Optimum control voltage design for constrained static shape control of piezoelectric structures

Design optimization of control voltage distribution for constrained static shape control of structures using piezoelectric actuators is investigated. Two cases are studied. In the first case, a scheme is developed to find the optimal control voltage distribution minimizing the square error between the desired and actuated shapes subject to a given control electric energy. The optimal control voltage constrained by control energy can be found after solving an algebraic equation in terms of the Lagrangian multiplier. An alternative form for this algebraic equation is derived by taking advantage of an eigenvalue problem of a real symmetrical matrix, which significantly reduces the computational cost for finding its roots. A procedure for finding the optimal control energy is also given. In the second case, a process of seeking the control voltage distribution with least control energy for any given square error tolerance between the actuated and desired shapes is presented. Finally, illustrative examples for the constrained shape control of thin plates are given to demonstrate the presented methods.

[1]  Hans Irschik,et al.  A review on static and dynamic shape control of structures by piezoelectric actuation , 2002 .

[2]  Junjiro Onoda,et al.  Actuator Placement Optimization by Genetic and Improved Simulated Annealing Algorithms , 1993 .

[3]  Grant P. Steven,et al.  Static shape control of composite plates using a curvature-displacement based algorithm , 2001 .

[4]  Manfred Hertwig,et al.  Shape Control of an Adaptive Mirror at Different Angles of Inclination , 1996 .

[5]  L. Kollár,et al.  Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified , 1994 .

[6]  Romesh C. Batra,et al.  Shape Control of Plates using Piezoceramic Elements , 1995 .

[7]  Gareth J. Knowles,et al.  Static shape control for adaptive wings , 1994 .

[8]  Robert M. Haralick,et al.  Constrained Transform Coding and Surface Fitting , 1983, IEEE Trans. Commun..

[9]  M. J. Balas,et al.  Optimal quasi-static shape control for large aerospace antennae , 1985 .

[10]  Romesh C. Batra,et al.  Shape Control of Vibrating Simply Supported Rectangular Plates , 1996 .

[11]  Santosh Kapuria,et al.  Three-dimensional piezothermoelastic solution for shape control of cylindrical panel , 1997 .

[12]  Chien-Chang Lin,et al.  Shape Control of Composite Plates by Bonded Actuators with High Performance Configuration , 1997 .

[13]  J. C. Bruch,et al.  Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams , 2000 .

[14]  Raphael T. Haftka,et al.  An analytical investigation of shape control of large space structures by applied temperatures , 1985 .

[15]  Sunil Kumar Agrawal,et al.  Modeling and Shape Control of Piezoelectric Actuator Embedded Elastic Plates , 1994 .

[16]  Bryan Kok Ann Ngoi,et al.  Shape Control of Beams by Piezoelectric Actuators , 2000 .

[17]  Grant P. Steven,et al.  Static Shape Control of Composite Plates Using a Slope-Displacement-Based Algorithm , 2002 .

[18]  B. Agrawal,et al.  Shape control of a beam using piezoelectric actuators , 1999 .