Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-29T07:36:23.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems with Persistent Excitation

Published online by Cambridge University Press:  05 May 2011

Liang-An Zheng ,
Shinn-Horng Chen  and
Jyh-Horng Chou
Liang-An Zheng*
Affiliation:
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, R.O.C.
Shinn-Horng Chen*
Affiliation:
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, R.O.C.
Jyh-Horng Chou*
Affiliation:
Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science & Technology, Kaohsiung, Taiwan 824, R.O.C.
*
*Associate Professor
*Associate Professor
**Professor
Get access

Abstract

Based on the frequency-shaping optimal control method, this paper proposes a time-domain robust disturbance rejection design approach for a class of uncertain flexible mechanical systems subject to persistent disturbances and time-varying parameter perturbations. In the approach, a frequency-shaping output filter is first employed to combine with the mechanical system and a Kalman filter to form an augmented system. Some eigenvalues of the frequency-shaping output filter coincide with the unstable poles of the disturbance dynamics to perform disturbance rejection. Then, for the designed closed-loop system to have asymptotic stability, a new robust stability condition is proposed. It is shown that, using the proposed stability condition, the resulting controller can suppress the persistent disturbance and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design approach.

Keywords

Frequency-shaping optimal controlActive vibration controlFlexible mechanical systemsRobust disturbance rejectionPersistent excitationTime-varying parameter perturbations
Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 4 , December 2002 , pp. 163 - 171
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Balas, M. J., “Active Control of Flexible Systems,” Journal of Optimization Theory and Applications, 25(3), pp. 415–436 (1978).CrossRefGoogle Scholar
2Balas, M. J., “Feedback Control of Flexible Systems,” IEEE Transactions Automatic Control, 23(4), pp. 673–679 (1978).CrossRefGoogle Scholar
3Balas, M. J., “Toward a More Practical Control Theory for Distributed Parameter Systems,” Control and Dynamic Systems 18, Academic Press, New York, pp. 361–421 (1982).Google Scholar
4Balas, M. J., Quan, R., Davidson, R. and Das, B., “Low-Order Control of Large Aerospace Structures using Residual Mode Filters,” Recent Advanced in Control of Nonlinear and Distributed Parameter Systems, Robust Control and Aerospace Applications, American Society of Mechanical Engineers, New York, pp. 157–165 (1988).Google Scholar
5Burrows, C. R., Keogh, P. S. and Tasaltin, R., “Closed-Loop Vibration Control of Flexible Rotors — An Experimental Study,” Proceedings of the Institution of Mech. Engineers, Part C: Mechanical Engineering Science, 207(1), pp. 1–17 (1993).Google Scholar
6Chou, J. H., “Robust Stability Bounds on Structured Time-Varying Independent Perturbations for Linear State-Space Models,” JSME International Journal, Series C, 37(4), pp. 733–738 (1994).Google Scholar
7Khot, N. S. and Heise, S. A., “Consideration of Plant Uncertainties in the Optimum Structural-Control Design,” AIAA Journal, 32(3), pp. 610–615 (1994).CrossRefGoogle Scholar
8Lin, C. L., Hsiao, F. B. and Chen, B. S., “Stabilization of Large Structural Systems under Mode Truncation, Parameter Perturbations and Actuator Saturations,” International Journal of Systems Science, 21(8), pp. 1423–1440 (1990).CrossRefGoogle Scholar
9Peres, P. L. D., De Pieri, E. R. and Abou-Kandil, H., “Robust Output Feedback Control Applied to Flexible Structures,” Proceedings of IFAC/ IFORS/IMACS Symposium on Large Scale Systems: Theory and Applications, Beijing, China, pp. 476–479 (1992).Google Scholar
10Seto, K. and Mitsuta, S., “A New Method for Making a Reduced-Order Model of Flexible Structures Using Unobservability and Uncontrollability and Its Application in Vibration Control,” JSME International Journal, Series C, 37(3), pp. 444–449 (1994).Google Scholar
11Gupta, N. K., “Frequency-Shaped Cost Functionals: Extension of Linear Quadratic Gaussian Design Methods,” Journal of Guidance and Control, 3(6), pp. 529–535 (1980).CrossRefGoogle Scholar
12Imai, H., Abe, N. and Kobayakawa, M., “Disturbance Attenuation by a Frequency-Shaped Linear-Quadratic-Regulator Method,” Journal of Guidance and Control, 9(4) (1986).Google Scholar
13Teo, C. L., “Frequency Reshaped Linear Quadratic Regulator with Application to the Controls of a Flexible Arm,” Ph.D. Dissertation, University of California, Berkeley (1988).Google Scholar
14Chen, C. T., “Introduction to Linear System Theory,” New York (1984).Google Scholar
15Chen, S. H., Chou, J. H. and Zheng, L. A., “Robust-Kalma-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems,” The Chinese Journal of Mechanics, 16(3), pp. 349–359 (2000).Google Scholar
16Meirovitch, L., “Dynamic and Control of Structures,” John Wiley & Sons (1990).Google Scholar
17Juang, J. N. and Balas, M. J., “Dynamics and Control of Large Spinning Spacecraft,” Journal of Astronautical Science, Vol. 28, No. 1, pp. 31–48 (1980).Google Scholar
18Maciejowski, J. M., “Multivariable Feedback Design,” Addison-Wesley (1993).Google Scholar
19Weinmann, A., “Uncertain Models and Robust Control,” Springer-Verlag, New York (1991).CrossRefGoogle Scholar
20Desoer, C. A. and Vidyasagar, M., “Feedback Systems: Input-Output Properties,” Academic Press, New York (1975).Google Scholar
21Fox, R. L., “Optimization Method for Engineering Design,” Addison-Wesley, New York (1971).Google Scholar
22Inman, D. J., “Vibration with Control, Measurement and Stability,” Prentice-Hall, Englewood Cliffs, New Jersey (1989).Google Scholar
23Nonami, K., Wang, J. W., Sampei M. and Mita, T., “Active Vibration Control of a Flexible Rotor using H-infinity Control Theory,” JSME International Journal, Series C, 35(3), pp. 393–399 (1992).Google Scholar