回差矩阵奇异值方法改进和MIMO系统稳定性分析

doi:10.12305/j.issn.1001-506X.2024.11.29

摘要/Abstract

摘要：

高速防空导弹大攻角飞行时, 耦合现象严重, 弹体的高动态响应特征进一步加剧通道耦合, 因此研究通道耦合下的系统稳定性至关重要。本文提出一种双通道控制模式下, 单通道断开、耦合通道视为内回路的传递函数矩阵, 并引入回差阵奇异值法计算系统稳定裕度。通过仿真将传统奇异值法和基于传递函数矩阵的奇异值改进法计算出的稳定裕度、单通道稳定裕度、双通道断开的稳定裕度和基于通道耦合下的稳定裕度, 结合系统的时域响应进行对比分析。结果表明, 改进回差阵奇异值法计算结果更精确, 通道耦合下的开环传递函数对系统稳定性描述更合理。

关键词: 防空导弹, 稳定裕度, 回差阵最小奇异值, 开环传递函数

Abstract:

The coupling phenomenon is serious when the high speed air defense missile flies at high angle of attack, and the high dynamic response characteristics of the missile body further aggravate the channel coupling, so it is very important to study the system stability under the channel coupling. In this paper, a transfer function matrix is proposed in the two-channel control mode, in which the single channel disconnected and coupled channels are regarded as internal loop, and the return difference matrix singular value method is introduced to calculate the stability margin. The stability margin calculated by the traditional singular value method and the improved singular value method based on the transfer function matrix, the stability margin of single channel, the stability margin of double channel disconnection and the stability margin based on channel coupling are compared and analyzed by combining the time-domain response of the system. The results show that the improved residual matrix singular value method can obtain more accurate results, and the open-loop transfer function under channel coupling is more reasonable to describe the stability of the system.

Key words: anti-aircraft missile, stability margin, minimum singular value of return difference matrix, open-loop transfer function

中图分类号:

V448.2

闫帅豪, 钱瑞, 魏明英, 郑勇斌. 回差矩阵奇异值方法改进和MIMO系统稳定性分析[J]. 系统工程与电子技术, 2024, 46(11): 3874-3882.

Shuaihao YAN, Rui QIAN, Mingying WEI, Yongbin ZHENG. Improvement of return difference matrix singular value method and stability analysis of MIMO system[J]. Systems Engineering and Electronics, 2024, 46(11): 3874-3882.

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状态	输入
状态	δ_y(s)	δ_x(s)
β(s)	$ G_{11}(s)=\frac{\beta(s)}{\delta_y(s)} $	$ G_{12}(s)=\frac{\beta(s)}{\delta_x(s)}$
γ_v(s)	$ G_{21}(s)=\frac{\gamma_v(s)}{\delta_y(s)}$	$ G_{22}(s)=\frac{\gamma_v(s)}{\delta_x(s)}$
w_x(s)	$ G_{31}(s)=\frac{w_x(s)}{\delta_y(s)}$	$ G_{32}(s)=\frac{w_x(s)}{\delta_x(s)}$
w_y(s)	$ G_{41}(s)=\frac{w_y(s)}{\delta_y(s)} $	$ G_{42}(s)=\frac{w_y(s)}{\delta_x(s)}$

参数	原始回差阵稳定裕度	新回差阵稳定裕度
频率点/(rad·s^－1)	7.33	6.84
幅值裕度/dB	3.45	7.41
相位裕度/(°)	18.85	33.35

通道	有无耦合	频率点	幅值裕度/dB	相位裕度/(°)
偏航通道 (古典断开法)	无耦合	w_g=99.2 w_c=14.6	16.3	68.1
偏航通道 (古典断开法)	有耦合	w_g=109 w_c=7.3	17.1	42.8
滚转通道 (古典断开法)	无耦合	w_g=101 w_c=37.9	9.12	67.2
滚转通道 (古典断开法)	有耦合	w_gL=5.84 w_gH=100 w_c=14.4	L: 7.12 H: 8.77	67.4
偏航通道 GY	有耦合	w_gL=19 w_gH=74.8 w_c=21.2	L=－1.9 H=16.1	2.68
滚转通道 GX	有耦合	w_g=98.7 w_c=23.9	13.2	65.4

通道	有无耦合	频率点	幅值裕度/dB	相位裕度/(°)
偏航通道 (古典断开法)	无耦合	w_g=99.2 w_c=14.5	16.3	68.1
偏航通道 (古典断开法)	有耦合	w_gL=3.01 w_gH=115 w_c=5.38	L=4.71 H=17.6	-13
滚转通道 (古典断开法)	无耦合	w_g=101 w_c=67.2	9.12	67.2
滚转通道 (古典断开法)	有耦合	w_gL=5.25 w_gH=101 w_c=3.51	L=1.38 H=9.12	-23.1
偏航通道 GY	有耦合	w_g=5.39 w_c=24.3	45.7	－18.3
滚转通道 GX	有耦合	w_g=98.7 w_c=23.9	13.2	65.4

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