进气道动态特性的传递函数多项式近似分析

Rational Polynomial Transfer Function Approximations for Supersonic Inlet Dynamics

进气道动态特性的小偏差封闭传递矩阵模型仅能得到频率特性数据,为了获得多项式形式的传递函数,提出了一种基于MATLAB的计算方法。基于频域辨识获得了结尾激波对放气量扰动的有理多项式传递函数近似模型,此模型的频率特性与原始频率特性吻合较好,比Pade近似方法更简单准确。利用模型降阶方法对高阶多项式函数进行简化,获得了低阶传递函数,低阶模型与高阶模型的时域响应较为一致,为激波位置控制系统设计奠定了基础。分析了激波处相对面积变化率对频域特性的影响,结果表明相对面积变化率越小,激波运动的稳态距离越大。

It is difficult to apply the closed-form matrix model of supersonic inlet to obtain the polynomial transfer function which was useful for control system design.The method was proposed to simplify the problem,which was based on MATLAB frequency domain identification tools for generating rational polynomial transfer functions.The transfer functions for normal shock were obtained by curve fitting in the frequency domain,which was in good agreement with the original frequency response and easier than Pade approximation.Further more,in order to simplify the transfer function,model reduction was introduced to obtain low order model for control system design.The results show that the step response of the low order model agrees well with the high order model.The effects of key parameter on shock dynamics were analyzed.The results reveal that the lower the area variation near the shock,the larger the displacement of the shock.