Champions League

List of the table of contents of this article:

• 1,Champions League 2, Why the smaller the damping ratio of the second-order system, the smaller the rise time
• 3, Performance index of monotonous response curve
• 4, The rising time of the second-order damping system is
5, The influence of damping ratio on the system porter diagram in a typical second-order system

Why the smaller the damping ratio of the second-order system, the smaller the rise time

1. Second-order system damping The smaller the ζ, the smaller the rising time tr; the larger the ζ, the greater the tr. The larger the natural frequency ωn, the smaller the tr, and vice versa, the greater the tr. The natural frequency has a angular velocity framework, and the damping ratio is an unmeasured parameter.

2. The damping ratio determines the oscillation performance (stability) of the second-order system. Increasing the damping ratio can weaken the oscillation performance of the system (enhancing the stability of the system), that is, reduce the over-modulation, reduce the number of shocks, but increase the rise time and peak time. For the molecular constant of the second-order system, it determines the size of the output value when the system is stable.

3. Mutual relationship. It can be seen from the dynamic performance index that the smaller the damping ratio, the smaller the rise time, the smaller the peak time, the greater the overmodulation, the greater the adjustment time, the greater the damping ratio, the greater the rise time, the greater the peak time, the smaller the overmodulation, the smaller the adjustment time, and the relationship between the peak time and the damping ratio is mutual.

4. Stability: The damping ratio also affects the stability of the system. For a second-order system, when the damping ratio is less than 1, the system is stable; when the damping ratio is greater than 1, the system is stable; but when the damping ratio is equal to 1, the system is in a critical stable state, and stability problems caused by the boundary situation may occur.

5. The maximum overmodulation in the dynamic performance index of the second-order system is only related to the damping ratio. It can be seen that the damping ratioThe frequency of the damping natural oscillation angle of the system is the main dynamic time domain characteristic parameter of the second-order measurement system.

Performance index of monotonous response curve

Reproducibility: refers to the fact that when a parameter is repeatedly measured with the same instrument under the condition that the measurement conditions remain unchanged, the difference between each measured value and the average value relative to the large scale range Percentage. This is an important indicator of the stability of instruments and meters. Generally, it needs to be checked during commissioning and daily verification.

At this time, the performance indicators of the transient response are: maximum overtuning σp - the maximum value of the response curve deviation from the steady-state value, which is often expressed as a percentage, that is, the maximum percentage over-tuning and the maximum over-tuning indicate the relative stability of the system.

Security: Security refers to the security of the test system that can protect user data.For the test system, security is a very important performance indicator, which is related to whether the test system can protect user data from leakage or attack.

Super modulation is the response process curve of the linear control system under the step signal input, that is, an index value of the step response curve to analyze the dynamic performance. Over-tuning is also called maximum deviation (maximum deviation) or over-dump. Deviation refers to the difference between the adjusted parameter and the given value.

The rising time of the second-order under-damping system is

the time it reaches the stable value for the first time. According to the query Baidu Education, the rising time of the second-order under-damping system is the time when the leap response curve of the system reaches a stable value for the first time.In automatic control, the second-order system with under-damping refers to the second-order system with a damping ratio greater than 0 and less than 1.

The smaller the damping ratio of the second-order system, the smaller the rise time tr; the larger the ζ, the greater the tr. The larger the natural frequency ωn, the smaller the tr, and vice versa, the greater the tr. The natural frequency has a angular velocity framework, and the damping ratio is an unmeasured parameter.

T1. The adjustment time of the second-order damping system is 3T1. When the unit step response of the second-order system lacking damping, the characteristic root of the characteristic equation of the closed-loop system is a pair of conjugated complex roots. Among the output, the damping oscillation angle frequency and the damping angle.

The influence of damping ratio on the system port diagram in a typical second-order system

1. Therefore, the change in the damping ratio will affect the oscillation frequency, amplitude and duration of the system.Stability: The damping ratio also affects the stability of the system.

2. The smaller the damping ratio of the second-order system, the smaller the rise time tr; the larger the ζ, the greater the tr. The larger the natural frequency ωn, the smaller the tr, and vice versa, the greater the tr. The natural frequency has a angular velocity framework, and the damping ratio is an unmeasured parameter.

3. When the damping ratio is less than 1, the unit step response curve of the system will oscillate.

4. The damping ratio determines the oscillation performance (stability) of the second-order system. Increasing the damping ratio can weaken the oscillation performance of the system (enhancing the stability of the system), that is, reduce the overmodulation, reduce the number of shocks, but increase the rise time and peak time. For the molecular constant of the second-order system, it determines the size of the output value when the system is stable.

5. ζ is the damping ratio.In general, with the continuous increase of ζ, the transient response graphic vibration amplitude of its system decreases and gradually tends to stabilize. When ζ=0, the system is in a non-damping state, and the transient response of the system is a periodic function of constant amplitude.