What is the magnitude of the oscillation of the second order system, and what is the time related to

The system is slow to respond.

Second-order system The control system is based on a mathematical model.

A form when classifying. It is a system that can be expressed as a second-order linear ordinary differential equation by mathematical model. The form of the solution of the second-order system can be determined by the corresponding transfer function.

w(s) to discriminate and divide. The general form of p(s) is the quadratic trinomial algebraic equation of the transformation operator s.

After standardization, it can be recorded as:

The root of the algebraic equation p(s)=0, four possible cases:

1.Two solid roots.

corresponding to two first-order systems in series. If both roots are negative, it is a stable case of aperiodic convergence.

2.When a1=0, a2>0, i.e., a pair of conjugated imaginary roots, will cause an equal-amplitude oscillation with a fixed frequency, which is a manifestation of system instability.

3.When a1<0, a1-4a2<0, that is, the conjugate double root.

In the case of positive and real parts, there is a divergent oscillation in the system, which is also a manifestation of instability.

4.When a1>0, a1-4a2<0, that is, the conjugate complex root has a negative real part, which corresponds to a convergent oscillation, and the numerical ratio of the real part and the imaginary part has a great influence on the output process. Generally in terms of damping coefficient.

to characterize, often taken.

In between, it is desirable. When >, the oscillation is not significant, and the output speed is slower. The output has obvious oscillations and large overshoots, and the attenuation is slow, which is also undesirable in the control system.

To put it simply, resistance is an obstruction, the damping ratio is high, the effect is that the response is slower, and the adjustment time of the response becomes longer, but the advantage is that the smoothness is good, the overshoot becomes smaller, and vice versa.

a. The system responds quickly, B. The system responds slowly, C. The natural frequency without damping, and d. The accuracy of the system is poor.

Hehe, I don't understand this, I'm sorry.

Regarding the frequency characteristics of the second-order oscillation link, the following statement is correct.

a.There is a resonance peak in the logarithmic amplitude frequency curve of the second-order oscillation link when the damping ratio is between (0, muffled masses.

b.The phase angle hysteresis of the second-order oscillation link is up to 180°

c.The logarithmic amplitude frequency characteristic curves of the second-order oscillation link and the second-order differential link are mirror-symmetrically symmetrical with respect to the 0db axis.

d.The second-order oscillating ring is a resonant peak at n.

Correct answer: ABC

Summary. The range of the arctan function is , so this expression is problematic. The correct one should be represented by the sum of multiple arctan functions.

This wrong expression in the book is wrong because it doesn't take into account the range of functions when simplifying. In fact, you don't have to think about this, you just need to write lz correctly, or you can look at this problem directly from the perspective of complex changing trends, don't limit yourself to expressions, so that you won't be wrong. I suggest that lz should not use the method of separating the real part from the imaginary part when doing the frequency domain characteristics, which is cumbersome and prone to errors.

It is best to use the methods of complex multiplication and division, amplitude multiplication and division, and amplitude and angle addition and subtraction, which are simple and not easy to make mistakes.

Hello, I am inquiring for you here, please wait a while, I will reply to you immediately Glad to answer for you, the second-order oscillation link, when W tends to zero, the phase frequency is 0 degrees, and when W is equal to Wn, the phase frequency is negative 90 degrees, can be understood according to the image of Arctan, but why when W tends to infinity, it is -180 degrees, simply use the multiplication of two inertial links to approximate the oscillation link, so it is easy to understand.

The range of the arctan function is , so this expression is problematic. The correct one should be represented by the sum of multiple arctan functions. This wrong expression in the book is wrong because it doesn't take into account the range of functions when simplifying.

In fact, you don't have to think about this, you just need to write lz correctly, or you can look at this problem directly from the perspective of complex changing trends, don't limit yourself to expressions, so that you won't be wrong. I suggest that lz should not use the method of separating the real part from the imaginary part when doing the frequency domain characteristics, which is cumbersome and prone to errors. It is best to use the methods of complex multiplication and division, amplitude multiplication and division, and amplitude and angle addition and subtraction, which are simple and not easy to make mistakes.

I hope the above is helpful to you If you are satisfied with me, please give me a thumbs up

The larger the angular frequency of the second-order system, the better the dynamic performance of the system or coarseness. （）

a.That's right. b.Mistake.

Correct answer to Zaobi case: Correct.