Simultaneous H∞ vibration control of fluid/plate system via reduced-order controller

The problem of active reduction of the structural vibrations induced by the sloshing of large masses of fuel inside partly full tank is considered. The proposed study focuses on an experimental device mimicking an aircraft wing made of an aluminum rectangular plate equipped with piezoelectric patches at the clamped end and with a cylindrical tip-tank, more or less filled with liquid. First, a representative finite dimensional model of the complete system containing the first 5 structural modes of the plate and the first 2 liquid sloshing modes is derived via a model matching procedure. A simultaneous H∞ control problem associated to the vibration attenuation problem for two different fillings of the tank is stated. Due to the large scale of the synthesis model and to the simultaneous performance requirements, a reduced-order H∞ controller is computed with HIFOO 2.0 and is compared with individual designs for different filling levels. Experimental results are finally provided illustrating the relevance of the chosen strategy.

[1]  Ian R. Petersen,et al.  Multivariable integral control of resonant structures , 2008, 2008 47th IEEE Conference on Decision and Control.

[2]  A. Oustaloup,et al.  Fractional robust control with iso-damping property , 2008, 2008 American Control Conference.

[3]  K Yamada,et al.  Hybrid vibration suppression of multiple vibration modes of flexible structures using piezoelectric elements and analog circuit , 2008 .

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

[5]  Clement Roos.  Generation of flexible aircraft LFT models for robustness analysis , 2009 .

[6]  C. Fuller,et al.  Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates , 1991 .

[7]  Jang Moo Lee,et al.  Robust LQG Control of an All-Clamped Thin Plate with Piezoelectric Actuators/Sensors , 1997 .

[8]  M. Géradin,et al.  Mechanical Vibrations: Theory and Application to Structural Dynamics , 1994 .

[9]  W. Siebert.  Circuits, Signals and Systems , 1985 .

[10]  Bo Bernhardsson,et al.  Constrained iterative learning control of liquid slosh in an industrial packaging machine , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  Brian P. Baillargeon,et al.  Active Vibration Suppression of Sandwich Beams using Piezoelectric Shear Actuators: Experiments and Numerical Simulations , 2005 .

[12]  W. Marsden.  I and J , 2012 .

[13]  Jean-Sébastien Schotté,et al.  Various modelling levels to represent internal liquid behaviour in the vibration analysis of complex structures , 2009 .

[14]  M. Grundelius.  Iterative optimal control of liquid slosh in an industrial packaging machine , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[15]  Joël Bordeneuve-Guibé,et al.  FEM design of a piezoelectric active control structure. Application to an aircraft wing model , 2004 .

[16]  Jingjun Zhang,et al.  Active Vibration Control of Flexible Structures Using Piezoelectric Materials , 2009, 2009 International Conference on Advanced Computer Control.

[17]  Malcolm J. Abzug,et al.  FUEL SLOSH IN SKEWED TANKS , 1996 .

[18]  Jonathan de Halleux,et al.  Stabilization of a 1-D tank containing a fluid modeled by the shallow water equations , 2004, Syst. Control. Lett..

[19]  Christophe Prieur,et al.  ACTIVE VIBRATION DAMPING OF A SMART FLEXIBLE STRUCTURE USING PIEZOELECTRIC TRANSDUCERS: H∞ DESIGN AND EXPERIMENTAL RESULTS , 2005 .

[20]  Pierre Rouchon,et al.  Dynamics and solutions to some control problems for water-tank systems , 2002, IEEE Trans. Autom. Control..

[21]  Juergen Becker,et al.  Comparison of piezoelectric systems and aerodynamic systems for aircraft vibration alleviation , 1998, Smart Structures.

[22]  D. Halim,et al.  Vibration control experiments on a piezoelectric laminate plate using spatial feedforward control approach , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[23]  Jang Moo Lee,et al.  Plate with piezoelectric actuators/sensors , 1997 .

[24]  S.O. Reza Moheimani,et al.  Optimal impedance design for piezoelectric vibration control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[25]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

[26]  Joël Bordeneuve-Guibé,et al.  ACTIVE CONTROL OF A STRUCTURE WITH SLOSHING PHENOMENA , 2006 .

[27]  K. K. Denoyer,et al.  DYNAMIC MODELLING AND VIBRATION SUPPRESSION OF A SWELLING STRUCTURE UTILIZING PIEZOELECTRIC SENSORS AND ACTUATORS , 1996 .

[28]  Jackson E. Bruce,et al.  The Impact of Structural Vibration on Flying Qualities of a Supersonic Transport , 2001 .

[29]  Sami Tliba,et al.  H∞ Controller Design for Active Vibration Damping of a Smart Flexible Structure Using Piezoelectric Transducers , 2003 .

[30]  C. SIAMJ.,et al.  ON THE NULL ASYMPTOTIC STABILIZATION OF THE TWO-DIMENSIONAL INCOMPRESSIBLE EULER EQUATIONS IN A SIMPLY CONNECTED DOMAIN , 1999 .

[31]  Michael A. Demetriou,et al.  An adaptive control scheme for a class of second order distributed parameter systems with structured perturbations , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[32]  Bogdan Robu,et al.  A controlled distributed parameter model for a fluid-flexible structure system: numerical simulations and experiment validations , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[33]  R. Potami,et al.  Actuator switching for vibration control of spatially distributed systems , 2007, 2007 American Control Conference.

[34]  Carey S. Buttrill,et al.  AIAA 2001-4006 The Impact of Structural Vibration on Flying Qualities of a Supersonic Transport , 2001 .

[35]  Raouf A. Ibrahim,et al.  Liquid Sloshing Dynamics: Acknowledgment , 2005 .

[36]  Amjad Tuffaha,et al.  Boundary feedback control in Fluid-Structure Interactions , 2008, 2008 47th IEEE Conference on Decision and Control.

[37]  S. Rubin.  Improved Component-Mode Representation for Structural Dynamic Analysis , 1975 .

[38]  N. C. Nigam,et al.  A mechanical model for liquid sloshing in a rectangular container , 1989 .

[39]  B. A. Winther,et al.  Reduced-Order Dynamic Aeroelastic Model Development and Integration with Nonlinear Simulation , 2000 .

[40]  Bin Li,et al.  Vibration suppression of a hard disk driver actuator arm using piezoelectric shunt damping with a topology-optimized PZT transducer , 2009 .

[41]  James D. Jones,et al.  Influence of Piezo-Actuator Thickness on the Active Vibration Control of a Cantilever Beam , 1995 .

[42]  Jean-Michel Coron,et al.  Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations , 2002 .

[43]  Christophe Prieur,et al.  CONTROL OF A CLAMPED-FREE BEAM BY A PIEZOELECTRIC ACTUATOR , 2006 .

[44]  Bogdan Robu.  Active vibration control of a fluid/plate system , 2010 .

[45]  A. Sano,et al.  Adaptive identification of MR damper for vibration control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[46]  Boeing Vertol Co.,et al.  Active Control of The Helicopter Rotor for Vibration Reduction , 1980 .

[47]  R. Blevins,et al.  Formulas for natural frequency and mode shape , 1984 .

[48]  Michael L. Overton,et al.  Multiobjective robust control with HIFOO 2.0 , 2009, 0905.3229.