Modeling of low frequency dynamics of a smart system and its state feedback based active control

Abstract Major physical systems/structures suffer from unwanted vibrations. For efficient working of such systems, these vibrations have to be controlled. In this paper, mathematical modeling of an aluminum cantilever beam with bonded multiple piezoelectric patches which act as the disturbance generator, sensor as well as control actuator has been presented. This piezoelectric laminate cantilever beam is assumed to be vibrating in a single degree of freedom i.e. in the flexural mode only and the corresponding state space models have been derived analytically using the finite element technique. Dominant modes of flexural vibration are identified from the frequency response of the developed model of the system and finally a state feedback controller based on pole placement technique is designed to actively suppress the vibrations. Through numerous simulations as well as experimental validation, the effectiveness of the active controller in damping the vibrations at various excitation frequencies as well as frequency ranges along the flexural mode is established.

[1]  Zhao-Bo Chen,et al.  Active vibration control of conical shells using piezoelectric materials , 2012 .

[2]  Rajiv Kumar,et al.  Algorithm to Detect and Segment Gurmukhi Handwritten Text into Lines, Words and Characters , 2011 .

[3]  Fabien Mieyeville,et al.  Robust active vibration control of piezoelectric flexible structures using deterministic and probabilistic analysis , 2014 .

[4]  W. Thomson.  Theory of vibration with applications , 1965 .

[5]  Daniel J. Inman,et al.  Finite element analysis and experimental study on dynamic properties of a composite beam with viscoelastic damping , 2013 .

[6]  Xi-Qiao Feng,et al.  Effect of surface stresses on the vibration and buckling of piezoelectric nanowires , 2010 .

[7]  Juntao Fei.  Active vibration control of flexible steel cantilever beam using piezoelectric actuators , 2005, Proceedings of the Thirty-Seventh Southeastern Symposium on System Theory, 2005. SSST '05..

[8]  Khaled A. Alhazza,et al.  Free vibrations control of a cantilever beam using combined time delay feedback , 2012 .

[9]  Intan Zaurah Mat Darus,et al.  Active vibration control of a flexible beam using system identification and controller tuning by evolutionary algorithm , 2015 .

[10]  E. Dragašius,et al.  The strength investigation of the composite material with implanted sensors , 2015 .

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

[12]  Andrew J. Fleming,et al.  Integrated strain and force feedback for high-performance control of piezoelectric actuators , 2010 .

[13]  Rajiv Kumar,et al.  Pole Placement Techniques for Active Vibration Control of Smart Structures: A Feasibility Study , 2007 .

[14]  Qiu Zhicheng,et al.  Acceleration sensors based modal identification and active vibration control of flexible smart cantilever plate , 2009 .

[15]  K. V. Gangadharan,et al.  Parametric modeling and FPGA based real time active vibration control of a piezoelectric laminate cantilever beam at resonance , 2015 .

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

[17]  Weui Bong Jeong,et al.  Active vibration control of beams using filtered-velocity feedback controllers with moment pair actuators , 2013 .

[18]  Fabien Mieyeville,et al.  Phase and gain control policies for robust active vibration control of flexible structures , 2013 .

[19]  Mehmet Kurt,et al.  Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection , 2014 .

[20]  Arun P. Parameswaran,et al.  Modeling and Control of Low Frequency Dynamics of a Smart System , 2016 .

[21]  Alper Erturk,et al.  Unified nonlinear electroelastic dynamics of a bimorph piezoelectric cantilever for energy harvesting, sensing, and actuation , 2014, Nonlinear Dynamics.

[22]  Liang Huang,et al.  Experimental study and numerical simulation of active vibration control of a highly flexible beam using piezoelectric intelligent material , 2014 .

[23]  Zhaobo Chen,et al.  Vibration control of beams with active constrained layer damping , 2008 .

[24]  Arkadiusz Mystkowski,et al.  Mu-Synthesis robust control of 3D bar structure vibration using piezo-stack actuators , 2016 .

[25]  Juntao Fei,et al.  Active Feedback Vibration Suppression of a Flexible Steel Cantilever Beam Using Smart Materials , 2006, First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06).

[26]  Aleksandar Simonović,et al.  Experimental studies on active vibration control of smart plate using a modified PID controller with optimal orientation of piezoelectric actuator , 2016 .

[27]  V. Varadan,et al.  Closed loop finite element modeling of active structural damping in the frequency domain , 1997 .

[28]  A Blanguernon,et al.  Active control of a beam using a piezoceramic element , 1999 .

[29]  Michael J. Brennan,et al.  Active vibration control using delayed resonant feedback , 2013 .

[30]  Hongguang Li,et al.  Adaptive pole placement control for vibration control of a smart cantilevered beam in thermal environment , 2013 .

[31]  K. V. Gangadharan,et al.  Active vibration control of a smart cantilever beam at resonance: A comparison between conventional and Real Time Control , 2012, 2012 12th International Conference on Intelligent Systems Design and Applications (ISDA).

[32]  K. V. Gangadharan,et al.  Modeling and design of field programmable gate array based real time robust controller for active control of vibrating smart system , 2015 .

[33]  T. C. Manjunath,et al.  Modeling and fast output sampling feedback control of a smart Timoshenko cantilever beam , 2005 .

[34]  K. V. Gangadharan,et al.  Active Vibration Control of a Smart Cantilever Beam on General Purpose Operating System , 2013 .

[35]  Saurabh Kumar,et al.  ACTIVE VIBRATION CONTROL OF SMART PIEZO CANTILEVER BEAM USING PID CONTROLLER , 2014 .

[36]  E. Crawley,et al.  Detailed Models of Piezoceramic Actuation of Beams , 1989 .

[37]  Seung-Bok Choi,et al.  Force Tracking Control of a Flexible Gripper Driven by Piezoceramic Actuators , 1997 .

[38]  Aleksandar Simonović,et al.  Experimental studies on active vibration control of a smart composite beam using a PID controller , 2013 .

[39]  Peter Wellstead,et al.  Pole assignment self-tuning regulator , 1979 .

[40]  J. L. Fanson,et al.  Positive position feedback control for large space structures , 1990 .

[41]  K. V. Gangadharan,et al.  Design and development of a model free robust controller for active control of dominant flexural modes of vibrations in a smart system , 2015 .