28 1. EXTRACTION OF UNCERTAIN MODEL OF DC-DC CONVERTERS
%numerator of vo(s)/io(s)
den_vo_io =[ den_vo_io;den1 ];
%denominator of vo(s)/io(s)
[num2 , den2 ]= tfdata(vo_vg ,'v');
num_vo_vg =[ num_vo_vg;num2 ];
den_vo_vg =[ den_vo_vg;den2 ];
[num3 , den3 ]= tfdata(vo_d ,'v');
num_vo_d =[ num_vo_d;num3 ];
den_vo_d =[ den_vo_d;den3 ];
end
disp(' Percentage of work done:')
disp(n/ NumberOfIteration *100)
%shows the progress of the loop
disp('')
end
disp('')
disp('vo(s)/d(s)')
disp('maximum of numerator coefficients :')
disp(max(num_vo_d))
disp('minimum of numerator coefficients :')
disp(min(num_vo_d))
disp('')
disp('maximum of denominator coefficients :')
disp(max(den_vo_d))
disp('minimum of denominator coefficients :')
disp(min(den_vo_d))
disp(' -------------')
disp('vo(s)/io(s)')
disp('maximum of numerator coefficients :')
disp(max(num_vo_io))
disp('minimum of numerator coefficients :')
disp(min(num_vo_io))
disp('')
disp('maximum of denominator coefficients :')
disp(max(den_vo_io))
disp('minimum of denominator coefficients :')
disp(min(den_vo_io))
1.5. EFFECT OF COMPONENT VARIATIONS 29
disp(' -------------')
disp('vo(s)/vg(s)')
disp('maximum of numerator coefficients :')
disp(max(num_vo_vg))
disp('minimum of numerator coefficients :')
disp(min(num_vo_vg))
disp('')
disp('maximum of denominator coefficients :')
disp(max(den_vo_vg))
disp('minimum of denominator coefficients :')
disp(min(den_vo_vg))
disp(' -------------')
e program randomly samples the component values (according to the given variations)
in each iteration. SSA is applied to the sampled values in order to obtain the transfer function
coefficients. Obtained coefficients are stored in an array. e program calculates and shows the
minimum/maximum value of each coefficient when iterations are finished.
e uncertain model of the studied Buck converter is shown in Table 1.4.
Table 1.4: Interval plant model of the transfer functions
?̃
?
(?)
?
̃
(?)
?̃
?
(?)
?
̃
?
(?)
?̃
?
(?)
?
̃
?
(?)
?̃
?
(?)
=
?
1
? + ?
0
?
̃
(?) ?
2
+ ?
1
? + ?
0
4.2793 × 10
3
<?
1
<1.1302 × 10
4
7.9196 × 10
8
<?
0
<1.9482 × 10
9
1.0076 × 10
3
<?
1
<1.6746 × 10
3
1.9979 × 10
7
<?
0
<3.3958 × 10
7
?̃
?
(?)
=
?
2
?
2
+ ?
1
? + ?
0
?
̃
?
(?) ?
2
+ ?
1
? + ?
0
-0.0883<?
2
<-0.045
-1.2407 × 10
4
<?
1
<-8.3366 × 10
3
-1.0087 × 10
7
<?
0
<-3.8357 × 10
6
1.0076 × 10
3
<?
1
<1.6746 × 10
3
1.9979 × 10
7
<?
0
<3.3958 × 10
7
?̃
?
(?)
=
?
1
? + ?
0
?
̃
?
(?) ?
2
+ ?
1
? + ?
0
38.4197<?
1
<118.2969
7.4277 × 10
6
<?
0
<1.6682 × 10
7
1.0076 × 10
3
<?
1
<1.6746 × 10
3
1.9979 × 10
7
<?
0
<3.3958 × 10
7
Step response of
ev
o
.s/
ev
g
.s/
(with coefficients randomly selected within the allowed bounds) is
shown in Fig. 1.12. is figure is produced with the aid of the following code.
30 1. EXTRACTION OF UNCERTAIN MODEL OF DC-DC CONVERTERS
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 0.002 0.004 0.006 0.008 0.01 0.012
Step Response
Amplitude
Time (sec)
Figure 1.12: Step response of
Qv
o
.s/
Qv
g
.s/
with randomly selected coefficients.
clc
%Defining the uncertain coefficients
b1_max =118.2969;
b1_nom =49.875;
b1_min =38.4197;
b1=ureal('b1',b1_nom ,'Range' ,[ b1_min , b1_max ]);
b0_max =1.6682 e7;
b0_nom =9975000;
b0_min =7.4277 e6;
b0=ureal('b0',b0_nom ,'Range' ,[ b0_min , b0_max ]);
a1_max =1.6746 e3;
a1_nom =1203;
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