Optimal configuration of piezoelectric sensors and actuators for active vibration control of a plate using a genetic algorithm

The purpose of this study is to suggest a new formulation for active vibration control of a rectangular plate based on the optimal positions/orientations of piezoelectric actuators/sensors attached to the plate. The free vibration and modal properties are derived by using Rayleigh–Ritz and the transient response by assumed modes methods based on the classical plate theory. Three criteria are proposed for optimal location of piezoelectric patches attached to the simply supported plate. In other words, the optimal positions/orientations of piezoelectric patches can be determined based on spatial controllability/observability gramians of the structure, as well as the consideration of residual modes to reduce the spillover effect. These criteria are used to achieve the optimal fitness function defined for a genetic algorithm optimizer to find the optimal locations/orientations of piezoelectric sensors/actuators. To control the vibrations of the plate, a negative velocity feedback control algorithm is designed. The results of simulations indicate that by locating piezoelectric patches in the optimal positions, the depreciation rate of the structure increases and the amplitudes of the plate vibrations reduce effectively. The effect of number of piezoelectric devices on the active damping property of the system is also analyzed.

[1]  S. Xie,et al.  Vibration control of a simply supported cylindrical shell using a laminated piezoelectric actuator , 2008 .

[2]  I. Bruant,et al.  A methodology for determination of piezoelectric actuator and sensor location on beam structures , 2001 .

[3]  Donald J. Leo,et al.  Engineering Analysis of Smart Material Systems: Leo/Smart Material Systems , 2008 .

[4]  Daniel J. Inman,et al.  Vibration with Control: Inman/Vibration with Control , 2006 .

[5]  Seok Heo,et al.  Active vibration control of smart grid structure by multiinput and multioutput positive position feedback controller , 2007 .

[6]  In Lee,et al.  Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms , 1999 .

[7]  Wei Liu,et al.  Optimal sensor placement for spatial lattice structure based on genetic algorithms , 2008 .

[8]  Xianmin Zhang,et al.  Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate , 2007 .

[9]  S.O.R. Moheimani,et al.  Considerations on placement of piezoceramic actuators that are used in structural vibration control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  A. Hać,et al.  Sensor And Actuator Location In Motion Control Of Flexible Structures , 1993 .

[11]  Mao Yiqi,et al.  Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate , 2010 .

[12]  L. Gallimard,et al.  Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm , 2010 .

[13]  D. Inman.  Vibration control , 2018, Advanced Applications in Acoustics, Noise and Vibration.

[14]  D. Leo.  Engineering Analysis of Smart Material Systems , 2007 .

[15]  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).

[16]  K. Liew,et al.  Active control of FGM plates with integrated piezoelectric sensors and actuators , 2001 .

[17]  S. N. Sivanandam,et al.  Introduction to genetic algorithms , 2007 .

[18]  S. Narayanan,et al.  Active vibration control of beams with optimal placement of piezoelectric sensor/actuator pairs , 2008 .

[19]  S. O. Reza Moheimani,et al.  Spatial Control of Vibration: Theory and Experiments , 2003 .

[20]  S. K. Sarangi,et al.  Active damping of geometrically nonlinear vibrations of laminated composite plates using vertically reinforced 1-3 piezoelectric composites , 2011 .

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

[22]  Ryoichi Chiba,et al.  Optimisation of material composition of functionally graded materials based on multiscale thermoelastic analysis , 2012 .

[23]  O. Hasançebi,et al.  Layout optimization of trusses using improved GA methodologies , 2001 .

[24]  Yaowen Yang,et al.  Integrated optimal design of vibration control system for smart beams using genetic algorithms , 2005 .

[25]  Shih-Ming Yang,et al.  Optimization of noncollocated sensor/actuator location and feedback gain in control systems , 1993 .

[26]  S. O. Reza Moheimani,et al.  An optimization approach to optimal placement of collocated piezoelectric actuators and sensors on a thin plate , 2003 .

[27]  R. J. Wynne,et al.  Modelling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithms , 1999 .