MATLAB: System response

transfer function

Hi everyone, i am trying to obtain a response of a first order system to a step input, however the output the graph depicts doesn't match with what i expected. would someone be kind enough to give me a push in the right direction. the script for the program is thus:

clear all clc k1 = 2e4; k2 = 2e7; k3 = 2e4; c = 2e10; num= [(k1*c) (k1*k2)]; den= [(c*k1*k3) (k1*k2*k3)]; P=tf(num,den); display (P) step (P), grid title('y3 with a step input') %ylim([0 1])

Regards

Best Answer

Your system P, as defined, is simply a gain. You can see that if you do

zpk(P)

ans =

5e-05 (s+0.001)
---------------
   (s+0.001)

You can even see it if you look carefully at your num and den formulas:

num = k1*c*s+k1*k2 =k1*(c*s+k2)

den = c*k1*k3*s+k1*k2*k3 = k1*k3*(c*s+k2)

Therefore

num/den = k1* (c*s+k2) / (k1*k3* (c*s+k2)) = 1/k3

This is exactly what you see when you look at step response.

In short, recheck your formulas.

Arkadiy

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MATLAB: I wanna obtain numerical values from a tf(num,den). How to do it

Use the evalfr (link) function:

num=[1 1 0]; den=[1 2 3 4];
G=tf(num,den);
s1=2+3i;
Gs1 = evalfr(G,s1)          % G(s1)=???

producing:

Gs1 =
          0.197938144329897 -     0.145360824742268i

MATLAB: FFT code on time series

hi Sam,

in case you have verified the properties of the signal in the above comment,we can proceed as the following :

We have a signal of length L=3950 taken every 12 hours for 2563.5 days. So formally the sampling rate is Fs= 3950/2563 =~1.54 Hz .

For these types of times series , the range is dynamically changing therefore we plot the frequency in dB to expand the low values and compress the high ones :

1)Solution 1:

Fs=1.55; %  
L=length(Thermocline);
N=ceil(log2(L));
FFTherm=fft(Thermocline,2^N);
f=(Fs/2^N)*(0:2^(N-1)-1);
Power=FFTherm.*conj(FFTherm);
figure,
semilogy(f,Power(1:2^(N-1)))
xlabel('  Frequency (Hz)'), ylabel(' Magnitude (w)'),
title('  Power Spectral Density'), grid on;

2) Solution : 2

 % Directly you type in the C.P :
  psd(Thermocline)

So the frequency is in the range [0,...,0.1] Hz. To see if this result, physically, makes sens, try to check :

"Stochastic climate models, Part I1, Application to sea-surface temperature anomalies and thermocline variability" by CLAUDE FRA NKIG NOUL :

And another paper: "MEAN AND EDDY DYNAMICS OF THE MAIN THERMOCLINE" by GEOFFREY K. VALLIS

http://www.princeton.edu/~gkv/papers/thermocline.pdf

These two papers give a general idea on how much an estimate of the frequency must be .

I hope this helps .

KHMOU Youssef.

Best Answer

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MATLAB: I wanna obtain numerical values from a tf(num,den). How to do it

MATLAB: FFT code on time series

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