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

Abstract

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

CLC Number:

V448.2

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.

Figures/Tables 17

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References 22

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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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Improvement of return difference matrix singular value method and stability analysis of MIMO system

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