Active vibration control of piezoelectric bonded smart structures using PID algorithm

Thin-walled structures are sensitive to vibrate under even very small disturbances. In order to design a suitable controller for vibration suppression of thin-walled smart structures, an electro-mechanically coupled finite element (FE) model of smart structures is developed based on first-order shear deformation (FOSD) hypothesis. Considering the vibrations generated by various disturbances, which include free and forced vibrations, a PID control is implemented to damp both the free and forced vibrations. Additionally, an LQR optimal control is applied for comparison. The implemented control strategies are validated by a piezoelectric layered smart plate under various excitations.

[1]  Li Cheng,et al.  Robust control of a vibrating plate using μ-synthesis approach , 2003 .

[2]  J. N. Reddy,et al.  A finite-element model for piezoelectric composite laminates , 1997 .

[3]  Rüdiger Schmidt,et al.  Large rotation theory for static analysis of composite and piezoelectric laminated thin-walled structures , 2014 .

[4]  Carlos A. Mota Soares,et al.  Optimal dynamic control of laminated adaptive structures using a higher order model and a genetic algorithm , 2008 .

[5]  H. G. Patel,et al.  FREE VIBRATIONS OF PLATE USING TWO VARIABLE REFINED PLATE THEORY , 2006 .

[6]  Levent Malgaca,et al.  Integration of active vibration control methods with finite element models of smart laminated composite structures , 2010 .

[7]  Jin-Chein Lin,et al.  Adaptive control of a composite cantilever beam with piezoelectric damping-modal actuators/sensors , 2005 .

[8]  Horn-Sen Tzou,et al.  Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang–bang control , 2007 .

[9]  L. H. He,et al.  Three‐Dimensional Analysis of Some Symmetric Hybrid Piezoelectric Laminates , 2000 .

[10]  V. Balamurugan,et al.  Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control , 2001 .

[11]  Santosh Kapuria,et al.  Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors , 2010 .

[12]  Magdalene Marinaki,et al.  Vibration control of beams with piezoelectric sensors and actuators using particle swarm optimization , 2011, Expert Syst. Appl..

[13]  J. Dias Rodrigues,et al.  Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies , 2006 .

[14]  Hazem Kioua,et al.  Piezoelectric induced bending and twisting of laminated composite shallow shells , 2000 .

[15]  Santosh Kapuria,et al.  An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers , 2001 .

[16]  T. S. Koko,et al.  Finite element analysis and design of actively controlled piezoelectric smart structures , 2004 .

[17]  Ya-Peng Shen,et al.  Optimal control of active structures with piezoelectric modal sensors and actuators , 1997 .

[18]  Shun-Qi Zhang,et al.  Static and dynamic FE analysis of piezoelectric integrated thin-walled composite structures with large rotations , 2014 .

[19]  Shun-Qi Zhang,et al.  Large rotation FE transient analysis of piezolaminated thin-walled smart structures , 2013 .

[20]  Peter C. Müller,et al.  Disturbance rejection control for vibration suppression of piezoelectric laminated thin-walled structures , 2014 .

[21]  J. N. Reddy,et al.  A GENERAL NON-LINEAR THIRD-ORDER THEORY OF PLATES WITH MODERATE THICKNESS , 1990 .

[22]  Renwen Chen,et al.  Energy Conversion Efficiency of Rainbow Shape Piezoelectric Transducer , 2012 .

[23]  R. Schmidt,et al.  LQR Control for Vibration Suppression of Piezoelectric Integrated Smart Structures , 2012 .

[24]  C.M.A. Vasques,et al.  Coupled three‐layered analysis of smart piezoelectric beams with different electric boundary conditions , 2005 .

[25]  Thang Duy Vu,et al.  Nonlinear Dynamic FE Simulation of Smart Piezolaminated Structures Based on First- and Third-Order Transverse Shear Deformation Theory , 2009 .

[26]  Guang Meng,et al.  Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study , 2006 .

[27]  Georgios E. Stavroulakis,et al.  Design and robust optimal control of smart beams with application on vibrations suppression , 2005, Adv. Eng. Softw..

[28]  Santosh Kapuria,et al.  First Order Shear Deformation Theory for Hybrid Cylindrical Panel in Cylindrical Bending Considering Electrothermomechanical Coupling Effects , 2002 .

[29]  Rajeev Kumar,et al.  Static and dynamic analysis of smart cylindrical shell , 2008 .

[30]  Liviu Librescu,et al.  Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures , 1975 .

[31]  Carlos A. Mota Soares,et al.  Optimal design in vibration control of adaptive structures using a simulated annealing algorithm , 2006 .

[32]  M. C. Ray,et al.  Exact solutions for dynamic analysis of composite plates with distributed piezoelectric layers , 1998 .

[33]  G. G. Sheng,et al.  Active control of functionally graded laminated cylindrical shells , 2009 .

[34]  Afzal Suleman,et al.  Modelling and design of adaptive composite structures , 2000 .

[35]  K. Y. Sze,et al.  A hybrid stress ANS solid‐shell element and its generalization for smart structure modelling. Part I—solid‐shell element formulation , 2000 .

[36]  Somasundaram Valliappan,et al.  Finite element analysis of a 'smart' damper for seismic structural control , 2003 .

[37]  J. N. Reddy,et al.  Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites , 2005 .

[38]  K. Y. Dai,et al.  Static and vibration control of composite laminates integrated with piezoelectric sensors and actuators using the radial point interpolation method , 2004 .

[39]  Shijie Zheng,et al.  Finite Element Analysis of Smart Structures with Piezoelectric Sensors/Actuators Including Debonding , 2004 .

[40]  Arthur W. Leissa,et al.  A higher order shear deformation theory for the vibration of thick plates , 1994 .

[41]  V. Balamurugan,et al.  Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators , 2003 .

[42]  D.G. Marinova,et al.  Robust control of smart beams in the presence of damage-induced structural uncertainties , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[43]  Junji Tani,et al.  VIBRATION CONTROL SIMULATION OF LAMINATED COMPOSITE PLATES WITH INTEGRATED PIEZOELECTRICS , 1999 .

[44]  Partha Bhattacharya,et al.  Finite element analysis and distributed control of laminated composite shells using LQR/IMSC approach , 2002 .

[45]  Xiaopeng Zhang,et al.  Topology optimization of piezoelectric layers in plates with active vibration control , 2014 .

[46]  Kok Keng Ang,et al.  Dynamic stability analysis of finite element modeling of piezoelectric composite plates , 2004 .

[47]  V. Piefort.  FINITE ELEMENT MODELLING OF PIEZOELECTRIC ACTIVE STRUCTURES: SOME AP- PLICATIONS IN VIBROACOUSTICS , 2001 .

[48]  Santosh Kapuria,et al.  An efficient coupled layerwise theory for dynamic analysis of piezoelectric composite beams , 2003 .

[49]  H. S. Tsou,et al.  Distributed Modal Identification and Vibration Control of Continua: Piezoelectric Finite Element Formulation and Analysis , 1990, 1990 American Control Conference.

[50]  I. Kucuk,et al.  Optimal vibration control of piezolaminated smart beams by the maximum principle , 2011 .

[51]  T. C. Manjunath,et al.  Vibration control of Timoshenko smart structures using multirate output feedback based discrete sliding mode control for SISO systems , 2009 .

[52]  Sudhakar A. Kulkarni,et al.  Finite element modeling of smart plates/shells using higher order shear deformation theory , 2003 .

[53]  Debabrata Chakraborty,et al.  Optimal vibration control of smart fiber reinforced composite shell structures using improved genetic algorithm , 2009 .

[54]  Jaehwan Kim,et al.  Interaction of active and passive vibration control of laminated composite beams with piezoceramic sensors/actuators , 2002 .

[55]  Ulrich Gabbert,et al.  Accurate Modeling of the Electric Field within Piezoelectric Layers for Active Composite Structures , 2007 .