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List of contents of this article:

• 1, < A href='#What is the closed-loop characteristic equation?' title='What is the closed-loop characteristic equation?' > What is the closed-loop characteristic equation?
• 2, closed-loop characteristic equation closed-loop characteristic equation and open-loop characteristic equation
• 3 、Solve a question (automatic control theory)

What is the closed-loop characteristic equation?

1. The closed-loop characteristic equation is 1+G(s) G(s) is the open-loop transfer function, Φ(s) is the closed-loop transfer function, so that the denominator = 0 is the closed-loop characteristic equation.

2. The closed-loop characteristic equation is 1+G(s) G(s) is the open-loop transfer function, Φ(s) is the closed-loop transfer function, so that the denominator = 0 is the closed-loop characteristic equation, and when the unit is fed back, h(s)=1. There are two types of open-loop transfer functions: the first one describes the dynamic characteristics of an open-loop system (a system without feedback).

3. The closed-loop characteristic equation is a polynomial equation whose root determines the stability and dynamic performance of the system. Specifically, the form of the closed-loop characteristic equation is 1+G(s) H(s)=0, where G(s) is the transfer function of the system and H(s) is the transfer function of the controller.

closed-loop characteristic equation closed-loop characteristic equation andThe open-loop characteristic equation

1. The closed-loop characteristic equation is: if the point on the s plane is a closed-loop pole, then the phase composed of zj and pi must satisfy the above two equations, and the modulus equation is related to Kg, while the phase angle equation is not related to Kg.

2. The closed-loop characteristic equation is 1+G(s). G(s) is an open-loop transfer function, Φ(s) is a closed-loop transfer function, and the denominator = 0 is a closed-loop characteristic equation.

3. The closed-loop characteristic equation is 1+G(s) G(s) is an open-loop transfer function, Φ(s) is a closed-loop transfer function, so that the denominator = 0 is a closed-loop characteristic equation. When the unit is fed back, h(s)=1. There are two types of open-loop transfer functions: the first one describes the dynamic characteristics of an open-loop system (a system without feedback).

4. If the open-loop transfer function GH=A/B, then fai=G/(1+GH), and the characteristic equation is 1+GH=0, that is, 1+A/B=0, that is, (A+B)/B=0, that is, A+B=0, that is, the intuitive numerator plus denominator.

Solve a problem (automatic control theory)

Automatic control principle exercise (20 points) Try the structure diagram equivalently simplified to find the transfer function of the system shown in the figure below. Solution: So: II. ( 10 points) The characteristic equation of the known system is to judge the stability of the system. If the closed-loop system is unstable, point out the number of poles in the right half of the s plane.

According to the meaning of the question, the input signal is r(t)=4+6t+3t^2, the open-loop transfer function of the unit feedback system is G(s)=frac{ 8(0.5s+1)}{ s^2(0.1s+1)}. First of all, we need to convert the input signal r(t) into the Laplace transformation form.

The first question should be clear first. Since there is the same root trajectory, the open-loop functions of A and B must be the same, because the root trajectory is completely drawn according to the open-loop function. GHA=GHB=K(s+2)/s^2(s+4), I use GH to express the open loop, so as not to be confused with the latter.

This question involves the time domain method in modern control theory. 1 First, find the state transfer matrix. There are many methods. The following is solved by the Lasian inverse transformation method, which is more convenient: SI-A=[S-1 0;—1 S-1] Annotation: The matrix is represented by Matlab here, and the semicomon is used as a sign of two lines.

a, using the current relationship, the following relational formula can be obtained, ui/R1 =-uo/R2 -C duo/dt, and the Lashi transformation on both sides can obtain the relational formula in the question. B. You can use the superposition principle of the linear circuit to make u1 and u2 zero respectively, find the corresponding uo1 and uo2, and then add them to uo, and then do the Lashi transform.