Active control of high-frequency vibration: Optimisation using the hybrid modelling method

Abstract This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time.

[1]  Dean Karnopp,et al.  Vibration Control Using Semi-Active Force Generators , 1974 .

[2]  Michael J. Brennan,et al.  Strategies for the active control of flexural vibration on a beam , 1995 .

[3]  R. Lyon,et al.  Power Flow between Linearly Coupled Oscillators , 1962 .

[4]  L. Cremer,et al.  Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies , 1973 .

[5]  R S Langley,et al.  On the reciprocity relationship between direct field radiation and diffuse reverberant loading. , 2005, The Journal of the Acoustical Society of America.

[6]  Stephen J. Elliott,et al.  Feedback stability limits for active isolation systems with reactive and inertial actuators , 2001 .

[7]  Robin S. Langley.  Mid and high-frequency vibration analysis of structures with uncertain properties , 2004 .

[8]  Robert J. Bernhard,et al.  Measurement of the Statistical Variation of Structural-Acoustic Characteristics of Automotive Vehicles , 1993 .

[9]  Stephen J. Elliott,et al.  Active vibration isolation using an inertial actuator with local displacement feedback control , 2004 .

[10]  William R. Saunders,et al.  Adaptive Structures: Dynamics and Control , 1998 .

[11]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[12]  Yildirim Hurmuzlu,et al.  A theoretical and experimental study of advanced control methods to suppress vibrations in a small square plate subject to temperature variations , 2007 .

[13]  André Preumont,et al.  Vibration Control of Active Structures: An Introduction , 2018 .

[14]  Richard H. Lyon.  Statistical energy analysis of dynamical systems : theory and applications , 2003 .

[15]  Stephen J. Elliott,et al.  Global control of a vibrating plate using a feedback-controlled inertial actuator , 2005 .

[16]  Abdul Muthalif,et al.  Active control of high-frequency vibration , 2008 .

[17]  Dino Sciulli,et al.  Virtual Skyhook Vibration Isolation System , 2002 .

[18]  D. Morgan.  An adaptive modal‐based active control system , 1990 .

[19]  Jim Woodhouse.  An approach to the theoretical background of statistical energy analysis applied to structural vibration , 1981 .

[20]  Andy J. Keane,et al.  Statistics of energy flows in spring-coupled one-dimensional subsystems , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.