This paper addresses identification and robust control of vibration of a flexible plate attached to the upper side of an enclosure. The frequency domain subspace methods and minimax-linear quadratic Gaussian (LQG) control are utilized to identify the model and to control the vibration of the flexible plate, respectively. In order to identify the model of the flexible plate, several frequency domain subspace identification algorithms with Instrumental Variable idea are used. Considering the fact that the flexible plate system is stable by nature, all identified unstable models are passed through a stabilized process using an iterative algorithm with different initial values. The first three modes of the plate are selected for control purposes, and the other modes are chosen as uncertainty term. To design the weighting function for the minimax-LQG controller, Chebychev and Yule–Walker filters are utilized to consider the effect of modeling uncertainty. These weights have a great effect on robust stability and performance of the control system. Simulation results are presented to show the effectiveness of the designed controllers for the reference model. Results confirm that some indexes that show the quality of the identified models can be used as suitable measures to predict performance of the designed controller.
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