Dynamic stabilization of an Euler-Bernoulli beam under boundary control and non-collocated observation

Systems and Control Letters

Volumn 57, Issue 9, 2008, Pages 740-749

  Guo, Bao Zhu ^a,c   Wang, Jun Min ^b   Yang, Kun Yi ^a  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b BEIJING INSTITUTE OF TECHNOLOGY   (China)

^c UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

Controllability and observability; Euler Bernoulli beam; Observer; Riesz basis; Stability

Indexed keywords

ARSENIC COMPOUNDS; SEDIMENTATION; STABILIZATION; STATE FEEDBACK; STATE SPACE METHODS; VIBRATION MEASUREMENT;

BENDING STRAINS; BOUNDARY CONTROLS; CLOSED-LOOP SYSTEMS; DYNAMIC STABILIZATION; EIGENFUNCTIONS; EULER BERNOULLI BEAMS; EXPONENTIAL STABILITY; FREE END; GROWTH CONDITIONS; OBSERVER (OBS); OUTPUT FEEDBACK CONTROLS; RIESZ BASES; STATE SPACES;

FEEDBACK;

EID: 47649089973     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2008.02.004     Document Type: Article

References (23)

1. Balas M. Modal control of certain flexible dynamic systems. SIAM J. Control Optim. 16 (1978) 450-462
2. Banks H.T., and Morris K.A. Input-output stability for accelerometer control systems. Control Theory Adv. Tech. 10 (1994) 1-17
3. Cannon R.H., and Schmitz E. Initial experiments on the end-point control of a flexible one-link robot. Int. J. Robot. Res. 3 (1984) 62-75
4. P.A. Chodavarapu, M.W. Spong, On Noncollocated control of a single flexible link, in: Pro. IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota, 1996, pp. 1101-1106
5. Curtain R.F. The Salamon-Weiss class of well-posed infinite dimensional linear systems: a survey. IMA J. Math. Control Inform. 14 (1997) 207-223
6. Curtain R.F., and Salamon D. Finite dimensional compensators for infinite dimensional systems with unbounded input operators. SIAM J. Control Optim. 24 (1986) 797-816
7. Deguenon A.J., Sallet G., and Xu C.Z. A Kalman observer for infinite-dimensional skew-symmetric systems with application to an elastic beam. Proc. of the Second International Symposium on Communications, Control and Signal Processing (2006), Marrakech, Morocco
8. Gressang R.V., and Lamont G.B. Observers for systems characterized by semigroups. IEEE Transactions on Automatic Control 20 (1975) 523-528
9. Guo B.Z., and Xu C.Z. The stabilization of a one-dimensional wave equation by boundary feedback with non-collocated observation. IEEE Trans. Automat. Control 52 (2007) 371-377
10. Guo B.Z. Riesz basis approach to the stabilization of a flexible beam with a tip mass. SIAM J. Control Optim. 39 (2001) 1736-1747
11. Guo B.Z., and Wang J.M. Riesz basis generation of an abstract second-order partial differential equation system with general non-separated boundary conditions. Numer. Funct. Anal. Optim. 27 3-4 (2006) 291-328
12. Guo B.Z., and Zhang X. The regularity of the wave equation with partial Dirichlet control and colocated observation. SIAM J. Control Optim. 44 5 (2005) 1598-1613
13. Inniss C., and Williams T. Sensitivity of the zeros of flexible structures to sensor and actuator location. IEEE Trans. Automat. Control 45 (2000) 157-160
14. Lasiecka I. Finite element approximations of compensator design for analytic generators with fully unbounded controls/observations. SIAM J. Control Optim. 33 (1995) 67-88
15. Liu L.Y., and Yuan K. Noncollocated passivity-based control of a single-link flexible manipulator. Robotica 21 (2003) 117-135
16. Luo Z.H., Guo B.Z., and Morgul O. Stability and Stabilization of Infinite Dimensional Systems with Applications (1999), Springer-Verlag, London
17. Mazja V. Sobolev Spaces (1985), Springer-Verlag, New York
18. Loix N., Kozanek J., and Foltete E. On the complex zeros of non-colocated systems. J. Struct. Control 3 (2006) 79-87
19. Russell D.L., and Weiss G. A general necessary condition for exact observability. SIAM J. Control Optim. 32 (1994) 1-23
20. Smyshlyaev A., and Krstic M. Backstepping observers for a class of parabolic PDEs. Syst. Control Lett. 54 (2005) 613-625
21. Udwadia F.E. Noncollocated point control of nondispersive distributed-parameter systems using time delays. Appl. Math. Comput. 42 (1991) 23-63
22. Weiss G. Admissible observation operators for linear semigroups. Isr. J. Math. 65 (1989) 17-43
23. Weiss G., and Curtain R.F. Dynamic stabilization of regular linear systems. IEEE Trans. Automat. Control 42 (1997) 4-21