What is a notch filter? Vibration suppression control by notch filter.

・In Japanese
premise knowledge
・Differential equation of motor and rotating body
・Transfer function
・How to draw a Bode plot

■What is a notch filter?

A notch filter is a filter that removes frequency components in a specific band, or a band stop filter. The transfer function is below. W_a is the frequency of the band to be removed, and ζ is the bandwidth of the frequency to be removed. When ζ is small, the width becomes small.

■Bode Plot of Notch Filter

The parameters are


The result drawn with Scilab is as follows. See how to draw a Bode plot in Scilab here.
==============================
s=poly(0,'s');
p=syslin('c',(s^2+141.4^2)/(s^2+2*141.4*s+141.4^2));
bode(p,1,1000);
==============================

■Application example of notch filter

Here, I explained that vibration occurs when a given force is applied to a low-rigidity rotating body. A notch filter is used to remove this vibration.



The transfer function and Bode plot for this system are shown below.



The parameters are below.
・J_m=0.01 , J_L=0.01 , K=100



＜Combining Notch Filters and Systems＞
When combining the above system with a notch filter, it becomes possible to eliminate the resonance of the system with the notch filter as follows.



When designed in Scilab, it is as follows.

■Notch filter simulation results

As below. The black line is the result with the notch filter, and the green line is the result without the filter. Vibration is suppressed. However, the phase is slightly delayed.

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