Design of Vibration Controllers for Flexible Beams Using the Mechatronic Design Quotient (MDQ) Approach

Abstract

When using linear dampers for the suppression of vibration in flexible structures, their mounting locations and the damping coefficients have to be chosen properly. In this article, an approach to the optimal design of linear dampers for vibration control in flexible beams based on the mechatronic design quotient (MDQ) is presented. This approach strives to make the optimal concurrent design of the dampers come as close as possible to the performance of an optimal sequential design of uncoupled subsystems. The MDQ approach provides a practical way to evaluate the performance of multi-criteria design. It also provides an insight into the performance degradation of various subsystems caused by dynamic coupling effects in the overall system. In the approach developed here, a cost function, based on the modal settling times, is first established from the design objective. Next, the optimal performance indices from the sequential and concurrent designs are obtained by selecting the coefficients and locations of the vibration dampers. These performance indices are used to determine the design corresponding to the highest MDQ value, which gives the overall optimal design. For performance evaluation, optimal design of active vibration controllers is carried out, using the linear quadratic regulator (LQR), and its MDQ value is established. The results from two case studies show that optimal linear dampers designed using the MDQ approach can achieve the performance of an optimal active controller. This approach can also provide an insight into the performance degradation in each subsystem (or sub-problem) due to the dynamic coupling effects in the overall system.

Keywords

Mechatronic design vibration control flexible beams concurrent design

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References

Ahmad, S. , Lew, J. S. , and Keel, L. H. , 2000, “Robust control of flexible structures against structural damage,” IEEE Transactions on Control Systems Technology 8(1), 170-182 .

Byun, J.-H. and Elsayed, E. A. , 1996, “A producibility index with process capability and manufacturing cost,” in Proceedings of the 5th Industrial Engineering Research Conference, Minneapolis, Minnesota, pp. 381-386 .

Choi, S. B. and Sohn, J. W. , 2006, “Chattering alleviation in vibration control of smart beam structures using piezofilm actuators: Experimental verification,” Journal of Sound and Vibration 294(3), 640-649

Chou, J. , Horng, I. R. , and Liao, W. H. , 1998, “Robust observer-based OMF vibration control of flexible linkage mechanisms using piezoelectric films,” International Journal of Mechanical Sciences 40(8), 749-759 .

De Silva, C. W. , 2003, “Sensing and information acquisition for intelligent mechatronic systems,” in Proceedings of the Symposium on Information Transition, Chinese Academy of Science, Hefei, China, pp. 9-18 .

De Silva, C. W. , 2006, Vibration Fundamentals and Practice,2nd Edition, CRC Press, Boca Raton, FL .

Ehmann, C. and Nordmann, R. , 2003, “Comparison of control strategies for active vibration control of flexible structures,” in Proceedings of the 6th Conference on Active Noise and Vibration Control Methods, May, Krakòw, Poland.

Gasparetto, A. , 2001, “Accurate modeling of a flexible-link planar mechanism by means of a linearized model in the state-space form for design of a vibration controller,” Journal of Sound and vibration 240(2), 241-262 .

Petersen, I. R. and Pota, H. R. , 2003, “Minimax LQG optimal control of a flexible beam,” IFAC Journal of Control Engineering Practice 11(11), 1273-1287

10.

Indri, M. and Tornambe, A. , 1994, “Robust trajectory tracking for flexible piezoelectric structures,” IEE Proceedings on Control Theory and Applications 141(5), 289-294 .

11.

Jung, W. J. , Jeong, W. B. , Hong, S. R. , and Choi, S. B. , 2004, “Vibration control of a flexible beam structure using squeeze-mode ER mount,” Journal of Sound and Vibration 273(1-2), 185-199

12.

Kar, I. , Miyakura, T. , and Seto, K. , 2000, “Bending and torsional vibration control of a flexible plate structure using H∞-based robust control law,” IEEE Transactions on Control Systems Technology 8(3), 545-553 .

13.

Manning, W. J. , Plummer, A. R. , and Levesley, M. C. , 2000, “Vibration control of a flexible beam with integrated actuators and sensors,” Smart Materials and Structures 9, 932-939 .

14.

Moulianitis, V. C. and Aspragathos, N. A. , 2002, “Integration of complexity in a mechatronics index,” in Proceedings of the 8th Mechatronics Forum International Conference, Netherlands, 1494-1502 .

15.

Ogata, K. , 2002, Modern Control Engineering, Prentice Hall, Englewood Cliffs, NJ ,

16.

Somaraju, R. , 2003, “Modelling and control of a single flexible beam,” Project Reports, University of Auckland .

17.

Ullman, D. G. , 1992, The Mechanical Design Process, McGraw-Hill, New York .

18.

Vaes, D. , Swevers, J. , and Sas, P. , 2005, “Experimental validation of different MIMO-feedback controller design methods,” Control Engineering Practice 13, 1439-1451 .

19.

Wani, M. F. and Gandhi, O. P. , 1999, “Development of maintainability index for mechanical systems,” Reliability Engineering & System Safety 65, 259-270 .

20.

Yannoulakis, N. J. , Joshi, S. B. , and Wysk, R. A. , 1994, “Quantitative measures of manufacturability for rotational parts,” Journal of Engineering Industry 116, 189-198 .

21.

Zames, G. , 1966, “On the input-output stability of time-varying nonlinear feedback systems, Part I,” IEEE Transactions on Automatic Control 11, 228-238 .

22.

Zames, G. , 1966, “On the input-output stability of time-varying nonlinear feedback systems, Part II,” IEEE Transactions on Automatic Control 11, 465-476 .

23.

Zhang, X. M. , Shao, C. J. , and Arthur, G. E. , 2002, “Active vibration controller design and comparison study of flexible linkage mechanism systems,” Mechanism and Machine Theory 37, 985-997 .