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List of the table of contents of this article:

• 1,Binance download iOS Why is the zero pole of the full-pass system related to virtual axis symmetry?
• 2, How to understand the zero pole of the automatic control system?
• 3, 4, z domain all-pass system zero pole distribution characteristics
• 5, What is the zero pole in the control system? Physical meaning?
• 6, How to find the zero pole of the system

Why is the zero pole of the full-pass system related to virtual axis symmetry?

1. If all the zeros and poles of the system are in the left half-plane, then this is the minimum phase system. If the poles and zeros of the system are related to virtual axis symmetry, then this is a full-way system. The use of complex numbers in signal analysis and other fields can conveniently represent periodic signals.

2. If all the zeros and poles of the system are in the left half-plane, then this is the minimum phase system. If the poles and zeros of the system are symmetrical about the virtual axis, then this is a full-way system.

3. Zero and poles appear in pairs. According to the information on the official website of China Mathematics Network, the distribution of zero poles in the Z-domain omni-pass system is characterized by zero points and poles that usually appear in pairs. Because the transfer function of the whole system is the ratio of the numerator polynomial to the denominator polynomial, if the denominator polynomial has a zero point, then the transfer function will also have only one zero point.

4. If all the zeros and poles of the system are in the left half-plane, then this is the minimum phase system. If the poles and zeros of the system are related to virtual axis symmetry, then this is a full-way system. Quantum mechanics: In quantum mechanics, complex numbers are very important because their theory is based on the infinite-dimensional Hilbert space in the complex domain.

5. The root of the stabilized system is in the left half-plane. The closer to the virtual axis, the slower the exponential attenuation is, but it may be close to the equal amplitude oscillation, which is difficult to stabilize.The farther away from the virtual axis, the faster the decay. If it is too far away, it will soon decay, which can be ignored. The virtual part of the pole corresponds to the sinusoidal oscillation. The larger the virtual part, the higher the frequency of the oscillation, that is, the more intense the oscillation.

6. If it is located in the right half-plane, the causal system is unstable; if it is located in the left half-plane, the causal system is stable; if it is located on the virtual axis, the system is critically stable. If all the zeros and poles of the system are in the left half-plane, then this is a minimum phase system.

How to understand the zero pole of the automatic control system?

Zero point--change the proportional relationship of each modal in the output. Polarity--Determining the motion mode of the system; determining the stability of the system.

A transfer function has three forms: 1. Only molecules, molecular polynomials = 0, and the solution obtained is zero. There is only a denominator, and another denominator polynomial = 0, and the solution obtained is the pole. There are molecules and denominators, so the solution of the molecule is the zero point, and the solution of the molecule is the pole.

Hello, the physical significance of zero poles is as follows. Reference 1 The main function of zero pole in physics is to analyze the frequency characteristics of the circuit and the stability of the system.In addition, relevant parameters such as the time domain response of the system can also be derived.

The pole is the root of the characteristic equation. The real part corresponds to the power of e, and the virtual part corresponds to the sine. The root of the stable system is in the left half-plane. The closer it is to the virtual axis, the slower the exponential decay, but it may be close to the equal amplitude oscillation, which is difficult to stabilize. The farther away from the virtual axis, the faster the decay. If it is too far away, it will soon decay, which can be ignored.

Can the zero pole of the system function be approximately

can be approximately, the reason is that infinity is not equal to 0 in the process of approaching the limit point of independent variables, so the denominator is about a common factor that is not 0, the value Unchanged. Concept: The function limit can be divided, and the use of ε-δ to define more is found in the proof of known limit values.

The zero-pole points of linear time-invariant systems are not equal in most cases. For example, H (s)=1/(s^2+3s+2) has no zero point, but two poles.

When finding the breakpoint of a function, the numerator and denominator cannot be divided. First of all, let's see what value the function x takes is meaningless. Obviously, the function is meaningless when x=±1.

As long as X is not equal to 0, it can be divided. Lim (2x/3x) = 2/3 is the same in three cases.

Does the questioner want to ask "Can the numerator and denominator of the breakpoint be approximately divided"? No. According to the mathematical formula of the query, the numerator and denominator of the breakpoint cannot be divided.

In the distribution map of zero poles: the zero point is represented by a circle, and the pole is represented by a fork. SystemThe poles of the left half-plane increase the stability of the system and make the adjustment time longer. The closer to the virtual axis, the greater the impact on the system. The zero point of the system can make the stability worse and shorten the adjustment time.

z domain omni-pass system zero pole distribution characteristics

zero points and poles appear in pairs. According to the information on the official website of China Mathematics Network, the distribution of zero poles in the Z-domain omni-pass system is characterized by zero points and poles that usually appear in pairs. Because the transfer function of the whole system is the ratio of the numerator polynomial to the denominator polynomial, if the denominator polynomial has a zero point, then the transfer function will also have only one zero point.

The zero pole is circled into a mirror symmetry in units. The zero pole, also known as the initial pole or the main pole, is an analysis.The main function of the physics term in the circuit is to analyze the frequency characteristics of the circuit and the stability of the system. In addition, relevant parameters such as the time domain response of the system can also be derived.

The amplitude of all frequency components does not change after a signal enters the full-pass system. The phase may change after a signal enters the full-pass system. The coefficients of the denominator and the numerator are in reverse order. All zero-pole pairs are conjugate on the Z plane.

For a full-pass network, when lossless is, for any frequency, the distance between each pair of zero poles and the jW axis is equal, that is, for virtual axis symmetry, the ratio is 1, so the transmission loss is 0. When w changes, the product of the mode from the pole to the jw point is equal to the product of the mode from the zero point to the jw point.

Does the zero pole in the control system have any physical significance

Zero point--change the proportional relationship of each modal in the output. Polarity--Determining the motion mode of the system; determining the stability of the system.

The pole is to make the denominator of the transfer function equal to zero, because the denominator is equal to zero (also infinitely close to zero), the expression of the transfer function is the largest, which is the so-called pole. Overview of Automatic Control Theory Automatic Control Theory is a theory about the composition, analysis and design of automatic control system.

The reason why the concept of zero pole point is introduced is to analyze the dynamic and steady-state performance of the system more intuitively. Because the above formula has four poles, it can be decomposed into the form of adding four true fractals, and then fourThe time-domain expression of the system is obtained by the inverse transformation of the true varicate, which can intuitively analyze the performance of the system.

The reason is to add an early dynamic correction signal in the dynamic process. Because the signal is in negative feedback, it will reduce the increase of the signal, which is equivalent to increasing damping and improving stability. In addition, the system increases the zero point and increases the phase angle margin, which improves the dynamic performance.

Zero pole, also known as the initial pole or main pole, is a physics term in the analysis circuit. Its main function is to analyze the frequency characteristics of the circuit and the stability of the system. In addition, relevant parameters such as the time domain response of the system can also be derived.

How to find the zero pole of the system

1. In the distribution diagram of the zero pole: the zero point is represented by a circle, and the pole is represented by a fork.The poles of the left half-plane of the system increase the stability of the system and make the adjustment time longer. The closer to the virtual axis, the greater the impact on the system. The zero point of the system can make the stability worse and shorten the adjustment time.

2. Zero pole point method of z transformation: experiment II Z transformation, zero pole point distribution and frequency analysis of discrete system, zero pole point does not contain constant proportional terms, 3+3x and 1+x are the same, so z, p, k are needed.

3. The numerator can be written as 3 (s-1), so s=1 is the zero point. The denominator can be written as (s+1+i) (s+1-i), so -(1+i) and -(1-i) are the two poles of the system. The zero-pole diagram only needs to mark these three points in the complex coordinate system. It's.