Cross-ply Laminated Composite Beams," in Journal of Sound and Vibration, vol. 176, no. 5, pp. 597 - 612, 1994.
[34] J.L. Fanson, and et al., "Positive position feedback control for structures," AIAA J., vol. 18, no. 4, pp. 717 - 723, 1992.
[35] P. Seshu, "Textbook of Finite Element Analysis," 1st Ed. Prentice Hall of India, New Delhi, 2004.
[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] 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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:63164", author = "T. C. Manjunath and B. Bandyopadhyay", title = "Modeling and FOS Feedback Based Control of SISO Intelligent Structures with Embedded Shear Sensors and Actuators", abstract = "Active vibration control is an important problem in
structures. The objective of active vibration control is to reduce the vibrations of a system by automatic modification of the system-s
structural response. In this paper, the modeling and design of a fast
output sampling feedback controller for a smart flexible beam system embedded with shear sensors and actuators for SISO system using
Timoshenko beam theory is proposed. FEM theory, Timoshenko beam theory and the state space techniques are used to model the
aluminum cantilever beam. For the SISO case, the beam is divided into 5 finite elements and the control actuator is placed at finite
element position 1, whereas the sensor is varied from position 2 to 5, i.e., from the nearby fixed end to the free end. Controllers are
designed using FOS method and the performance of the designed FOS controller is evaluated for vibration control for 4 SISO models
of the same plant. The effect of placing the sensor at different locations on the beam is observed and the performance of the
controller is evaluated for vibration control. Some of the limitations of the Euler-Bernoulli theory such as the neglection of shear and
axial displacement are being considered here, thus giving rise to an accurate beam model. Embedded shear sensors and actuators have
been considered in this paper instead of the surface mounted sensors
and actuators for vibration suppression because of lot of advantages. In controlling the vibration modes, the first three dominant modes of
vibration of the system are considered.", keywords = "Smart structure, Timoshenko beam theory, Fast output sampling feedback control, Finite Element Method, State space model, SISO, Vibration control, LMI", volume = "2", number = "3", pages = "330-20", }
