Investigation of the near-grazing behavior in hard-impact oscillators using model-based TS fuzzy approach

被引：14

作者：

Mehran, Kamyar ^{[1
]}

Zahawi, Bashar ^{[1
]}

Giaouris, Damian ^{[1
]}

机构：

[1] Newcastle Univ, Sch Elect Elect & Comp Engn, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

NONLINEAR DYNAMICS | 2012年 / 69卷 / 03期

关键词：

Takagi-Sugeno fuzzy approach; Non-smooth Lyapunov theory; Linear Matrix Inequality; Impact oscillator; Grazing; BORDER-COLLISION BIFURCATIONS; STABILITY ANALYSIS; SYSTEMS; DESIGN; DYNAMICS;

D O I：

10.1007/s11071-012-0348-8

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

An impact oscillator is a non-smooth dynamical system with discontinuous state jumps whose dynamical behavior illustrates a variety of non-linear phenomena including a grazing bifurcation. This specific phenomenon is difficult to analyze because it coincides with an infinite stretching of the phase space in the neighborhood of the grazing orbit, resulting in the well-known problem of the square-root singularity of the Jacobian of the discrete-time map. A novel Takagi-Sugeno fuzzy model-based approach is presented in this paper to model a hard impacting system as a non-smooth dynamical system including discontinuous jumps. Employing non-smooth Lyapunov theory, the structural stability of the system is analyzed to predict the onset of the destabilizing chaotic behavior. The proposed stability results, formulated as a Linear Matrix Inequality (LMI) problem, demonstrate how the new method can detect the loss of stability just before the grazing bifurcation.

引用

页码：1293 / 1309

页数：17