Authors: ZaiHua Wang HaiYan Hu
Publish Date: 2010/02/26
Volume: 53, Issue: 2, Pages: 345-352
Abstract
It begins with the study of damping representation of a linear vibration system of single degree of freedom SDOF from the view point of fractional calculus By using the idea of stability switch it shows that the linear term involving the fractionalorder derivative of an order between 0 and 2 always acts as a damping force so that the unique equilibrium is asymptotically stable Further based on the idea of stability switch again the paper proposes a scheme for determining the stable gain region of a linear vibration system under a fractionalorder control It shows that unlike the classical velocity feedback which can adjust the damping force only a fractionalorder feedback can adjust not only the damping force but also the elastic restoring force and in addition a fractionalorder PD α control can either enlarge the stable gain region or narrow the stable gain region For the dynamic systems described by integerorder derivatives the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay in the open left halfplane while for the systems with fractionalorder derivatives the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay within a sector in the complex plane Analysis shows that the proposed method based on the idea of stability switch works effectively in the stability analysis of dynamical systems with fractionalorder derivatives
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