Multi-Objective Robust Active Vibration Control of an Arbitrary Thick Piezolaminated Beam

A multi-objective mixed / robust output feedback control synthesis with additional regional pole placement constraints in a linear matrix inequalities (LMI) framework is adopted for active vibration suppression of a simply supported, arbitrary thick, piezolaminated beam with continuously integrated sensor and actuator layers, in the face of high frequency unmodeled dynamics (residual uncertainties) and external disturbance. The structural formulation is based on a spatial state-space approach using the exact linear two-dimensional piezoelasticity theory and involving local/global transfer matrices. To assist control system design, subspace-based multivariable system identification is carried out by using the first four modes in the frequency range of 0–4000 rad/sec for control purpose, while the remaining high frequency (residual) modes in the control bandwidth are left as the uncertainty of modeling. The dynamic performance of vibration control system is demonstrated in both frequency and time domains for a three-layered sandwich beam including three pairs of piezoelectric actuator/sensor (Ba2NaNb5O15/PZT4) segments asymmetrically collocated on both sides of an orthotropic core for two different types of loading (i.e., impulsive load and random disturbance). The accuracy of dynamic analysis is established with the aid of a commercial finite element package and the data available in the literature.

[1]  P. C. Dumir,et al.  Segmented Sensors and Actuators for Thick Plates and Shells Part i: Analysis Using Fsdt , 1999 .

[2]  Wei Chen,et al.  Optimal sensor design and control of piezoelectric laminate beams , 2004, IEEE Transactions on Control Systems Technology.

[3]  M Vagia,et al.  A literature review on modeling and control design for electrostatic microactuators with fringing and squeezed film damping effects , 2010, Proceedings of the 2010 American Control Conference.

[4]  Hans Irschik,et al.  A review on static and dynamic shape control of structures by piezoelectric actuation , 2002 .

[5]  Pascal Gahinet,et al.  H/sub /spl infin// design with pole placement constraints: an LMI approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Lucy Edery-Azulay,et al.  Active damping of piezo-composite beams , 2006 .

[7]  Liviu Librescu,et al.  A general linear theory of laminated composite shells featuring interlaminar bonding imperfections , 2001 .

[8]  M. C. Ray,et al.  Exact analysis of coupled electroelastic behaviour of a piezoelectric plate under cylindrical bending , 1992 .

[9]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[10]  N. Ganesan,et al.  DYNAMIC RESPONSE OF NON-UNIFORM COMPOSITE BEAMS , 1997 .

[11]  M.A. Demetriou,et al.  H-Infinity Control of a Force-Actuated Flexible Beam Using an Analytical Bound Approach and Non Collocated Disturbance , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[12]  Yavuz Yaman,et al.  ACTIVE VIBRATION CONTROL OF A SMART BEAM , 2004 .

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

[14]  H. S. Tzou Distributed Modal Identification and Vibration Control of Continua: Theory and Applications , 1990, 1990 American Control Conference.

[15]  C. I. Tseng,et al.  Distributed vibration control and identification of coupled elastic/piezoelectric systems: Finite element formulation and applications , 1991 .

[16]  J. C. Bruch,et al.  Integral Equation Approach for Beams with Multi-Patch Piezo Sensors and Actuators , 2002 .

[17]  P. K. Palani,et al.  Active Vibration Control in Smart Structures , 2014 .

[18]  Chul H. Park,et al.  Vibration control of beams using multiobjective state-feedback control , 2006 .

[19]  Chul H. Park,et al.  Analytical development of a robust controller for smart structural systems , 2005 .

[20]  S. O. Reza Moheimani,et al.  Spatial 𝒽2 control of a piezoelectric laminate beam: experimental implementation , 2002, IEEE Trans. Control. Syst. Technol..

[21]  Senthil S. Vel,et al.  Exact solution for the vibration and active damping of composite plates with piezoelectric shear actuators , 2005 .

[22]  S. Moheimani,et al.  Experimental Implementation of Spatial Control on a Piezoelectric-Laminate Beam , 2001 .

[23]  C. W. Lim,et al.  A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator , 2005 .

[24]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[25]  T. C. Manjunath,et al.  Vibration Suppression of Timoshenko Beams with Embedded Piezoelectrics Using POF , 2008 .

[26]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[27]  Chen Qiang,et al.  Vibration Control of a Smart Beam Using H8 Control , 2011, 2011 Fourth International Conference on Intelligent Computation Technology and Automation.

[28]  Ian R. Petersen,et al.  Broadband disturbance attenuation over an entire beam , 1997, 1997 European Control Conference (ECC).

[29]  Horn-Sen Tzou,et al.  A Piezothermoelastic Thin Shell Theory Applied to Active Structures , 1994 .

[30]  Santosh Kapuria,et al.  Exact 2D piezoelasticity solution of hybrid beam with damping under harmonic electromechanical load , 2004 .

[31]  Leon Y. Bahar,et al.  A state space approach to elasticity , 1975 .

[32]  Santosh Kapuria,et al.  Active vibration control of piezoelectric laminated beams with electroded actuators and sensors using an efficient finite element involving an electric node , 2010 .

[33]  N. K. Chandiramani,et al.  Optimal vibration control of a rotating composite beam with distributed piezoelectric sensing and actuation , 2004 .

[34]  Gangbing Song,et al.  Adaptive robust sliding-mode control of a flexible beam using PZT sensor and actuator , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

[35]  K. Chandrashekhara,et al.  Free vibration of composite beams using a refined shear flexible beam element , 1992 .

[36]  P. C. Dumir,et al.  SEGMENTED SENSORS AND ACTUATORS FOR THICK PLATES AND SHELLS PART II: PARAMETRIC STUDY , 1999 .

[37]  Lennart Ljung,et al.  System identification toolbox for use with MATLAB , 1988 .

[38]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[39]  Indra Narayan Kar,et al.  Bending and torsional vibration control of a flexible plate structure using H∞-based robust control law , 2000, IEEE Trans. Control. Syst. Technol..

[40]  P. Seshu,et al.  Active vibration control of a smart beam , 2003, Other Conferences.

[41]  Zhifei Shi,et al.  Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature , 2009 .

[42]  Colin H. Hansen,et al.  High frequency spatial vibration control using H ∞ method , 2007 .

[43]  Rajiv Kumar,et al.  Active Vibration Control of Beams by Combining Precompressed Layer Damping and ACLD Treatment: Performance Comparison of Various Robust Control Techniques , 2012 .

[44]  D. Marinova Robust control of composite beams , 2009 .

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

[46]  Horn-Sen Tzou,et al.  A Study of Segmentation of Distributed Piezoelectric Sensors and Actuators, Part I: Theoretical Analysis , 1994 .

[47]  Edvaldo Assunção,et al.  Observer-based state-feedback versus H-infinity output feedback control solved by LMI approach for applications in smart structures , 2005 .

[48]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[49]  Horn-Sen Tzou,et al.  Spatial Microscopic Actuations of Shallow Conical Shell Sections , 2005 .

[50]  Faruk Firat Calim,et al.  Free and forced vibrations of non-uniform composite beams , 2009 .

[51]  M. Vagia,et al.  Robust PID-control design for an electrostatic micromechanical? actuator with structured uncertainty , 2007, 2007 Mediterranean Conference on Control & Automation.

[52]  Mi-Ching Tsai,et al.  Robust and Optimal Control , 2014 .

[53]  S.O. Reza Moheimani,et al.  Spatial /spl Hscr//sub 2/ norm of flexible structures and its application in model order selection , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[54]  Horn-Sen Tzou,et al.  A Study of Segmentation of Distributed Piezoelectric Sensors and Actuators, Part II: Parametric Study and Active Vibration Controls , 1994 .

[55]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

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

[57]  Hongguang Li,et al.  Adaptive vibration control of micro-cantilever beam with piezoelectric actuator in MEMS , 2006 .

[58]  T. Naik,et al.  Dynamic response of a cantilever in liquid near a solid wall , 2003 .

[59]  Manouchehr Salehi,et al.  Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators , 2008 .

[60]  Dongchang Sun,et al.  Distributed Piezoelectric Element Method for Vibration Control of Smart Plates , 1997 .

[61]  S. O. Reza Moheimani,et al.  Piezoelectric Transducers for Vibration Control and Damping , 2006 .

[62]  Ioan Ursu,et al.  A Review of H∞ Robust Control of Piezoelectric Smart Structures , 2008 .

[63]  Chyanbin Hwu,et al.  Vibration suppression of composite sandwich beams , 2004 .

[64]  K. Chandrashekhara,et al.  Robust Vibration Control of Composite Beams Using Piezoelectric Devices and Neural Networks , 1997 .

[65]  Li Dao-kui Robust Vibration Control of Flexible Piezoelectric Structure Based on Structured Singular Value Theory , 2006 .

[66]  P.K.C. Wang FEEDBACK CONTROL OF VIBRATIONS IN A MICROMACHINED CANTILEVER BEAM WITH ELECTROSTATIC ACTUATORS , 1998 .

[67]  E. Assunção,et al.  Observer-based state-feedback versus H∞ output feedback control solved by LMI approach for applications in smart structures , 2004 .

[68]  S. O. R. Moheimani,et al.  Experimental implementation of spatial H/sub /spl infin// control on a piezoelectric-laminate beam , 2002 .

[69]  Wang Yong AN EXPERIMENTAL STUDY ON REDUCED ORDER H_∞ CONTROL OF A FLEXIBLE BEAM , 2007 .

[70]  Yavuz Yaman,et al.  Application of spatial H8 control technique for active vibration control of a smart beam , 2007, ICINCO-SPSMC.

[71]  C. W. Lim,et al.  On functionally graded beams with integrated surface piezoelectric layers , 2006 .

[72]  Amr M. Baz,et al.  Robust control of active constrained layer damping , 1996, Smart Structures.

[73]  Yavuz Yaman,et al.  ACTIVE VIBRATION CONTROL OF A SMART PLATE , 2002 .

[74]  Jingjun Zhang,et al.  Active Vibration Control of Piezoelectric Intelligent Structures , 2010, J. Comput..

[75]  Der-An Wang,et al.  Modal space vibration control of a beam by using the feedforward and feedback control loops , 2002 .

[76]  Gangbing Song,et al.  Active vibration suppression of a flexible beam with piezoceramic patches using robust model reference control , 2007 .