Abstract
Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hu, H.Y., On dynamics in vibration with time delay. Chinese Journal of Vibration Engineering, 1997, 10(3): 273–279 (in Chinese).
Hu, H.Y. and Wang, Z.H., Singular perturbation methods for nonlinear dynamic systems with time delays. Chaos, Solitons and Fractals, 2007, doi: 10.1016/j.chaos.2007.07.048.
Wang, Z.H. and Hu, H.Y., Stabilization of vibration systems via delayed state difference feedback. Journal of Sound and Vibration, 2006, 296(1–2): 117–129.
Xu, J., Chung, K.W. and Chan, C.L., An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks. SIAM Journal of Applied Dynamical Systems, 2007, 6(1): 29–60.
Xu, J. and Chung, K.W., Effects of time delayed position feedback on a van der Pol-Duffing oscillator. Physica D, 2003, 180: 17–39.
Abdel-Rohman, M., Time-delay effects on active damped structures. Journal of Engineering Mechanics, 1987, 113(11): 1709–1719.
Chung, L.L., Reinhorn, A.M. and Soong, T.T., Experiments on active control of seismic structures. Journal of Engineering Mechanics, 1998, 114(2): 241–256.
Cai, G.P. and Hong, J.Z., Optimal control method for seismically excited building structures with time-delay in control. Journal of Engineering Mechanics, ASCE, 2002, 128(6): 602–612.
Xiao, M. and Cao, J.D., Bifurcation analysis and chaos control for Lu system with delayed feedback. International Journal of Bifurcation and Chaos, 2007, 17(12): 4309–4322.
Hosek, M. and Olgac, N., A single-step automatic tuning algorithm for the delayed resonator vibration absorber. IEEE/ASME Transactions on Mechatronics, 2002, 7(2): 245–255.
Cai, G.P. and Lim, C.W., Optimal tracking control of flexible hub-beam system with time delay. Multibody System Dynamics, 2006, 16(4): 331–350.
Yuan, F., Effects of delayed feedback control on stability in the cantilever pipe conveying fluid. Master dissertation of Tongji University, 2008 (in Chinese).
Qiu, Z.C., Zhang, X.M., Wu, H.X. and Zhang, H.H., Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. Journal of Sound and Vibration, 2007, 301: 521–543.
Sun, Z.X., Theory and Application of Computer Control. Beijing: Tsinghua University Press, 1989 (in Chinese).
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 10772112 and 10472065), the Key Project of Ministry of Education of China (No. 107043) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070248032).
Rights and permissions
About this article
Cite this article
Chen, L., Pan, J. & Cai, G. Active Control of a Flexible Cantilever Plate with Multiple Time Delays. Acta Mech. Solida Sin. 21, 257–266 (2008). https://doi.org/10.1007/s10338-008-0829-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-008-0829-y