TR: Bug with BODE plotter ?

[Perrichon Pierre]

De : Perrichon Pierre [mailto:perrichon.pierre at wanadoo.fr] 
Envoyé : mardi 6 avril 2010 08:33
À : 'users at lists.scilab.org'
Objet : 

 

Dear,

 

I am studying different methods to translate un simple transfer function
from %s to %z, and try different methods to track the better one, with a
frequency approach.

-          Continuous (this is the base in %s)

-          Euler method

-          Bilinear method

-          Impulse response

 

Then, I plot the different graphs using the BODE instruction.

The plot is apparently not correct, because It shows that the Impulse method
is the better one, except that the continuous curve has been shifted (see
and compare graph 1 and 2)

 

I had to redraw all the graphs using the repfreq, dbphi, and plot2d
instructions to get correct results, which show that the Bilinear method is
the best one (graph 4)

 

So I think there is a bug in the Bode plot, or a method error (SIMO // SISO
?)

 

Could you confirm ?

 

Here is my program (also in the attached file)

 

// Programme P2_2

// 06-04-2010

//----------------

s=%s;

z=%z;

 

Te=0.0003;                               // Sample time

Fmin=1;                                        //Hertz

Fmax=1000;                               // Hertz

//--------------------------------------------------------------------------
------------------------------------------------

K=0.43;

T=0.0075;

a=0.2;

//--------------------------------------------------------------------------
------------------------------------------------

FT0=K*(1+T*s)/(1+a*T*s);                       // Continuous system

FT0 = syslin('c', FT0);

FT10_0 = tf2ss(FT0);

 

//--------------------------------------------------------------------------
------------------------------------------------

pz=(1-z^-1)/Te;                                //  Euler Transform

 

FT1 = K*(1+T*pz)/(1+a*T*pz);             

FT1 = syslin(Te, FT1 );

FT10_1 = tf2ss(FT1);

 

//--------------------------------------------------------------------------
------------------------------------------------

pz=2/Te*(1-z^-1)/(1+z^-1);                     // Bilinear transform

 

FT2 = K*(1+T*pz)/(1+a*T*pz);

FT2 = syslin(Te, FT2 );

FT10_2 = tf2ss(FT2);

 

//--------------------------------------------------------------------------
------------------------------------------------

b=1/(a*T);                               // Invariance impulsionnelle

c=1/a;

EXP=exp(-b*Te);

N=c*(z-1) + 1 - EXP;

D=z-EXP;

FT3=K*(N/D);

FT3 = syslin(Te, FT3 );

FT10_3 = tf2ss(FT3);

 

//--------------------------------------------------------------------------
------------------------------------------------

scf(1);clf();                            // Create and clear screen 1

bode([FT10_0],Fmin,Fmax);

legends(['Continu';], [1;], with_box=%t, opt=4 );

//--------------------------------------------------------------------------
------------------------------------------------

scf(2);clf();                            // Create and clear screen 2

bode([FT10_0;FT10_3],Fmin,Fmax);

legends(['Continu';'Invariance'], [1;2], with_box=%t, opt=4 );

 

//--------------------------------------------------------------------------
------------------------------------------------

scf(3);clf();                            // Create and clear screen 3

bode([FT10_0;FT10_1;FT10_2;FT10_3],Fmin,Fmax);

legends(['Continu';'Euler';'Bilineaire';'Invariance';], [1;2;3;4],
with_box=%t, opt=4 );

//--------------------------------------------------------------------------
------------------------------------------------

frq=Fmin:0.01:Fmax;

 

[frq0,rep0] =repfreq(FT10_0,frq);

[db0,phi0]=dbphi(rep0);

 

[frq1,rep1] =repfreq(FT10_1,frq);

[db1,phi1]=dbphi(rep1); 

 

[frq2,rep2] =repfreq(FT10_2,frq);

[db2,phi2]=dbphi(rep2); 

 

[frq3,rep3] =repfreq(FT10_3,frq);

[db3,phi3]=dbphi(rep3); 

 

//Affichage

//------------

scf(4);clf();                            // Create and clear screen 4

xgrid();

subplot(2,1,1);

plot2d('ln',frq,db0,style=1);

plot2d('ln',frq,db1,style=2);

plot2d('ln',frq,db2,style=3);

plot2d('ln',frq,db3,style=4);

legends(['Continu';'Euler';'Bilineaire';'Invariance';], [1;2;3;4],
with_box=%t, opt=4 );

xtitle('', 'Fréquence Hz','Magnitude (Db)');

 

subplot(2,1,2);

plot2d('ln',frq,phi0,style=1);

plot2d('ln',frq,phi1,style=2);

plot2d('ln',frq,phi2,style=3);

plot2d('ln',frq,phi3,style=4);

xgrid();

xtitle('', 'Fréquence (Hz)','Phase (degré)');

 

 

Best regards

 

 

P.Perrichon

 

 

 

Nous protégeons notre environnement : n'imprimez ce mail que si nécessaire.
:._______________



 

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20100406/6f7e6c71/attachment.htm>
-------------- next part --------------
An embedded and charset-unspecified text was scrubbed...
Name: P2_2.txt
URL: <https://lists.scilab.org/pipermail/users/attachments/20100406/6f7e6c71/attachment.txt>