当前位置：网站首页>A trick to teach you to easily understand Potter's map

A trick to teach you to easily understand Potter's map

2022-07-26 05:28:00 【Uncle wheat】

Click on the above “ Uncle wheat ”, choice “ Roof placement / Official account of star standard ”

Welfare dry goods , First time delivery

Bode Plots Its main function is to express the frequency characteristics of the system , Including amplitude frequency characteristics and phase frequency characteristics . Suppose there is a system for following sine waves , When inputting a sine wave , The output is also a sine wave , But input 、 The output will vary in amplitude and phase , In the time domain, as shown in the figure below .

It can be seen from the above figure that the amplitude gain of the system at a certain frequency is 20lg(1.4/2.0)=-3.1dB, phase shift （ Lag angle ） by -45°（ Negative numbers indicate lag ）. When the input frequency is different , Amplitude gain and phase shift will also change , Obviously, it is difficult to express the output of the system at different frequencies in the time domain , Baud diagram is introduced here , It is used to express the characteristics of the system at different frequencies , That is, the proportion of amplitude change and the degree of phase shift . Define the abscissa of the Bode diagram as frequency , The ordinate is the gain and phase shift and is expressed in logarithmic form （ Logarithm can magnify coordinates ）. We change the frequency of the input signal , And measure the amplitude and phase shift of the output signal at different frequencies , And calculate the coordinate conversion , The following open-loop and closed-loop bode diagrams of an ideal motor can be drawn .

The Bode diagram of the ideal motor in the figure above is divided into two curves, open-loop and closed-loop , Closed loop system means that the output signal is fed back to the input to participate in the control , Different information can be read from the two curves . Through the amplitude frequency curve and phase frequency curve of the open-loop system, the amplitude margin and phase margin of the system can be obtained to judge the stability of the system . It is specified that when a certain frequency signal is input, the amplitude gain is 0dB when , Phase shift angle of output at this frequency +180° Is the phase margin of the open-loop system . The phase margin of the system shown in the figure below is 180°+（-147°）=33°. Specify when a certain frequency signal is input , The output phase shift of the system is -180°（ Output flip ） when , Its output amplitude gain is the gain margin of the system （ Amplitude margin ）, The amplitude margin of the system in the figure below is 0-32.5dB=32.5dB

The amplitude margin of the above system is 32.5dB, The phase margin is 33dB, System stability . In order to ensure the stability of the system under closed-loop control , Generally, the phase margin of the system is greater than 45°. When the amplitude margin of the system is 0, The phase margin is 0 There will be self-excited oscillation , It is an unstable system in control . The following analysis shows that the gain is 0dB, The phase shift is -180° The characteristics of the system . As shown in the figure below PID Control system , When the open-loop gain of the system at a certain frequency is 0dB, The open-loop phase shift is -180°, Feedback is introduced to form a closed-loop control .PID Control input ERR=INPUT-OUTPUT, The open-loop output phase shift of the system is -180°, Because the calculated error value will double , It forms a positive feedback system , The system is unstable .

In tune PID Parameter time , The step response of the system under different parameters is shown in the figure below , It can be divided into underdamped 、 Overdamping 、 Critical damping system .