关键词: 亚临界Hopf分岔, 超临界Hopf分岔, 非线性控制, 多尺度法

Abstract:

We considered a class of retarded onedegreeoffreedom nonlinear system, namely, the regenerative model of chatter in a lathe machine tool. The time delay influence on the stability of the system solutions was analyzed with the aid of multiple scales. Nonlinear displacement feedback control can be used to suppress the selfsustained oscillation caused by Hopf bifurcation. The results of the theory analysis and numerical simulation show that the designed controller is valid for the cutting chatter system.

Key words: subcritical Hopf bifurcation, supercritical Hopf bifurcation, nonlinear control, method of multiple scales