一类多时间尺度机电耦合系统降阶及稳定一致性

Model reduction and stability consistency of a class of multi-time scale electromechenical coupling system

针对一类机电耦合系统,讨论了非线性多时间尺度系统与其相应的简化降阶系统稳定性一致问题,给出了稳定一致性的条件;讨论了多时间尺度系统(原始系统)和降阶系统的稳定域边界问题,分析了非线性多时间尺度系统稳定域边界对摄动参数ε的连续依赖性,给出了稳定边界对ε连续依赖的条件.研究表明不论对系统的平衡点稳定性还是稳定域来说,在可接受的条件下略去快动态是合理的.

For a class of electromechanical coupling system, this paper discusses the stability consistency between the nonlinear multi-time scale model and the relevant reduced order model, and gives the conditions of stability consistence. The continuous dependence of the stability boundary on the perturbation parameter ε for a multi-time scale system is revealed. The necessary condition for this dependence is given. It is concluded that the negligence of the fast dynamics is rational in the analysis of equilibrium stability and stability region .