Optimal Sizes and Placements of Piezoelectric Actuators and Sensors for an Inflated Torus

Abstract

One of the limitations of a piezoelectric actuator is the amount of force it can exert. Hence, it is important to optimize the locations and sizes of the actuators so that the required control effort is minimal. Similarly, to obtain good signal-to-noise ratio, sensors should be chosen to provide maximum output for the vibration in the modes of interests. These problems become more critical as the number of actuators and sensors increases, and the mode shapes become more complicated. This is true for the case of an inflated torus. In this study, we try to find optimum places and sizes of actuators and sensors attached to an inflated toroidal shell using a genetic algorithm. Using the expressions for the generalized forces and sensor voltages, modal forces and modal sensing constants are determined. To obtain a cumulative performance measure for all the controlled and observed modes, controllability and observability indices are used. Using these performance indices, optimal locations and sizes of the actuators and sensors are determined so that the actuators and sensors provide good control and sensing authorities in the considered modes. Finally, vibration suppression of the inflated torus using these actuators and sensors has been demonstrated using an optimal control technique.

Get full access to this article

View all access options for this article.

References

Budiansky, B. 1968 . “Notes on Nonlinear Shell Theory,” Journal of Applied Mechanics , 35 : 393 - 401 .

Callahan, J. and Baruh, H. 1999 . “Modal Sensing of Circular Cylinder Shells Using Segmented Piezoelectric Elements,” Smart Materials and Structures , 8 : 125 - 135 .

Chattopadhyay, A. and Seeley, C.E. 1995 . “A Coupled Controls/Structures Optimization Procedure for the Design of Rotating Composite Box Beams with Piezoelectric Actuators,” Smart Structures and Materials , 4 : 170 - 178 .

Chen, S. and Cao, Z. 2000 . “A New Method for Determining Locations of Piezoelectric Sensor/Actuator for Vibration Control of Intelligent Structures,” Journal of Intelligent Material Systems and Structures , 11 : 108 - 115 .

Clark, L.R. and Fuller, C.R. 1992 . “Optimal Placement of Piezoelectric Actuators and Polyvinylidene Fluoride Errors Sensors in Active Structural Acoustic Control Approaches,” Journal of the Acoustical Society of America , 92 : 1521 - 1533 .

Deb, K. 1996 . Optimization for Engineering Design: Algorithms and Examples , Prentice Hall of India , New Delhi .

Goldberg, D.E. 1989 . Genetic Algorithms in Search, Optimization & Machine Learning , Addison-Wesley, Reading, MA .

Hac, A. and Lui, L. 1993 . “Sensor and Actuator Location in Motion Control of Flexible Structures,” Journal of Sound and Vibration , 167 ( 2 ): 239 - 261 .

Jha, A.K. 2002. Vibration Analysis and Control of an Inflated Toroidal Satellite Component Using Piezoelectric Actuators and Sensors, PhD Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA.

10.

Jha, A.K. , Inman, D.J. and Plaut, R.H. 2002 . “Free Vibration Analysis of an Inflated Toroidal Shell,” Journal of Vibration and Acoustics , 124 : 387 - 396 .

11.

Kim, S.J. and Jones, D. 1991 . “Optimal Design of Piezoactuators for Active Noise and Vibration Control,” AIAA Journal , 29 ( 12 ): 2047 - 2053 .

12.

Kim, S.J. , Hwang, J.S. , Mok, J. and Ko, H.M. 2001 . “Active Vibration Control of Composite Shell Structure Using Modal Sensor/Actuator System,” Proceedings of SPIE , 4327 : 688 - 697 .

13.

Lee, C.K. 1990 . “Theory of Laminated Piezoelectric Plates for the Design of Distributed Sensors/Actuators. Part I: Governing Equations and Reciprocal Relationships,” Journal of the Acoustical Society of America , 87 : 1144 - 1158 .

14.

Leleu, S. , Abou-Kandil, H. and Bonnassieux, Y. 2000. “Piezoelectric Actuators and Sensors Location for Active Control of Flexible Structures,” Proceedings of the IEEE International Measurement Technology Conference , Baltimore, Maryland, USA , pp. 818 - 823 .

15.

Main, J.A. , Garcia, E. and Howard, D. 1994 . “Optimal Placement and Sizing of Paired Pizoactuators in Beams and Plates,” Smart Materials and Structures , 3 : 373 - 381 .

16.

Maji, A.K. and Starnes, M.A. 2000 . “Shape Measurement and Control of Deployable Membrane Structures,” Experimental Mechanics , 40 ( 2 ): 154 - 159 .

17.

Meirovitch, L. 1990 , Dynamics and Control of Structures , Wiley , New York .

18.

Padula, S.L. and Kincaid, R.K. 1999 . “Optimization Strategies for Sensor and Actuator Placement,” NASA/TM-1999-209126.

19.

Padula, S.L. , Palumbo, D.L. and Kincaid, R.K. 1998. “Optimal Sensor/Actuator Locations for Active Structural Acoustic Control,” 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference, AIAA Paper No. 98-1865 , Long Beach, California .

20.

Plaut, R.H. , Goh, J.K.S. , Kigudde, M. and Hammerand, D.C. 2000 . “Shell Analysis of an Inflatable Arch Subjected to Snow and Wind Loading,” International Journal of Solids and Structures , 37 : 4275 - 4288 .

21.

Sadri, A.M. , Wright, J.R. and Wyne, R.J. 1999 . “Modeling and Optimal Placement of Piezoelectric Actuators in Isotropic Plates Using Genetic Algorithms,” Smart Structures and Materials , 8 : 490 - 498 .

22.

Salama, M., Kuo, C.P., Garba, J., Wada, B. and Thomas, M. 1994. “On-Orbit Shape Correction of Inflatable Structures,” Jet Propulsion Laboratory Technical Report.

23.

Sanders, J.L. 1959. “An improved first approximation Theory for Thin Shells,” NASA Report 24.

24.

Sun, D. and Tong, L. 2001 . “Modal Control of Smart Shells by Optimized Discretely Distributed Piezoelectric Transducers,” International Journal of Solids and Structures , 38 : 3281 - 3299 .

25.

Tinker, M.L. 1998 . “Passively Adaptive Inflatable Structure for the Shooting Star Experiment,” AIAA Paper No. 98-1986, pp. 2320 - 2326 .

26.

Tzou, H.-S. 1993 . Piezoelectric Shells: Distributed Sensing and Control of Continua , Kluwer Academic Publishers , Dordrecht, The Netherlands .

27.

Tzou, H.-S. and Fu, H.Q. 1994 . “A Study of Segmentation of Distributed Piezoelectric Sensors and Actuators, Part I: Parametric Study and Active Vibration Controls,” Journal of Sound and Vibration , 172 ( 2 ): 261 - 275 .

28.

Varadan, V.V. , Kim, J. and Varadan, V.K. 1997 . “Optimal Placement of Piezoelectric Actuators for Active Noise Control,” AIAA Journal , 35 ( 3 ): 526 - 533 .

29.

Wang, Q. and Wang, C.M. 2001 . “A Controllability Index for Optimal Design of Piezoelectric Actuators in Vibration Control of Beam Structures,” Journal of Sound and Vibration , 241 ( 3 ): 507 - 518 .

30.

Williams, T. 1990 . “Closed-Form Grammians and Model Reduction for Flexible Space Structures,” IEEE Transactions on Automatic Control , 35 ( 3 ): 379 - 382 .

31.

Yang, S.M. and Lee, Y.J. 1993 . “Vibration Suppression with Optimal Sensor/Actuator Location and Feedback Gain,” Smart Materials and Structures , 2 : 232 - 239 .