Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T09:10:55.328Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems

Published online by Cambridge University Press:  05 May 2011

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

Abstract

This paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise),and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.

Keywords

Flexible mechanical systemsActive vibration controlRobust stabilityFrequency-shaping optimal feedback controlTime-varying parameter perturbations
Type
Articles
Information
Journal of Mechanics , Volume 16 , Issue 3 , September 2000 , pp. 145 - 155
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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
5Lin, 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).Google Scholar
6Nonami, 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
7Peres, P. L. D., De Pieri, E. R. and Abou-Kandil, H., “Robust Output Feedback Control Applied to Flexible Structures,” Proc. IFAC/IFORS/IMACS Symposium on Large Scale Systems: Theory and Applications, Beijing, China, pp. 476–479 (1992).Google Scholar
8Burrows, C. R., Keogh, P. S. and Tasaltin, R., “Closed-Loop Vibration Control of Flexible Rotors — an Experimental Study,” Proc. of the Institution of Mech. Engineers, Part C: Mechanical Engineering Science, 207(1), pp. 1–17 (1993).Google Scholar
9Khot, N. S. and Heise, S. A., “Consideration of Plant Uncertainties in the Optimum Structural-Control Design,” AIAA Journal, 32(3), pp. 610–615 (1994).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
11Seto, K., Toba, Y. and Matsumoto, Y., “Reduced Order Modeling and Vibration Control Methods for Flexible Structures Arranged Parallel,” Proc. American Control Conference, Seattle, Washington, pp. 2344–2348 (1995).Google Scholar
12Curtain, R. F. and Zwart, H., An introduction to Infinite-Dimensional Linear System Theory, Spring-Verlag, Berin (1995).Google Scholar
13Khot, N. S. and Oz, H., “Structural-Control Optimization with H-2 and H-Infinity Norm Bounds,” Optimal Control Applications and Methods, 18, pp. 297–311 (1997).Google Scholar
14Chou, J. H., Chen, S. H. and Chao, C. H., “Robust Stabilization of Flexible Mechanical Systems Under Noise Uncertainties and Time-Varying Parameter Perturbations,” Journal of Vibration and Control, 4(2), pp. 167–185 (1998).Google Scholar
15Teo, C. L. and Tomizuka, M., “Frequency-Shaped Cost Functionals: Output or Input Weighting,” Proc. of the IEEE 28th Conference on Decision and Control, Tampa, Florida, pp. 2389–2390 (1989).Google Scholar
16Borowiec, J. and Tzes, A., “Frequency-Shaped Implicit Force Control Flexible Link Manipulators,” Proc. of the 1995 IEEE International Conference on Robotics and Automation, Nagoya, Japan, pp. 913–918 (1995).CrossRefGoogle Scholar
17Kirk, D. E., Optimal Control Theory, Prentice-Hall, Englewood Cliffs, New Jersey (1970).Google Scholar
18Gupta, N. K., “Frequency-Shaped Cost Functionals: Extension of Linear-Quadratic-Gaussian Design Methods,” J. of Guidance and Control, 3(6), pp. 529–535 (1980).Google Scholar
19Weinmann, A., Uncertain Models and Robust Control, Springer-Verlag, New York (1991).Google Scholar
20Chou, J. H., “Robust Stability Bounds on Structured Time-Varying Independent Perturbations for Linar State-Space Models,” JSME International Journal, Series C, 37(4), pp. 733–738 (1994).Google Scholar
21Chou, J. H. and Horng, I. R., “On Sufficient Conditions for the Stability of Interval Matrices,” Proc. of the 4th National Conference of the Chinese Society of Mechanical Engineers, Taiwan, pp. 1377–1381 (1987).Google Scholar
22Fox, R. L., Optimization Method for Engineering Design, Addison-Wesley, New York (1971).Google Scholar
23Anderson, B. D. O., Moore, J. B. and Mingori, D. L., “Relation Between Frequency-Dependent Control and State Weighting in LQG Problems,” Optimal Control Applications and Methods, 8(2), pp. 109–127 (1987).CrossRefGoogle Scholar
24Inman, D. J., Vibration with Control, Measurement and Stability, Prentice-Hall, Englewood Cliffs, New Jersey (1989).Google Scholar