From bode to transfer function
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Raymond
le 5 Mai 2014
Commenté : Arkadiy Turevskiy
le 5 Mai 2014
I'm trying to get a transfer function out of the bode plot data. I've tried multiple functions(using this and this) yet when I plot both an example function and the solution the functions give me, it doesn't match.
So first I made the example:
examp1=tf([1],[1 -4 3])
[AMP PHA W]=bode(examp1)
which is a function with 2 poles. Then with tfest I made(copy/paste):
gain = squeeze(AMP);
phase = squeeze(PHA);
whz = squeeze(W);
response = gain.*exp(1i*phase*pi/180);
Ts = 0.1; % your sampling time
w=whz*2*pi; %convert Hz to rad/sec
gfr = idfrd(response,w,Ts);
sys=tfest(gfr,2);
bode(sys)
hold on
bode(examp1)
within the tfest function the 2nd value should be 2, correct? Since we have 2 poles in the original function. Yet in the end, when we compare the 2 bodes, they aren't much alike.
How should I do this?
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Arkadiy Turevskiy
le 5 Mai 2014
Modifié(e) : Arkadiy Turevskiy
le 5 Mai 2014
You need to set tfestoptions Focus property to "prediction" to allow for unstable systems (your system has two unstable poles).
Here is the code that gives a perfect fit (also note that bode returns frequency vector in rad/time unit, so there is no need to convert to hz as you were doing).
examp1=tf([1],[1 -4 3]);
[AMP PHA W]=bode(examp1);
gain = squeeze(AMP);
phase = squeeze(PHA);
w = squeeze(W);
response = gain.*exp(i*phase*pi/180);
Ts = 0.1; % your sampling time
gfr = idfrd(response,w,Ts);
Options = tfestOptions;
Options.Focus = 'prediction';
tf1 = tfest(gfr, 2, 1, Options, 'Ts', 0.1);
P = bodeoptions;
P.PhaseWrapping = 'on';
bodeplot(examp1,tf1,P);
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Arkadiy Turevskiy
le 5 Mai 2014
Modifié(e) : Arkadiy Turevskiy
le 5 Mai 2014
As for the other question, about now knowing the number of poles and zeros beforehand, there is no "sceintific" way to come up with best options - try a bunch of different options and number of poles and zeros and pick the one combination that gives the best fit. You can use compare to automate this.
You may also look at estimating a state space instead of a transfer function, using ssest. When you call this function, you can specify system order as a vector, say [1 10], and the function will then return a plot helping you choose the best order as shown here .
If needed, you can then convert the identified state-s[ace model into a transfer function using tf .
Arkadiy Turevskiy
le 5 Mai 2014
Finally, the system has two unstable poles because the poles (at 1 and 3) are both positive numbers. The pole is stable if real part is less than zero, and unstable if it is >0, which is your case. I am not going to explain why- read wikipedia or take a look at any introductory controls textbook.
To convince yourself in MATLAB quickly:
s=tf('s');
sys1=1/(s-1); %positive pole at 1
step(sys1); %unstable response
Now for the negative pole:
sys2=1/(s+1); % pole at -1
close all;
step(sys2); %stable response
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