Feedback control of a vibrating beam by stiffening action
In a recent article, \textit{H. H. E. Leipholz} and \textit{M. Abdel-Rohman} [Ing.-Arch. 56, 55-70 (1986; Zbl 0573.73096)] proposed a new feedback control law by which excessive structural vibrations are counteracted by applying forces to stiffen the structure. The advantage of this type of control mechanism is that single actuators only need to be placed at each end of the beam to provide the required stiffening action. In the present study, such a control is applied to a dynamically loaded beam with the objective of keeping its deflection within given bounds. Moreover, a deadband region of off-control is introduced by requiring the control to remain inactive when the deflection is below a certain limit. This type of on-off control, which tolerates oscillations within certain bounds [\textit{L. Meirovitch}, \textit{H. F. Landigham} and \textit{H. Van Oez}, Acta Astronaut. 4, 985-1010 (1977; Zbl 0373.93028)], has the advantage of not using the actuators continuously. The stability of the control scheme is demonstrated in the Appendix. Numerical results are given relating the feedback control to reduction in dynamic deflection as compared to an uncontrolled beam. The amount of force spent during the control process is also determined and its relation to deflection is investigated.
scientific article; zbMATH DE number 4068406