Control Bandwidth & Closed Loop Bandwidth Meaning?

[koochiee]

Can anyone tell me if Control bandwidth and closed loop bandwidth means the same thing? If not what does control bandwidth mean?
Please & Thank you!

 

[NascentOxygen]

A photo showing the context of "control bandwdth" usage might be helpful.

 

[koochiee]

The Bode Plot below was given and, I've marked for the Gain Margin & Phase Margin. They're asking how much the gain should be improved to get the Control Bandwidth to 3 rad/s.

 

[NascentOxygen]

It probably does mean the closed loop bandwidth. So how will you answer it?

They actually used the word "improved"??

 

[koochiee]

Actually it was the gain required to improve control BW to 3 rad/s. And I first thought that I'd shift the gain curve 40dBs (according to the figure). But I'm not quite certain. I would really appreciate any help.

 

[donpacino]

koochiee your hypothesis is correct. The easiest way to increase the bandwidth is to increase the dc gain on the system by 40 dB.

 

[koochiee]

Thank you donpacino! Can you explain how this happens? How control bandwidth increases when the gain is increased. From looking at the figure I can say how much I should increase the gain by (40dB). But physically how do I interpret it? I've looked through my notes and textbooks and I can't find anything on control bandwidth, and I've also sent my teacher an email. I have to wait until next week to get an answer. And I can't finish this sum until then :( Again thank you for the responses.

 

[NascentOxygen]

koochiee your hypothesis is correct. The easiest way to increase the bandwidth is to increase the dc gain on the system by 40 dB.

Careful! The graph doesn't show DC gain ...

 

[donpacino]

DC ~ very low frequency. I am assuming that the magnitude and phase stays constant at frequencies < 0.001.
Even if the magnitude and phase did crazy things outside the scope of the graph, the effects of increase the DC gain by 10 dB would be the same (assuming the system isn't changed in some other way)

 

[donpacino]

In systems such as these your phase and gain margin are very important.
Basically all you need to know for now is that your control bandwidth is either where the magnitude becomes less than 0 dB (I think you already knew that).

Your system has a pole at ~0.2 rad/s. that means that frequency after 0.2 rad/s is going to decrease from the dc gain by 20 db/dec (dec=decade). The effect that a pole or zero has on a system is independent of the other poles or zeros or dc gain of the system. This means that regaurdless of the DC gain, after the pole the gain will drop by a factor of 20 db/dec.

If you want to change the control bandwidth to 6 rad/s, you need to move the zero crossover frequency to 6 rad/s. The magnitude at 6 rad/s in the base system is -40 dB. Therefore you need to add 40 dB.

The control bandwidth is the bandwidth in which signals will have a meaningful effect on the circuit. With this system, if there is a 1 GHz signal (say from a wifi router nearby) you can see that it will have zero effect on your circuit (which is a good thing). However if there is somehow a 0.01 Hz signal, it will be amplified in your system.

does that make sense?

 

[koochiee]

Thank you for your response.