On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 615-623.

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

DOI : 10.1051/cocv:2004028
Classification : 47F, 35K
Mots-clés : beam equation, disturbance rejection, noncollocated control, strong stability
@article{COCV_2004__10_4_615_0,
     author = {Guo, Bao-Zhu and Zhang, Qiong},
     title = {On harmonic disturbance rejection of an undamped {Euler-Bernoulli} beam with rigid tip body},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {615--623},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {4},
     year = {2004},
     doi = {10.1051/cocv:2004028},
     mrnumber = {2111083},
     zbl = {1088.93008},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2004028/}
}
TY  - JOUR
AU  - Guo, Bao-Zhu
AU  - Zhang, Qiong
TI  - On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2004
SP  - 615
EP  - 623
VL  - 10
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2004028/
DO  - 10.1051/cocv:2004028
LA  - en
ID  - COCV_2004__10_4_615_0
ER  - 
%0 Journal Article
%A Guo, Bao-Zhu
%A Zhang, Qiong
%T On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2004
%P 615-623
%V 10
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2004028/
%R 10.1051/cocv:2004028
%G en
%F COCV_2004__10_4_615_0
Guo, Bao-Zhu; Zhang, Qiong. On harmonic disturbance rejection of an undamped Euler-Bernoulli beam with rigid tip body. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 615-623. doi : 10.1051/cocv:2004028. http://www.numdam.org/articles/10.1051/cocv:2004028/

[1] R.H. Cannon, Jr. and E. Schmitz, Inital experiments on the end-point control of a flexible one-link Robot. Inter. J. Robotics Res. 3 (1984) 62-75.

[2] G. Chen, M.C. Delfour, A.M. Krall and G. Payre, Modeling, stabilization and control of serially connected beam. SIAM J. Control Optim. 25 (1987) 526-546. | MR | Zbl

[3] P.A. Chodavarapu and M.W. Spong, On noncolocted control of a single flexible link, in Proc. of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota (April 1996) 1101-1106.

[4] B.Z. Guo and Q. Song, Tracking control of a flexible beam by nonlinear boundary feedback. J. Appl. Math. Stochastic Anal. 8 (1995) 47-58. | MR | Zbl

[5] B.Z. Guo, Riesz basis approach to the tracking control of a flexible beam with a tip rigid body without dissipativity. Optim. Methods Softw. 17 (2002) 655-681. | MR | Zbl

[6] T. Hämäläinen and S. Pohjolainen, A finite dimensional robust controller for systems in the CD-algebra. IEEE Trans. Autom. Control 45 (2000) 421-431. | MR | Zbl

[7] S. Lee and J.L. Junkins, Explicit generalization of Langrange's equations for hybrid coordinate dynamic systems, J. Guid. Control Dyn. 15 (1992) 1443-1452. | Zbl

[8] Z.H. Luo, B.Z. Guo and Ö. Morgül, Stability and Stabilization of Linear Dimensional Systems with Applications. Springer-Verlag, London (1999). | MR

[9] J.C. Oostveen and R.F. Curtain, Robustly stabilizing controllers for dissipative infinite-dimensional systems with collocated actuators and sensors. Automatica 36 (2000) 337-348. | MR | Zbl

[10] R. Rebarber and G. Weiss, Internal model based tracking and disturbance rejection for stable well-posed systems. Automatica, in press. | Zbl

[11] Y. Sakawa, F. Matsuno and S. Fukushima, Modeling and feedback control of a flexible arm. J. Rob. Syst. 2 (1985) 453-472.

[12] Y. Sakawa and Z.H. Luo, Modeling and control of coupled bending and torsional vibrations of flexible beam. IEEE Trans. Autom. Control 34 (1989) 970-977. | MR | Zbl

[13] V.A. Spetor and H. Flashner, Modeling and design implification of noncollocated control in flexible systems. J. Dyn. Syst. Meas. Control 112 (1990) 186-193.

[14] G. Weiss and R. Rebarber, Optimizability and estimatability for infinite-dimensional linear systems. SIAM J. Control Optim. 39 (2001) 1204-1232. | MR | Zbl

[15] K. Yuan and L. Liu, Achieving mininmum phase transfer function for a noncollocated single-link flexible manipulator. Asian J. Control 2 (2000) 179-191.

Cité par Sources :