This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising.
Keywords: collocation, piezoelectric sensors/actuators, positive-real systems, topology optimization
@article{COCV_2005__11_4_673_0,
author = {Degryse, Emmanuel and Mottelet, St\'ephane},
title = {Shape optimization of piezoelectric sensors or actuators for the control of plates},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {673--690},
year = {2005},
publisher = {EDP Sciences},
volume = {11},
number = {4},
doi = {10.1051/cocv:2005025},
mrnumber = {2167879},
zbl = {1081.49029},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2005025/}
}
TY - JOUR AU - Degryse, Emmanuel AU - Mottelet, Stéphane TI - Shape optimization of piezoelectric sensors or actuators for the control of plates JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 673 EP - 690 VL - 11 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2005025/ DO - 10.1051/cocv:2005025 LA - en ID - COCV_2005__11_4_673_0 ER -
%0 Journal Article %A Degryse, Emmanuel %A Mottelet, Stéphane %T Shape optimization of piezoelectric sensors or actuators for the control of plates %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 673-690 %V 11 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2005025/ %R 10.1051/cocv:2005025 %G en %F COCV_2005__11_4_673_0
Degryse, Emmanuel; Mottelet, Stéphane. Shape optimization of piezoelectric sensors or actuators for the control of plates. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 673-690. doi: 10.1051/cocv:2005025
[1] , Shape optimization by the homogenization method. Springer-Verlag, New York (2002). | Zbl | MR
[2] , and, Smart material structures, modelling, estimation and control. Res. Appl. Math. Masson, Paris (1996). | Zbl
[3] and, Finite Element Approximation on Elliptic Optimal Design. C.R. Acad. Sci. Paris Ser. I 338 729-734 (2004). | Zbl
[4] and, Necessary and sufficient conditions for robust stability of linear distributed feedback systems. Internat. J. Control 35 (1982) 255-267. | Zbl
[5] and, Robust control with respect to coprime factors of infinite-dimensional positive real systems. IEEE Trans. Autom. Control 37 (1992) 868-871. | Zbl
[6] and, Equivalence of input-output stability and exponential stability for infinite dimensional systems. J. Math. Syst. Theory 21 (1988) 19-48. | Zbl
[7] , A synthesis of Time and Frequency domain methods for the control of infinite dimensional systems: a system theoretic approach, in Control and Estimation in Distributed Parameter Systems, H.T. Banks Ed. SIAM (1988) 171-224.
[8] , Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim. 26 (1988) 697-713. | Zbl
[9] , Étude d'une nouvelle approche pour la conception de capteurs et d'actionneurs pour le contrôle des systèmes flexibles abstraits. Ph.D. Thesis, Université de Technologie de Compiègne, France (2002).
[10] ,, and, Theoretical, numerical and experimental discussion on the use of piezoelectric devices for control-structure interaction. Eur. J. Mech A/solids 11 (1992) 181-213.
[11] , A Course in Control Theory. Lecture notes in control and information sciences. Springer-Verlag Berlin (1988). | Zbl
[12] and, Stability results for the wave equation with indefinite damping. J. Diff. Equations 132 (1996) 338-352. | Zbl
[13] and, Right half plane poles and zeros and design tradeoffs in feedback systems. IEEE Trans. Autom. Control 30 (1985) 555-565. | Zbl
[14] and, Approximation theory for Linear-Quadratic-Gaussian control of flexible structures. SIAM J. Control Optim. 29 (1991) 1-37. | Zbl
[15] , Systèmes dynamiques dissipatifs et applications. Masson, Paris (1990). | Zbl | MR
[16] and, Optimal shape and position of the actuators for the stabilization of a string. Syst. Control Lett. 48 (2003) 199-209. | Zbl
[17] and, A spillover phenomenon in the optimal location of actuators. SIAM J. Control Optim., to appear. | Zbl | MR
[18] and, Sensitivity of the zeros of flexible structures to sensor and actuator location. IEEE Trans. Autom. Control 45 (2000) 157-160. | Zbl
[19] , and, Singular internal stabilization of the wave equation. J. Differential Equations 145 (1998) 184-215. | Zbl
[20] , Perturbation theory for linear operators. Springer-Verlag, Berlin (1980). | Zbl
[21] , control for distributed parameter systems: a state-space approach. Birkaüser, Boston (1993). | Zbl | MR
[22] and, Non-dissipative boundary stabilization of the wave equation via boundary observation. J. Math. Pures Appl. 63 (1984) 59-80.
[23] , Optimization by Vector Space Methods. John Wiley and Sons, New York (1969). | Zbl | MR
[24] and, On the lack of controllability of wave equations: a Gaussian beam approach. Asymptotic Analysis 32 (2002) 1-26. | Zbl
[25] , Programmation Mathématique: théorie et algorithmes, tome 2. Dunod, Paris (1983). | Zbl | MR
[26] , Dynamic boundary control of an Euler-Bernoulli beam. IEEE Trans. Autom. Control 37 (1992) 639-642.
[27] , Controllability and stabilization of a canal with wave generators. SIAM J. Control Optim. 38 (2000) 711-735. | Zbl
[28] , Hyperstability of Automatic Control Systems. Springer, New York (1973).
[29] and, A method of structure/control design Integration based on finite frequency conditions and its application to smart arm structure design, Proc. of SICE 2002, Osaka, (August 2002).
[30] and, Sensitivity of structural models for non collocated control systems. Trans. ASME 111 (1989) 646-655. | Zbl
[31] and, Regularity of plate equations with control concentrated in interior curves. Proc. Roy. Soc. Edinburg A 127 (1997) 1005-1025. | Zbl
[32] , Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment. Technical Report TR96-01, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD (July 1995). | Zbl
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