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List of the contents of this article:

• 1, How to find the pole of a system and judge whether the system is stable?
• 2, How to judge the stability of the system by the Krasovsky method?
• 3
   、 How to judge the stability of the system?
• 4, How to judge the stability of the system by amplitude margin and phase angle margin?

How to find the pole of a system and judge whether the system is stable?

The stability of a linear system is the main performance indicator of the system. The methods to judge the stability of a linear system include algebraic method, root trajectory method and Nyquist judgment method.

When the input amplitude of the system is not zero and the input frequency makes the system output infinite (the system is stable and the oscillation occurs), this frequency value is the pole. Frequency is the number of times periodic changes are completed per unit time. It is the quantity that describes the frequency of periodic movement. It is commonly represented by the symbol f or ν, the unit is one second, and the symbol is s-1.

The system function is known. First, find the pole of the system function. According to the position of the pole, the stability of the system can be judged. The problem finally comes down to solving the root of a monadic multiple equation, that is, solving the equation, and the value obtained can also judge its stability.

The key to using judgments is to establish a table. For how to create a table, please refer to the relevant examples or textbooks. To use the judgment to determine the stability of the system, you need to know the closed-loop transfer function of the system or the characteristic equation of the system.

Question 1: Signal and System How to judge whether a signal system is stable? The left half-plane of the pole falling on the S plane is a stable system, falling on the virtual axis is critically stable, and falling on the right half-plane is an unstable system.

If the system function is known, then according to the above method, the pole of the system function can be determined first, and then the stability of the system can be judged according to the position of the pole. Therefore, the problem finally comes down to solving the root of the monadic multiple equation, that is, solving the equation.

How to judge the stability of the system by the Krasovsky method?

The negative matrix can provide better numerical stability. When using the Krasovsky method to solve a system of linear equations, it is necessary to calculate the inverse matrix and determinant values of the matrix. If the matrix is negative, its inverse matrix and determinant values exist and are stable, which helps to improve the accuracy and stability of the numerical solution.

Correct answer: Krasovsky's theorem is a sufficient and necessary condition for judging the asymptotic stability of a steo-stational system.

Beijing 54 coordinate system (BJZ54) Beijing 54 coordinate system is a center-centric earth coordinate system. A point on the earth can be positioned at longitude L5 latitude M54 and earth height H54. It is a coordinate system based on the Krasovsky ellipsoid and generated after local flat difference. Its coordinates can be defined in detail. Refer to the references [Zhu Huatong 1990].

How to judge the stability of the system?

1. The stability of a linear system is the main performance indicator of the system. The methods for judging the stability of a linear system include algebraic method, root trajectory method and Nyquist judgment method.

2. The stability of the amplitude margin and phase angle margin judgment system is aimed at the minimum phaseless system.When the system is stable: the amplitude margin is 1 and the phase angle margin is 0; the larger the amplitude margin and the phase angle margin, the more stable the system is. When the criticality of the system is stable: amplitude margin = 1, phase angle margin = 0. When the system is unstable: amplitude margin 1, phase angle margin 0.

3. The methods for determining the stability of the system are as follows: Nyquist stability judgment and root trajectory method. They judge the stability of the closed-loop system according to the open-loop characteristics of the control system. These methods are not only applicable to single-variable systems, but also for multi-variable systems after popularization. Stability theory: a branch of differential equations.

How to judge the stability of the system by amplitude margin and phase angle margin?

1. If the phase angle margin is greater than zero, the system is stable, and vice versa is unstable.

2. The amplitude margin is GM0 and the phase angle PM margin is 0, but a prerequisite must be met for stability determination using this judgment: the open-loop transfer function of the system must be the minimum phase system.

3. Observing the stability of the system through the Bird diagram requires two parameters: phase margin and amplitude margin. If the phase margin is greater than zero and the amplitude margin is greater than zero at the same time, the system is stable; if one is not satisfied, it is unstable. Generally, the phase margin greater than or equal to 45 degrees in engineering is a system with better dynamic performance.

4. If the amplitude of the system is less than or equal to 1, then the system is stable. In the Bird diagram, the unit amplitude corresponds to MdB=0. In the example: When the phase is -180°, the amplitude is about –18dB, so the system is stable.