How can I determinate the delay and the time constant from script?

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Ákos 2013-2-15

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Hi!

I have an input and an output vector, for example:

in=[0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1]
out=[0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 2; 12; 17; 20; 21; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22]

If you want to see it in a figure, type the following code to the Command Window:

in=[0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1];
out=[0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 2; 12; 17; 20; 21; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22; 22];
x=(1:1:30);
plot(x,in,'red')
hold
plot(x,out,'blue')
hold

I would like to determinate the delay and the time constant. I have System Identification Toolbox, and I can determinate the delay in GUI mode (Td=2.864), but I would like to determinate it in a matlab script. Which functions have to use, and how? Maybe I have to use the delayest function, but it doesn't works in this way:

DATA=iddata(out,in,0.1)
delayest(DATA)

The result is 0.

So I think this is not the right way. Can somebody write me an example to this two vector?

Thanks in advance!

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Answer 1

Image Analyst 2013-2-18

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What about just thresholding and using find()? Let's say that you say a signal starts when its amplitude exceeds some threshold:

thresholdValue = 0.5;
inStartTime = find(in > thresholdValue, 1, 'first')
outStartTime = find(out > thresholdValue, 1, 'first')
lagTime = outStartTime - inStartTime

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Answer 2

Ákos 2013-2-19

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It is not too simple, because the problem, that there is a big noise on the signal, the initial value is oscillate with random amplitudes between 0 and even 0.3 * average of final value, and the final value is oscillate too.

But I found the way, how can I use the functions of System Identification Toolbox right:

DATA=iddata(out,in,0.1);
model=arx(DATA,[1,1,1]);
type = idproc('P1D');
result=procest(DATA,type);
fprintf('Td= %f sec, Tp1= %f sec', result.Td, result.Tp1);

But really thank you for trying to help.

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Answer 3

Rajiv Singh 2013-2-19

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Try impulse response estimation based approaches, assuming you are able to find a good FIR model for data (which you can ascertain using COMPARE)

m=impulseest(DATA); h = impulseplot(m); showConfidence(h,3)

The first response value that is significantly out of 3 sd region is at t = 0.3 which indicates a 3 sample (0.3 sec) delay. See:

http://www.mathworks.com/help/ident/examples/model-structure-selection-determining-model-order-and-input-delay.html?prodcode=ID&language=en

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Image Analyst 2013-2-20

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Answer 4

Ákos 2013-2-20

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编辑：Ákos 2013-2-20

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Thank you, it's a helpful answer, but according to the compare funcion, the DATA, and the impulseest(DATA) does not fit well.

Here is my measured datas:

http://dl.dropbox.com/u/43098689/data.txt

If you Import the data file as a matrix, and you use the following code, you can see my system (Input in the 5th column (this is a duty cycle [%]), output in the 3rd column):

in=data(:,5);
out=data(:,3);
x=0.1:0.1:length(in)/10;
plot(x,out,'blue');
hold
plot(x,100*in,'red');
hold

Blue line shows the output, and the red line shows the input(*100). This is a nonlinear system, and i would like to determinate the delay and the time constant.

You can choose one part of the full system with this code (you can change the value of variable 'which'):

which=5;
dc_begin_vector=[1 638 1925 3237 4115 5071 6043 7065 7985 9326 10512 11802 14400 15547 16920 18249 19447 20715 21987 23319 24667 25925 27095];
sample_out_full=data(:,3);
sample_in_full=data(:,5);
sample_out=sample_out_full((dc_begin_vector(which)-100):((dc_begin_vector(which+1))-1));
sample_in=sample_in_full((dc_begin_vector(which)-100):((dc_begin_vector(which+1))-1));
sample_out=sample_out-min(sample_out);
sample_in=sample_in-min(sample_in);
x_axis=0.1:0.1:(length(sample_out)/10);
plot(x_axis,sample_out,'blue')
hold
plot(x_axis,100*sample_in,'red')
hold

If you can determinate the delay and the time constant to this one part, it's good for me.

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Image Analyst 2013-2-20

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