Random Vibration Controller

I'm looking for some guidance on how random vibration control is
performed.  I've read that the reference signal is a PSD (power spectral
density) rather than a time domain signal.  And that the feedback from the
accelerometer (time block of data) is converted to the frequency domain by
an FFT, and compared to the reference spectrum to close the loop.  Then an
IFFT is performed to produce the drive signal. That is a simplified
explanation, but one large point that I'm missing is how can any
significant bandwidth be achieved if the data is processed in blocks.  For
instance, if the spectrum has a frequency resolution of 5 Hz, it seems
that the blocks of data would need to be 200 mSec long.  Is it that an FFT
is performed on every sample and averaged?
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On Fri, 17 Apr 2015 14:39:58 -0500, smc123 wrote:

> I'm looking for some guidance on how random vibration control is
> performed.  I've read that the reference signal is a PSD (power spectral
> density) rather than a time domain signal.  And that the feedback from
> the accelerometer (time block of data) is converted to the frequency
> domain by an FFT, and compared to the reference spectrum to close the
> loop.  Then an IFFT is performed to produce the drive signal. That is a
> simplified explanation, but one large point that I'm missing is how can
> any significant bandwidth be achieved if the data is processed in
> blocks.  For instance, if the spectrum has a frequency resolution of 5
> Hz, it seems that the blocks of data would need to be 200 mSec long.  Is
> it that an FFT is performed on every sample and averaged?

It boils down to your definition of bandwidth.  The bandwidth of the 
energy on the table is as high as the table is capable of, but the 
bandwidth of the loop itself is low.

By an large (I assume), once you get your test article bolted to the 
table, then the transfer function from the coil terminals to the table 
acceleration is constant.

In a perfect world would know this transfer function ahead of time.  You 
would also know how much hell you wanted to shake out of the table at what 
frequencies.  To achieve this, you would just generate white noise and 
condition it with a transfer function whose frequency response is the 
spectral shape of the desired shaking, then again by the inverse transfer 
function of the table.

The world isn't perfect, so instead you start with a guess at the spectral 
response of the table.  Then you shake the table based on that guess, and 
as information comes back from the accelerometer about how the table is 
actually shaking, you either update your guess or you just update the 
transfer function you're using to generate white noise, with the aim of 
increasing or decreasing the strength of the shaking at the frequencies 
that are important to you.

If the amount of time it takes to complete a test is unimportant, the 
controller only needs to update faster than the properties of the combined 
system of table and test article change.  Since that's probably pretty 
damned slow, the speed that the controller updates can be dictated by some 
sort of accuracy/test time tradeoff.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim, Thank you for the response and explanation.  I think I know what I
was missing, but please correct me if I'm wrong.  I was thinking that the
random signal with content of say 5 Hz to 2 kHz needed to be controlled in
a closed loop way much like an amplifier does, and the closed loop
bandwidth would need to be somewhat greater than 2 kHz.  But instead it
looks like controlling the PSD is actually a way of controlling the energy
in each frequency bin and not the time signal itself.  So it seems similar
to an automatic gain control where the modulation is being controlled
rather than the signal in time.  And the bandwidth of the control loop can
be very low as you explained because the system transfer function should
not be changing. 

Thanks,
Steve

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On Sun, 19 Apr 2015 20:36:05 -0500, smc123 wrote:

> Tim, Thank you for the response and explanation.  I think I know what I
> was missing, but please correct me if I'm wrong.  I was thinking that
> the random signal with content of say 5 Hz to 2 kHz needed to be
> controlled in a closed loop way much like an amplifier does, and the
> closed loop bandwidth would need to be somewhat greater than 2 kHz.  But
> instead it looks like controlling the PSD is actually a way of
> controlling the energy in each frequency bin and not the time signal
> itself.  So it seems similar to an automatic gain control where the
> modulation is being controlled rather than the signal in time.  And the
> bandwidth of the control loop can be very low as you explained because
> the system transfer function should not be changing.

That sounds like you understand things.

-- 
www.wescottdesign.com

>On Sun, 19 Apr 2015 20:36:05 -0500, smc123 wrote:
>
>> Tim, Thank you for the response and explanation.  I think I know what
>I
>> was missing, but please correct me if I'm wrong.  I was thinking that
>> the random signal with content of say 5 Hz to 2 kHz needed to be
>> controlled in a closed loop way much like an amplifier does, and the
>> closed loop bandwidth would need to be somewhat greater than 2 kHz. 
>But
>> instead it looks like controlling the PSD is actually a way of
>> controlling the energy in each frequency bin and not the time signal
>> itself.  So it seems similar to an automatic gain control where the
>> modulation is being controlled rather than the signal in time.  And
>the
>> bandwidth of the control loop can be very low as you explained
>because
>> the system transfer function should not be changing.
>
>That sounds like you understand things.
>
>-- 
>www.wescottdesign.com

Thanks, again
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