Realistic determination of the optimal size and location of piezoelectric actuator/sensors

We address the problem of obtaining the optimal size and location of piezoelectric actuator/sensors. An optimization problem is formulated for a general beam which can be subject to any boundary and may have as many piezoelectric patches as needed. The proposed optimization criterion is based on the beam modal cost and modal controllability. By adding a penalty term to the criterion, the size of the actuator/sensor can be reduced to a practical and reasonable size. Thus there is no need to pre-select the size of the actuator/sensor. The optimal size and location for beams with various boundary conditions are determined for a single pair and for two pairs of piezoelectric patches. The results in this paper are in very good agreement with those reported by other investigators. A comparison is also made between the performance of two pairs of actuators and the performance of a single pair. It has been shown that the two pair actuators can control the bending vibration more efficiently than a single pair.

[1]  E. Crawley,et al.  Detailed Models of Piezoceramic Actuation of Beams , 1989 .

[2]  H. Saunders,et al.  Book Reviews : DYNAMICS OF STRUCTURES R.W. Clough & J. Penzien McGraw-Hill Book Co., New York, New York (1975) , 1976 .

[3]  John L. Junkins,et al.  Measure of controllability for actuator placement , 1991 .

[4]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[5]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[6]  Rong C. Shieh,et al.  Governing equations and finite element models for multiaxial piezoelectric beam sensors/actuators , 1994 .

[7]  Ephrahim Garcia,et al.  A Self-Sensing Piezoelectric Actuator for Collocated Control , 1992 .

[8]  Singiresu S Rao,et al.  Distributed modeling and actuator location for piezoelectric control systems , 1996 .

[9]  C. K. Lee.  Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships , 1990 .

[10]  Robert L. Clark,et al.  Implementation of an adaptive piezoelectric sensoriactuator , 1996 .

[11]  A. Hamdan,et al.  Measures of Modal Controllability and Observability for First- and Second-Order Linear Systems , 1989 .

[12]  Craig A. Rogers,et al.  Experimental Verification of Optimal Actuator Location and Configuration Based on Actuator Power Factor , 1995 .

[13]  Youdan Kim,et al.  Optimal sizing and placement of piezo actuators for active flutter suppression , 1995, Smart Structures.

[14]  S. Yang,et al.  Modal Analysis Of Stepped Beams With Piezoelectric Materials , 1994 .

[15]  Santosh Devasia,et al.  Piezoelectric actuator design for vibration suppression: placement and sizing , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[16]  S. Poh,et al.  Performance of an active control system with piezoelectric actuators , 1988 .

[17]  Horn-Sen Tzou,et al.  Intelligent Structural Systems , 1992 .

[18]  Youdan Kim,et al.  Introduction to Dynamics and Control of Flexible Structures , 1993 .

[19]  S. Poh,et al.  Experimental implementation of the modified independent modal space control method , 1990 .