Abstract
An adaptive modal positive position feedback (AMPPF) method is presented for controlling the vibration and shape of flexible structures. The proposed strategy combines the attractive attributes of the independent modal space control (IMSC) of Meirovitch and the positive position feedback (PPF) of Goh and Caughey. The controller is designed in the uncoupled modal space using only modal position signals to damp the vibration of undamped modes. The parameters of the AMPPF controller are also adjusted in an adaptive manner in order to follow the performance of an optimal reference model. In this way, optimal damping and zero steady state errors can be achieved even in the presence of uncertain or changing structural parameters. The adaptation laws governing the stable variation in the AMPPF controller parameters are derived using the Lyapunov stability theorem. The effectiveness of the AMPPF in controlling the vibration and shape of a variable mass cantilevered beam is demonstrated experimentally. The performance obtained with the AMPPF algorithm is compared with those of other classical control algorithms. The results obtained emphasize the potential of the AMPPF algorithm as an efficient means for controlling flexible structures with uncertainties in real time. © 1997 by John Wiley & Sons, Ltd
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