Question on Damping and signal attenuation.

[1a2s3d4f]

damping ratio second order sqrt(2)

Hi everyone,

I am confuse the different between when a system damping, it reduce the amplitude oscillation. We can specify the system to be critical damp (when the ratio is =1) or over damp (when ratio >1) or under damp (when the ratio is <1).

As for signal attenuation, it also reduce the signal amplitude (the signal attenuation and damping ratio are bout use to reduce the amplitude of a system).

I understand that the damping ratio is defined as signal attenuation factor to it resonant frequency.
I am so confuse the purpose of know both damping ratio and signal attenuation factor.

Thanks

 

[Kral]

damping ratio vs cutoff frequency

1a2s3d4f,
Damping Ratio (Z) and Cutoff Frequency (w0) completely define the response of a 2nd order system in both the time domain and the frequency domain. The transfer function of a 2nd order system is K/(s^2 +2Zw0 + w0^2), where K is the DC gain. The lower the damping ratio (below 1), the more oscillatory the step response will be, and the higher the peak in the frequency response (below w0) will be. A damping ratio greater than 1 will have no oscillations in the step response, and no peak in the frequency response. In addition, a damping ratio >1/(Sqrt(2)) will have no peak in the frequency response. If you substitue jw for s in the transfer function and plot the amplitude vs frequency, you can see the effect of Z on the frequency response for various values of Z.
Regards,
Kral

 

[1a2s3d4f]

Dear Kral,

Thanks so much for your clear explanation. I did understand better on the relationship between damping ratio (Z) and cutoff frequency (Wo). My understand is that we need to transform the second order system in to the form of K/(s^2 +2Zw0 + w0^2). We then use the form to find their Z and w0. I am wondering are there any Matlab command that automatically convert the second order system in to the form (K/(s^2 +2Zw0 + w0^2)). If matlab cannot perform such operation, can you advice me to the tool to perform such operation.
I do not understand, how does the system bandwidth can be determined in such cases. In my analog design class, I remember we did talk about the bandwidth of the system (we taking a -3-db factor or the different between the upper and lower cutoff frequency).

Again thanks for clear up my confusion on damping factor and cut off frequency.

Thanks

 

[Kral]

1a2s3d4f,
I'm not a MATLAB expert, but I'd be very surpised if MATLAB could not handle this problem. Regarding the determination of the bandwidth, this can be calculated by setting the gain equal to 1/SQRET(2), which is the -3dB point, substituting jw for s, and solving for w.
Regards,
Kral