This paper presents various experimental verifications for the theoretical analysis results of vibration suppression to a smart flexible beam bonded with a piezoelectric actuator by a velocity feedback controller and an extended state observer (ESO). During the state feedback control (SFC) design process for the smart flexible beam with the pole placement theory, in the state feedback gain matrix, the velocity feedback gain is much more than the displacement feedback gain. For the difference between the velocity feedback gain and the displacement feedback gain, a modified velocity feedback controller is applied based on a dynamical model with the Hamilton principle to the smart beam. In addition, the feedback velocity is attained with the extended state observer and the displacement is acquired by the foil gauge on the root of the smart flexible beam. The control voltage is calculated by the designed velocity feedback gain multiplied by the feedback velocity. Through some experiment verifications for simulation results, it is indicated that the suppressed amplitude of free vibration is up to 62.13% while the attenuated magnitude of its velocity is up to 61.31%. Therefore, it is demonstrated that the modified velocity feedback control with the extended state observer is feasible to reduce free vibration. 1. Introduction In recent years, a smart system, which consists of a cantilever beam bonded with a piezoelectric actuator, has drawn much interest of many researchers [1–5]. At the same time, the controller designs based on positioning control and vibration suppression of the smart system have attracted wide attention around the world [6]. Especially for dynamic modeling task and vibration reduction work of a smart cantilever beam with piezoelectric materials, there have been lots of studies on suppressing vibration with a designed controller [7]. For example, a full-order model is developed using assumed model expansion and the Lagrangian approach for a flexible cantilever beam bonded with a PZT patch to control a base motion [8], a finite element model of the three-layered smart beam is utilized to reduce vibration by a velocity feedback controller [9], and the multimodal vibration suppression of a smart flexible cantilever beam with piezoceramic actuator and sensor by using a pole placement method is proposed [10]. As for adopted control law to suppress vibration of mechanical system, in the past several years, many researchers have committed to the work on vibration control of a smart beam with piezoelectric sensor and actuator by a variety of
References
[1]
V. Fakhari and A. Ohadi, “Nonlinear vibration control of functionally graded plate with piezoelectric layers in thermal environment,” Journal of Vibration and Control, vol. 17, no. 3, pp. 449–469, 2011.
[2]
H. Gu and G. Song, “Active vibration suppression of a flexible beam with piezoceramic patches using robust model reference control,” Smart Materials and Structures, vol. 16, no. 4, pp. 1453–1459, 2007.
[3]
M. Marinaki, Y. Marinakis, and G. E. Stavroulakis, “Fuzzy control optimized by a multi-objective particle swarm optimization algorithm for vibration suppression of smart structures,” Structural and Multidisciplinary Optimization, vol. 43, no. 1, pp. 29–42, 2011.
[4]
O. Bilgen, M. Amin Karami, D. J. Inman, and M. I. Friswell, “The actuation characterization of cantilevered unimorph beams with single crystal piezoelectric materials,” Smart Materials and Structures, vol. 20, no. 5, Article ID 055024, 2011.
[5]
D. Ezhilarasi, M. Umapathy, and B. Bandyopadhyay, “Design and experimental evaluation of simultaneous periodic output feedback control for piezoelectric actuated beam structure,” Structural Control and Health Monitoring, vol. 16, no. 3, pp. 335–349, 2009.
[6]
Z. C. Qiu, “Adaptive nonlinear vibration control of a Cartesian flexible manipulator driven by a ballscrew mechanism,” Mechanical Systems and Signal Processing, vol. 30, pp. 248–266, 2012.
[7]
G. Meng, L. Ye, X. Dong, and K. Wei, “Closed loop finite element modeling of piezoelectric smart structures,” Shock and Vibration, vol. 13, no. 1, pp. 1–12, 2006.
[8]
M. Dadfarnia, N. Jalili, Z. Liu, and D. M. Dawson, “An observer-based piezoelectric control of flexible Cartesian robot arms: theory and experiment,” Control Engineering Practice, vol. 12, no. 8, pp. 1041–1053, 2004.
[9]
C. M. A. Vasques and J. Dias Rodrigues, “Active vibration control of a smart beam through piezoelectric actuation and laser vibrometer sensing: simulation, design and experimental implementation,” Smart Materials and Structures, vol. 16, no. 2, pp. 305–316, 2007.
[10]
V. Sethi and G. Song, “Multimodal vibration control of a flexible structure using piezoceramic sensor and actuator,” Journal of Intelligent Material Systems and Structures, vol. 19, no. 5, pp. 573–582, 2008.
[11]
D. Ezhilarasi, M. Umapathy, and B. Bandyopadhyay, “Design and experimental evaluation of piecewise output feedback control for structural vibration suppression,” Smart Materials and Structures, vol. 15, no. 6, pp. 1927–1938, 2006.
[12]
Z.-C. Qiu, J.-D. Han, X.-M. Zhang, Y. Wang, and Z. Wu, “Active vibration control of a flexible beam using a non-collocated acceleration sensor and piezoelectric patch actuator,” Journal of Sound and Vibration, vol. 326, no. 3–5, pp. 438–455, 2009.
[13]
S. N. Mahmoodi and M. Ahmadian, “Modified acceleration feedback for active vibration control of aerospace structures,” Smart Materials and Structures, vol. 19, no. 6, Article ID 065015, 10 pages, 2010.
[14]
A. Zabihollah, R. Sedagahti, and R. Ganesan, “Active vibration suppression of smart laminated beams using layerwise theory and an optimal control strategy,” Smart Materials and Structures, vol. 16, no. 6, pp. 2190–2201, 2007.
[15]
S. M. Khot, N. P. Yelve, R. Tomar, S. Desai, and S. Vittal, “Active vibration control of cantilever beam by using PID based output feedback controller,” Journal of Vibration and Control, vol. 18, no. 3, pp. 366–372, 2012.
[16]
Q. Hu, J. Cao, and Y. Zhang, “Robust backstepping sliding mode attitude tracking and vibration damping of flexible spacecraft with actuator dynamics,” Journal of Aerospace Engineering, vol. 22, no. 2, pp. 139–152, 2009.
[17]
K. Gurses, B. J. Buckham, and E. J. Park, “Vibration control of a single-link flexible manipulator using an array of fiber optic curvature sensors and PZT actuators,” Mechatronics, vol. 19, no. 2, pp. 167–177, 2009.
[18]
Y. Zhang, X. Zhang, and S. Xie, “Adaptive vibration control of a cylindrical shell with laminated PVDF actuator,” Acta Mechanica, vol. 210, no. 1-2, pp. 85–98, 2010.
[19]
Q. Hu, “Robust adaptive attitude tracking control with L2-gain performance and vibration reduction of an orbiting flexible spacecraft,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, vol. 133, no. 1, Article ID 011009, 11 pages, 2011.
[20]
H. Ji, J. Qio, A. Badel, and K. Zhu, “Semi-active vibration control of a composite beam using an adaptive SSDV approach,” Journal of Intelligent Material Systems and Structures, vol. 20, no. 4, pp. 401–412, 2009.
[21]
H. Ji, J. Qiu, A. Badel, Y. Chen, and K. Zhu, “Semi-active vibration control of a composite beam by adaptive synchronized switching on voltage sources based on LMS algorithm,” Journal of Intelligent Material Systems and Structures, vol. 20, no. 8, pp. 939–947, 2009.
[22]
M. Ahmadian and D. J. Inman, “Adaptive modified positive position feedback for active vibration control of structures,” Journal of Intelligent Material Systems and Structures, vol. 21, no. 6, pp. 571–580, 2010.
[23]
J. Lin and W. S. Chao, “Vibration suppression control of beam-cart system with piezoelectric transducers by decomposed parallel adaptive neuro-fuzzy control,” JVC/Journal of Vibration and Control, vol. 15, no. 12, pp. 1885–1906, 2009.
[24]
Q. L. Hu, “Robust adaptive sliding mode attitude control and vibration damping of flexible spacecraft subject to unknown disturbance and uncertainty,” Transactions of the Institute of Measurement and Control, vol. 34, no. 4, pp. 436–447, 2012.
[25]
X. Xue and J. Tang, “Robust and high precision control using piezoelectric actuator circuit and integral continuous sliding mode control design,” Journal of Sound and Vibration, vol. 293, no. 1-2, pp. 335–359, 2006.
[26]
D. Sun, J. K. Mills, J. Shan, and S. K. Tso, “A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement,” Mechatronics, vol. 14, no. 4, pp. 381–401, 2004.
[27]
J. Roos, J. C. Bruch Jr., J. M. Sloss, S. Adali, and I. S. Sadek, “Velocity feedback control with time delay using piezoelectrics,” in Proceedings of the SPIE The International Society for Optical Engineering: smart Structures and Materials 2003 Modeling, Signal Processing, and Control, vol. 5049, pp. 233–240, March 2003.
[28]
P. Gardonio and S. J. Elliott, “Smart panels with velocity feedback control systems using triangularly shaped strain actuators,” Journal of the Acoustical Society of America, vol. 117, no. 4, pp. 2046–2064, 2005.
[29]
Y. Huang and J. Han, “Analysis and design for the second order nonlinear continuous extended states observer,” Chinese Science Bulletin, vol. 45, no. 21, pp. 1938–1944, 2000.
[30]
A. J. Hillis, “Active motion control of fixed offshore platforms using an extended state observer,” Proceedings of the Institution of Mechanical Engineers I, vol. 224, no. 1, pp. 53–63, 2010.
[31]
R. Zhang and C. Tong, “Torsional vibration control of the main drive system of a rolling mill based on an extended state observer and linear quadratic control,” Journal of Vibration and Control, vol. 12, no. 3, pp. 313–327, 2006.
[32]
Y. Dong, M. X. Jun, and C. Hua, “Realization of DESO filter on DSP and its application,” Journal of Academy of Armored Force Engineering, vol. 24, no. 3, pp. 57–61, 2010.
