利用自振的耦合非线性系统研究

本文提出一种利用自振的双输入一双输出耦合非线性系统的研究方法,导出了耦合非线性系统产生自振的解析条件,确定了耦合程度及系统参数与自振参数之间的关系;还采用了调究方波占空比分析法及振荡线性化分析法研究自振的耦合系统的等效线性化模型。

On Coupled Nonlinear System Using Self-Excited Oscillation

The limit cycle analysis method for SISO (single-input single-output) non-linear system has been well established. When coupled system having nonlinearcharacter was to be designed, it was usually simplified into a single loop byassuming decoupling and by using a linearized model, it was customary to cou-sider that the self-excited oscillation caused by nonlinear character is detri-mental and therefore should be eliminated. However, the present authors areof the opinion that self-excited oscillation can be beneficial when properlyhandled. Up to now, to the best of the authors' knowledge, no paper in theopen literature has dealt with this beneficial effect of self-excited oscillation. This paper's contribution is that the authors propose a method for analy-zing DIDO (double-input double-output) coupled nonlinear system using self-excited oscillation. The mathematical conditions, under which self-excited oscil-lation occurs are derived; the mathematical equation relating the degree of coup-ling to parameters of coupled nonlinear system and parameters of self-excitedoscillation is obtained. It is shown that proper handling of self-excited oscil-lation is effective in improving the accuracy of the system. Our proposed me-thod gives satisfactory results when applied to the analysis and design of aninfrared tracking system. Besides, the authors employ two methods-the duty ratio method and theoscillation linearization method-to study the input-output characteristics of theequivalent linearized model of coupled system having self-excited oscillation.Our study shows that, when such an equivalent system is used in missileguidance, the requirements of proportional navigation can be met.