This paper explores the vibration control of Rayleigh oscillator (a self-excited system), by using positive position feedback method. Both linear and nonlinear stability analyses are performed. The stability regions and optimal system parameters are obtained by performing linear stability analysis, and nonlinear analysis is performed using describing function method to get the amplitude and frequency of the system. The effect of time-delay on system performance is also studied in this paper. It is observed that the existence of time-delay can be unfavourable; however, the situation can be improved by increasing the loop gain. However, it is impossible to design a system without time-delay present in the feedback circuit. Therefore, to nullify the effect of uncertain time-delay, authors have intentionally introduced a preselected time-delay in the feedback circuit and re-optimized to stabilize the static equilibrium of the delayed system. Numerical simulations performed in MATLAB SIMULINK confirm the results of the theoretical analysis obtained.

本文采用正位置反馈方法研究了瑞利振荡器（自激系统）的振动控制。进行线性和非线性稳定性分析。通过进行线性稳定性分析获得稳定性区域和最优系统参数，并使用描述函数方法进行非线性分析以获得系统的振幅和频率。本文还研究了时延对系统性能的影响。据观察，延时的存在可能是不利的。但是，可以通过增加环路增益来改善这种情况。但是，不可能设计出在反馈电路中不存在时间延迟的系统。因此，要消除不确定时间延迟的影响，作者有意在反馈电路中引入了预选的延时，并对其进行了重新优化以稳定延时系统的静态平衡。在MATLAB SIMULINK中进行的数值仿真证实了所获得的理论分析结果。