Stability determination method of absolute value system based on double-sine input description function

A technology for describing functions and determining methods, which is applied in electrical digital data processing, special data processing applications, instruments, etc., to achieve the effects of wide application range, accurate judgment, and strong operability

Pending Publication Date: 2019-07-05
BEIJING INST OF CONTROL ENG
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] The technical problem of the present invention is: to overcome the constraints of the existing technology limited by the second-order system, specific system, etc., to

Method used

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  • Stability determination method of absolute value system based on double-sine input description function
  • Stability determination method of absolute value system based on double-sine input description function
  • Stability determination method of absolute value system based on double-sine input description function

Examples

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Embodiment 1

[0091] The structure of the guidance and control system of a hypersonic vehicle is as follows: figure 2 As shown, based on Lyapunov linearization and linear reduction order simplification, we get image 3 system. where the linear part transfer function is

[0092]

[0093] Each parameter in the above formula is a known model parameter or control parameter; k s is the known nonlinear part parameter;

[0094] The TD form of the fastest-tracking differentiator is

[0095]

[0096] In the above formula, v is the input of TD, η 1 is the output, and p is a known design parameter.

[0097] When A=0.00049896rad, k=0.3824, ω=6.7130rad / s, θ 0 When the value ranges from 0 to 360° (with an interval of 1°), the reciprocal curve of the description function of the nonlinear part and the Nyquist curve of the linear part are drawn respectively in Figure 4 , Figure 5 . when θ 0 = 202°, ​​1 / N A with G s (jω) distance and 1 / N B with G s The sum of the distances of (j2ω) is ...

Embodiment 2

[0099] A low-pass filter is connected in series after the tracking differentiator of Example 1, see Figure 7 . Similar to the process of example 1, traverse A, k, ω, θ in the range of attention 0 , it is found that there is no periodic oscillation in the system, and the actual roll rudder bias response can be seen in Figure 8 .

[0100] Increase the model parameter k s To the original 16 times, when A=0.000013254rad, k=0.1647, ω=11.5712rad / s, θ 0 The value range is 0~360°, the interval is 1°, and the reciprocal curve of the description function of the nonlinear part and the Nyquist curve of the linear part are drawn respectively. Figure 9 , Figure 10 . It can be found that when θ 0 =55°, 1 / N A with G s (jω) distance and 1 / N B with G s The sum of the distances of (j2ω) is 0.01206. It is predicted that the system with increased model parameters has double sinusoidal oscillations, so the stability margin of the original system is 24dB.

[0101] By comparing the a...

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Abstract

The invention discloses a stability determination method of an absolute value system based on a double-sine input description function. The method comprises the following steps: firstly, replacing a derivable nonlinear part of an original system with a Lyapunov linearization result of the derivable nonlinear part; drawing an Nyquist curve of the linear part of the new system; calculating a double-sine input description function of the nonlinear part by adopting a numerical method, drawing a reciprocal curve of the double-sine input description function, analyzing whether the closed-loop systemcan generate periodic oscillation or not according to the intersection condition of the two curves, and amplifying model parameters until the oscillation condition is met if the oscillation cannot begenerated, thereby obtaining the stability margin of the system. According to the method, the limitation of a second-order system, a specific system and the like on the existing method is overcome, and a universal method is provided for researching the stability of an absolute value system.

Description

technical field [0001] The invention relates to a stability analysis method, which is mainly used for the stability research of complex systems containing absolute value functions. Background technique [0002] At present, there is no general stability analysis method for complex systems with absolute value functions. Absolute value nonlinearity widely exists in rudder-controlled moving body models such as aircraft, missiles, and ships, and a large class of nonlinear controllers. When the system stability margin is low, asymmetric oscillations are likely to occur. The existing analysis methods based on phase plane and Lyapunov function are limited by second-order systems and specific systems, and cannot be used for stability analysis of complex systems with absolute value functions. Contents of the invention [0003] The technical problem of the present invention is: to overcome the constraints of the existing technology limited by the second-order system, specific system...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/20Y02E60/00
Inventor 陈上上何英姿龚宇莲黄盘兴
Owner BEIJING INST OF CONTROL ENG
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