Active control of a piezo-composite rotating beam using coupled plant dynamics

Optimal control of a thin-walled rotating beam is considered using a higher-order shear deformation theory (HSDT). The beam is pretwisted, doubly tapered, and carries a tip rotor. It comprises an orthotropic host with surface-embedded transversely isotropic piezoelectric sensor-actuator pairs. Spanwise and thicknesswise variation of the electric field applied to actuators is considered. This yields a coupled electro-mechanical system, wherein all displacement variables are coupled via the electric field. Hence, coupling between bending-transverse shear and extension-twist occurs even when the ply angle configuration has circumferentially uniform stiffness. Optimal LQR control with state feedback is used to obtain the control input, i.e., charge density (hence voltage) applied to actuators. Parametric studies involving ply-angle, rotation speeds of beam and rotor, pretwist, taper, rotor mass, and saturation constraint on actuator voltage, are performed. The HSDT yields lowest coupled natural frequencies (as compared to unshearable and first-order shear models) thus providing conservative data, useful for passive and active control designs. The present plant model, with spanwise varying electric field, yields an order-of-magnitude reduction in settling time and control voltage, and lower response, vis-a-vis the decoupled approach.

[1]  Ohseop Song,et al.  Adaptive vibrational behavior of cantilevered structures modeled as composite thin-walled beams , 1993 .

[2]  Donald L. Kunz Multimode control of a rotating, uniform, cantilever beam , 2001 .

[3]  Shueei-Muh Lin,et al.  PD control of a rotating smart beam with an elastic root , 2008 .

[4]  Sen-Yung Lee,et al.  Instability and vibration of a rotating Timoshenko beam with precone , 2009 .

[5]  R. Strawn,et al.  Conservative full-potential model for unsteady transonic rotor flows , 1987 .

[6]  S. Mohammadi,et al.  Damping Behavior of Semi-passive Vibration Control using Shunted Piezoelectric Materials , 2008 .

[7]  Heow-Pueh Lee Vibration on an Inclined Rotating Cantilever Beam With Tip Mass , 1993 .

[8]  Francesco dell’Isola,et al.  On a model of layered piezoelectric beams including transverse stress effect , 2004 .

[9]  J. Hutchinson,et al.  An introduction to the elastic stability of structures , 1976 .

[10]  C. W. Lim,et al.  Active control of a flexible hub-beam system using optimal tracking control method , 2006 .

[11]  Ji-Hwan Kim,et al.  Vibration control of pre-twisted rotating composite thin-walled beams with piezoelectric fiber composites , 2007 .

[12]  Kexiang Wei,et al.  Vibration control of variable speed/acceleration rotating beams using smart materials , 2006 .

[13]  Inderjit Chopra,et al.  Refined Structural Dynamics Model for Composite Rotor Blades , 2001 .

[14]  Maurizio Porfiri,et al.  Numerical methods for modal analysis of stepped piezoelectric beams , 2006 .

[15]  Maurizio Porfiri,et al.  Piezoelectric Passive Distributed Controllers for Beam Flexural Vibrations , 2004 .

[16]  Hong Hee Yoo,et al.  Vibration Analysis of Rotating Pre-Twisted Blades with a Concentrated Mass , 2001 .

[17]  C. Mei,et al.  Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam , 2008 .

[18]  Nesbitt W. Hagood,et al.  Damping of structural vibrations with piezoelectric materials and passive electrical networks , 1991 .

[19]  H. Tzou Piezoelectric Shells: Distributed Sensing and Control of Continua , 1993 .

[20]  Mohammad Hosseini,et al.  Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials , 2007 .

[21]  W. Gawronski Dynamics and control of structures : a modal approach , 1998 .

[22]  Maurizio Porfiri,et al.  Identification of electromechanical modal parameters of linear piezoelectric structures , 2007 .

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

[24]  Shueei-Muh Lin,et al.  In-plane vibrational analysis of rotating curved beam with elastically restrained root , 2008 .

[25]  Guo-Ping Cai,et al.  Dynamics studies of a flexible hub-beam system with significant damping effect , 2008 .

[26]  Samuel F. Asokanthan,et al.  Modal characteristics of a flexible beam with multiple distributed actuators , 2004 .

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

[28]  Scott R. White,et al.  Thick-walled composite beam theory including 3-d elastic effects and torsional warping , 1997 .

[29]  Marek Pietrzakowski,et al.  Piezoelectric control of composite plate vibration: Effect of electric potential distribution , 2008 .

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

[31]  J. Potter Matrix Quadratic Solutions , 1966 .

[32]  J. R. Banerjee,et al.  Free vibration of rotating tapered beams using the dynamic stiffness method , 2006 .

[33]  Liviu Librescu,et al.  Optimal Vibration Control of Thin-Walled Anisotropic Cantilevers Exposed to Blast Loadings , 2000 .

[34]  Mohammad Hosseini,et al.  Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method , 2007 .

[35]  P. Seshu,et al.  Multi-objective optimization of piezo actuator placement and sizing using genetic algorithm , 2009 .

[36]  L. Meirovitch Principles and techniques of vibrations , 1996 .

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

[38]  Charles E. Smith,et al.  Vibration Modes of Centrifugally Stiffened Beams , 1982 .

[39]  Ji-Hwan Kim,et al.  Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors , 2006 .

[40]  Ohseop Song,et al.  Vibration of pretwisted adaptive rotating blades modeled as anisotropic thin-walled beams , 2001 .

[41]  N. K. Chandiramani,et al.  Optimal control of a pretwisted shearable smart composite rotating beam , 2007 .