Excessive vibration in flexible structures is a problem encountered in many different fields, causing fatigue of structural components. Passive techniques, though sometimes limited in their capabilities, have been used in the past to attenuate vibrations. Recently active techniques have been developed to enhance vibration control performance beyond that provided by their passive counterparts. Most often, the focus of active control methods has been to suppress structure displacements. In cases where vibration results in structure failures, displacement suppression may not be the best choice of control approaches (it can, in fact, increase dynamic loads which would be even more harmful to supports) . This paper presents two optimal control methods for attenuating steady state vibrations in flexible structures. One method minimizes shaft displacements while another minimizes dynamic reaction forces. The two methods are applied to a model of a typical flexible structure system and their results are compared. It is found that displacement minimization can increase loads, while load minimization decreases loads.
Lewis, D.E., and Allaire, P.E., 1987, “Rotor to Base Control of Rotation Machinery to Minimize Transmitted Force", Structural Control, H.H.E. Leipholz (Ed.), Matimas Nijhoff Publishers, Dordrecht, The Netherlands, pp. 408-425.
Bong, W. and Marcelo, G. 1992, “Control Synthesis for Flexible Space Structures Excited by Persistent Disturbance", Journal of Guidance, Control, and Dynamics, Vol.15, No.5, pp.73-80.
Stengel, R.F., 1986, Stochastic Optimal Control, John Wiley and Sons, New York, NY.
Burdess, J.S. and Metcalfe, A.V., 1983, “Active Control of Forced Harmonic Vibration in Finite Degree of Freedom Structures with Negligible Natural Damping", Journal of Sound and Vibration, Vol. 91, No.3, pp. 48-59.
Kim, J.H., Clark, W.W., and Marangoni, R. D., 1993, “Feedback Techniques for Minimizing Bearing Loads in Rotating Machinery", Second Conference on Recent Advances in Active Control of Sound and Vibration, Fuller, C.R., Silcox, R.J., and Burdisso, R.A. (Eds.), Blacksburg, VA, pp. 885-896.
Hanseen, O. E. and Bell, K., 1979, “On the Accuracy of Mode Superposition Analysis in Structural Dynamics", Earthquake Engineering and Structural Dynamics, Vol. 7, pp. 405-411.
Sievers, L.A. and von Flotow, A.H., 1989, “Comparison of Two LQG-Based Methods for Disturbance Rejection", Proceedings of the 28 IEEE Conference on Decision and Control, Tampa, FL, pp. 483-485.
Meirovitch, L., 1990, Dynamics and Control Structures, John Wiley & Sons, New York.