A computational scheme for the optimal sensor/actuator placement of flexible structures using spatial H2 measures

Abstract This paper develops a spatial H 2 norm-based computational scheme for finding the optimal locations of sensors and actuators in controlled flexible structures. As the optimization index, the spatial H 2 norm of the closed-loop transfer matrix from the disturbance to the distributed controlled output is used. The design of the optimal spatial H 2 controller is based on the reduced model of the flexible structure, which contains the dominant modes that have the largest contribution to the system's spatial H 2 norm. The proposed genetic algorithm (GA) is subsequently used to solve the resulting nonlinear optimization problem. The effectiveness of the proposed scheme is demonstrated by a numerical example on the vibration control of a plate structure. Simulation results also show that the spatial H 2 norm is a better performance index to be used in the structural vibration control when the vibration reduction is required over a continuous area on the structure.

[1]  Dikai Liu,et al.  Combinatorial optimal design of number and positions of actuators in actively controlled structures using genetic algorithms , 2004 .

[2]  Michael A. Demetriou,et al.  Optimal actuator/sensor location for active noise regulator and tracking control problems , 2000 .

[3]  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).

[4]  Hou-Cheng Huang,et al.  Static and Dynamic Analyses of Plates and Shells , 1989 .

[5]  Zhikun Hou,et al.  A new approach to suppress spillover instability in structural vibration control , 2004 .

[6]  S. Chemishkian,et al.  Intelligent algorithms for H/sub /spl infin//-optimal placement of actuators and sensors in structural control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[7]  S. O. Reza Moheimani,et al.  Spatial 𝒽2 control of a piezoelectric laminate beam: experimental implementation , 2002, IEEE Trans. Control. Syst. Technol..

[8]  Michael A. Demetriou.  Integrated Actuator–Sensor Placement and Hybrid Controller Design of Flexible Structures Under Worst Case Spatiotemporal Disturbance Variations , 2004 .

[9]  Robert E. Skelton,et al.  Space structure control design by variance assignment , 1985 .

[10]  Michael A. Demetriou,et al.  Optimal location of sensors and actuators for an active noise control problem , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Wodek Gawronski.  Actuator and sensor placement for structural testing and control , 1997 .

[12]  K. Lim.  Method for Optimal Actuator and Sensor Placement for Large Flexible Structures , 1992 .

[13]  S. Chemishkian,et al.  H/sub /spl infin//-optimal mapping of actuators and sensors in flexible structures , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[14]  M. Balas.  MODAL CONTROL OF CERTAIN FLEXIBLE DYNAMIC SYSTEMS , 1978 .

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

[16]  S. O. Reza Moheimani.  Minimizing the effect of out-of-bandwidth dynamics in the models of reverberant systems that arise in modal analysis: implications on spatial H Control , 2000, Autom..

[17]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[18]  Leonard Meirovitch,et al.  Dynamics And Control Of Structures , 1990 .

[19]  Ian R. Petersen,et al.  Spatial balanced model reduction for flexible structures , 1999, Autom..

[20]  D. E. Goldberg,et al.  Genetic Algorithms in Search, Optimization & Machine Learning , 1989 .

[21]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[22]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[23]  Frederick E. Petry,et al.  Genetic Algorithms , 1992 .