Controller Design for Euler-Bernoulli Smart Structures Using Robust Decentralized FOS via Reduced Order Modeling
This paper features the modeling and design of a
Robust Decentralized Fast Output Sampling (RDFOS) Feedback
control technique for the active vibration control of a 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 aluminium beam. Using model
order reduction technique, the reduced order model of the higher
order system is obtained based on dominant Eigen value retention
and the Davison technique. RDFOS feedback controllers are
designed for the above 5 multivariable-multimodel plant. The closed
loop responses with the RDFOS feedback gain and the magnitudes of
the control input are obtained and the performance of the proposed
multimodel smart structure system is evaluated for vibration control.
[1] Baily, T. and Hubbard Jr., J.E., "Distributed Piezoelectric Polymer
Active Vibration Control of A Cantilever Beam", J. of Guidance,
Control and Dynamics, Vol. 8, no. 5, pp. 605 - 611, 1985.
[2] Crawley, E.F. and De Luis, J., "Use of Piezoelectric Actuators as
Elements of Intelligent Structures", AIAA J., Vol. 25, pp. 1373-1385,
1987.
[3] Culshaw, B., "Smart Structures - A Concept or A Reality," J. of Systems
and Control Engg., Vol. 26, no. 206, pp. 1- 8, 1992.
[4] Choi, S.B., Cheong, C. and S. Kini. (1995), "Control of Flexible
Structures by Distributed Piezo-film Actuators and Sensors", J. of
Intelligent Materials and Structures, 16, 430 - 435.
[5] Fanson, J. L. and Caughey, T.K., "Positive Position Feedback Control
For Structures," AIAA J., Vol. 18, no. 4, 717-723, 1990.
[6] Hanagud, S., Obal, M.W. and Callise, A.J., "Optimal Vibration Control
By The Use of Piezoceramic Sensors and Actuators", J. of Guidance,
Control and Dynamics, Vol. 15, no. 5, pp. 1199 - 1206, 1992.
[7] Hwang, W. and Park H.C., "Finite Element Modeling of Piezoelectric
Sensors and Actuators", AIAA J., Vol. 31, no. 5, pp. 930 - 937, 1993.
[8] Syrmos, V.L., Abdallah, P., Dorato, P. and Grigoriadis, K., "Static
Output Feedback A Survey", Automatica, Vol. 33, no. 2, pp.125 -137,
1997.
[9] Werner, H. and Furuta, K., "Simultaneous Stabilization Based on Output
Measurements", Kybernetika, Vol. 31, no. 4, pp. 395 - 411, 1995.
[10] Werner, H., "Multimodal Robust Control by Fast Output Sampling - An
LMI Approach," Automatica, Vol. 34, no. 12, pp. 1625 - 1630, 1998.
[11] Yong-Yan Cao, Lam, J. and Sun, Y.X. "Static Output Feedback
Stabilization: An LMI Approach", Automatica, Vol. 34, no. 12, pp.
1641-1645, 1998.
[12] Rao, S. 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.
[13] Mark Balas, J., "Feedback Control of Flexible Structures," IEEE Trans.
Automat. Contr., Vol. AC-23, no. 4, pp. 673-679, 1978.
[14] Herbert Werner and Tile Meister, "Robust Control of a Laboratory
Aircraft Model Via Fast Output Sampling," Control Engineering
Practice, Vol. 7, pp. 305-313, 1999.
[15] Hwang Woo Seok and Hyun Chul Park, "Finite element modeling of
piezo-electric sensors and actuators," IEEE Trans. Automat. Contr. Vol.
31, no. 5, pp. 930 - 937, 1993.
[16] Chammas, A. B. and C. T. Leondes, "Pole placement by piecewise
constant output feedback," Int. J. Contr., Vol. 29, no. 1, pp. 31-38,
1979.
[17] Davison, E.J., "A method for simplifying linear dynamical systems,"
IEEE Trans. Auto. Contr., Vol. AC-11, pp. 93-101, 1966.
[18] Lamba, S.S. and Rao, S.V., "On the suboptimal control via the
simplified model of Davison," IEEE Trans. Auto. Contr., Vol. AC-19,
pp. 448-450, 1974.
[19] Mahmoud, M.S. and G.M. Singh, "Large scale systems modeling,"
Pergamon Press, Oxford, 1981.
[20] Aoki, M., "Control of large scale dynamic systems by aggregation,"
IEEE Trans. Auto. Contr., Vol. AC-13, no. 3, 246-253, 1968.
[21] Manjunath, T.C., and B. Bandyopadhyay., "Controller Design for Euler-
Bernoulli Smart Structures Using Robust Decentralized POF via
Reduced Order Modeling", Vol. 3, no.3, pp. 205-221, 2006.
[22] Umapathy, M., 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.
[23] Rajeev, G., Bandyopadhyay, B., and Kulkarni A.M., "Robust
decentralized periodic output feedback technique based power system
stabilizer for multi machine power system", IEE Proc., Control Theory
Appl., Vol. 152, pp. 3-8, 2005.
[1] Baily, T. and Hubbard Jr., J.E., "Distributed Piezoelectric Polymer
Active Vibration Control of A Cantilever Beam", J. of Guidance,
Control and Dynamics, Vol. 8, no. 5, pp. 605 - 611, 1985.
[2] Crawley, E.F. and De Luis, J., "Use of Piezoelectric Actuators as
Elements of Intelligent Structures", AIAA J., Vol. 25, pp. 1373-1385,
1987.
[3] Culshaw, B., "Smart Structures - A Concept or A Reality," J. of Systems
and Control Engg., Vol. 26, no. 206, pp. 1- 8, 1992.
[4] Choi, S.B., Cheong, C. and S. Kini. (1995), "Control of Flexible
Structures by Distributed Piezo-film Actuators and Sensors", J. of
Intelligent Materials and Structures, 16, 430 - 435.
[5] Fanson, J. L. and Caughey, T.K., "Positive Position Feedback Control
For Structures," AIAA J., Vol. 18, no. 4, 717-723, 1990.
[6] Hanagud, S., Obal, M.W. and Callise, A.J., "Optimal Vibration Control
By The Use of Piezoceramic Sensors and Actuators", J. of Guidance,
Control and Dynamics, Vol. 15, no. 5, pp. 1199 - 1206, 1992.
[7] Hwang, W. and Park H.C., "Finite Element Modeling of Piezoelectric
Sensors and Actuators", AIAA J., Vol. 31, no. 5, pp. 930 - 937, 1993.
[8] Syrmos, V.L., Abdallah, P., Dorato, P. and Grigoriadis, K., "Static
Output Feedback A Survey", Automatica, Vol. 33, no. 2, pp.125 -137,
1997.
[9] Werner, H. and Furuta, K., "Simultaneous Stabilization Based on Output
Measurements", Kybernetika, Vol. 31, no. 4, pp. 395 - 411, 1995.
[10] Werner, H., "Multimodal Robust Control by Fast Output Sampling - An
LMI Approach," Automatica, Vol. 34, no. 12, pp. 1625 - 1630, 1998.
[11] Yong-Yan Cao, Lam, J. and Sun, Y.X. "Static Output Feedback
Stabilization: An LMI Approach", Automatica, Vol. 34, no. 12, pp.
1641-1645, 1998.
[12] Rao, S. 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.
[13] Mark Balas, J., "Feedback Control of Flexible Structures," IEEE Trans.
Automat. Contr., Vol. AC-23, no. 4, pp. 673-679, 1978.
[14] Herbert Werner and Tile Meister, "Robust Control of a Laboratory
Aircraft Model Via Fast Output Sampling," Control Engineering
Practice, Vol. 7, pp. 305-313, 1999.
[15] Hwang Woo Seok and Hyun Chul Park, "Finite element modeling of
piezo-electric sensors and actuators," IEEE Trans. Automat. Contr. Vol.
31, no. 5, pp. 930 - 937, 1993.
[16] Chammas, A. B. and C. T. Leondes, "Pole placement by piecewise
constant output feedback," Int. J. Contr., Vol. 29, no. 1, pp. 31-38,
1979.
[17] Davison, E.J., "A method for simplifying linear dynamical systems,"
IEEE Trans. Auto. Contr., Vol. AC-11, pp. 93-101, 1966.
[18] Lamba, S.S. and Rao, S.V., "On the suboptimal control via the
simplified model of Davison," IEEE Trans. Auto. Contr., Vol. AC-19,
pp. 448-450, 1974.
[19] Mahmoud, M.S. and G.M. Singh, "Large scale systems modeling,"
Pergamon Press, Oxford, 1981.
[20] Aoki, M., "Control of large scale dynamic systems by aggregation,"
IEEE Trans. Auto. Contr., Vol. AC-13, no. 3, 246-253, 1968.
[21] Manjunath, T.C., and B. Bandyopadhyay., "Controller Design for Euler-
Bernoulli Smart Structures Using Robust Decentralized POF via
Reduced Order Modeling", Vol. 3, no.3, pp. 205-221, 2006.
[22] Umapathy, M., 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.
[23] Rajeev, G., Bandyopadhyay, B., and Kulkarni A.M., "Robust
decentralized periodic output feedback technique based power system
stabilizer for multi machine power system", IEE Proc., Control Theory
Appl., Vol. 152, pp. 3-8, 2005.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64090", author = "T.C. Manjunath and B. Bandyopadhyay", title = "Controller Design for Euler-Bernoulli Smart Structures Using Robust Decentralized FOS via Reduced Order Modeling", abstract = "This paper features the modeling and design of a
Robust Decentralized Fast Output Sampling (RDFOS) Feedback
control technique for the active vibration control of a 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 aluminium beam. Using model
order reduction technique, the reduced order model of the higher
order system is obtained based on dominant Eigen value retention
and the Davison technique. RDFOS feedback controllers are
designed for the above 5 multivariable-multimodel plant. The closed
loop responses with the RDFOS feedback gain and the magnitudes of
the control input are obtained and the performance of the proposed
multimodel smart structure system is evaluated for vibration control.", keywords = "Smart structure, Euler-Bernoulli beam theory, Fastoutput sampling feedback control, Finite Element Method, Statespace model, Vibration control, LMI, Model order Reduction.", volume = "2", number = "4", pages = "550-20", }
