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Robust Stabilization of Flexible Mechanical Systems Under Noise Uncertainties and Time-Varying Parameter Perturbations

Department of Mechanical Engineering, National Yunlin University of Science and Technology, Touliu, Yunlin 640, Taiwan

Shinn-Horng Chen

Department of Mechanical Engineering, National Kaohsiung Institute of Technology, Kaohsiung 807, Taiwan

Chien-Hsiang Chao

Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

This article presents a new time domain approach to treat the active stabilization (active vibration control) problem of flexible mechanical systems under (1) mode truncation, (2) nonlinear/linear time- varying parameter perturbations, (3) noise (input noise and measurement noise), and (4) noise uncertainties. In the proposed approach, the residual model is viewed as an additive perturbation to the controlled dynamics. A new robust stability condition is derived for the flexible mechanical system that is controlled by a linear-quadratic-Gaussian (LQG)-based controller and subject to mode truncation, noise uncertainties, and nonlinear/linear time-varying parameter perturbations. The proposed new condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effect, and additive time-varying parameter perturbations. Finally, two examples are given to confirm the presented approach.

Key Words: Flexible mechanical systems • robust stabilization • noise uncertainties • parameter perturbations

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