Quantitative robust linear parameter varying H_∞ vibration control of flexible structures for saving the control energy

Abstract

Quantitative robust linear parameter varying H∞ vibration control of flexible structures for saving the control energy. Abstract In this article, a general and systematical quantitative robust linear parameter varying (LPV) control method is proposed for active vibration control of LPV flexible structures such that a complete set of control objectives can be considered, especially, the reduction of necessarily required control energy. To achieve this goal, phase and gain control policies are employed in LPV H ∞ control designs for suitable selection of weighting functions. The designed parameter-dependent H ∞ controller allows us to explicitly consider the time-varying parameters of the dynamical models for saving the control energy and achieving other control objectives such as the specification of vibration reduction and qualitative robustness properties to both parametric and dynamic uncertainties. Then, various reliable robustness analyses are conducted to quantitatively verify the robustness properties of the closedloop system. The design processes and the effectiveness of the proposed control method are illustrated by active vibration control of a non-collocated piezoelectric cantilever beam excited by an external position-varying forcewhich is the disturbance to be rejected. This plant has typical positiondependent dynamics and is modeled as an LPV system whose time-varying parameter is the actual position of the disturbance. The numerical simulations demonstrate that, compared to the classical H ∞ control and the acceleration feedback control, the proposed control method allows to compute a quantitatively robust parameter (force position) dependent controller whose benefit is to require less control energy and smaller control input, while satisfying the same control objectives in the frequency domain. KeywordsLPV H ∞ control, phase and gain control policies, saving the control energy, parametric and dynamic uncertainties Problem statementSince lightweight components are widely used in practical structures for miniaturization and efficiency, these structures become more flexible and more susceptible to vibrations, which may cause significant noises, harmful

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