I m working on the college project. In this we r given a black-box
model (in MATLAB SIMULINK) for identification. I am exciting the plant
with +(-)20% of operating point signal (PRBS ranging from 0.4 to 0.6
m3/hr for operating point of 0.4 m3/hr).
Problem: The output signal is having much of noise content. The
(variance of output found with no excitation)
ratio = --------------------------------------------- = 0.8
(Variance of output signal with PRBS input)
which (i suppose) is noise to signal ratio. This ratio seems to be
very high.
I m wondering what type of measures i can take to gaurantee good
process model.
For identification i m using Matlab identification toolbox.
Thank you.
rgds,
Rahul

PRBS? Signal processing and controls classes, in particular, are bad
about inventing abbreviations that are peculiar to the text at hand.
your "ratio" is noise over signal+noise. Normally you are interested in
signal/noise, and you get there by measuring (signal+noise)/noise. So
your signal+noise over noise = 1.25, which ain't good.
I'm not familiar with the Matlab identification toolbox, but you want to
look for some way that you can increase the signal to noise ratio. The
way that is conceptually easiest is to just take repeated measurements
and average the outputs. As long as the "noise" has no DC content and
is independent of the signal then the variance of the sum of the
(incoherent) noise will climb linearly with the number of repetitions,
while the variance of the sum of the (coherent) response to input will
climb as the square of the number of repetitions.
There are system identification schemes, particularly the least-squares
solutions used in adaptive control systems, that do this implicitly. If
you don't like the idea of explicitly repeating your measurement and
averaging you could find out if Matlab supports such a beast and use
that instead.
In my old age I've taken to thinking of these system ID problems as
stakes in hard ground, however, and rather than looking for the shiniest
new set of tools at the system ID store I usually go for that old,
beat-up, _heavy_ sledge hammer sitting in the corner of the shed.

Is there any guarantee that the "noise" isn't an intentionally generated
carrier, modulated by the input? What is the spectrum of the "noise" when
there is no input?

Thanks for such informative replies.
I have checked the SIMULINK model given to me. I found that white
noise is added to input signal(to plant). White noise is also added to
output(as measurement noise).
This added noise has no relation with constant input.
White Noise White Noise
| |
| _______ |
const Input V + | | V +
------------O-------|Process|---------->O----------> measured output
+ |_______| +
I have taken 512 point fast fourier transform(FFT) of noise data and
found that most of power is within first 50 points. Approximate curve
looks like,
0.7 l
l * *
l * *
l * *
l * *
P l * *
o l * *
w l * *
e l * *
r l * *
l * *
Sp l * *
ec l * *
tr l *** *
um l * ** *
l * *************************** *
0 l-------------------------------------
0 50 256 512
Mean of noise is zero. Here sampling time is 1 min.
I m basically chemical engineer so it may happen that i haven't put
enough information to answer question. If such is case, pls let me
know.

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