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Thomas Dehaeze
2021-05-20 11:14:26 +02:00
parent afcd720965
commit c114cdbc58
13 changed files with 292 additions and 260 deletions
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@@ -167,10 +167,10 @@ exportFig('figs/weight_formula.pdf', 'width', 'wide', 'height', 'normal');
[[file:figs/weight_formula.png]]
#+begin_src matlab
n = 2; w0 = 2*pi*11; G0 = 1/10; G1 = 1000; Gc = 1/2;
n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 1/2;
n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
#+end_src
@@ -216,35 +216,28 @@ And we do the $\mathcal{H}_\infty$ synthesis using the =hinfsyn= command.
#+RESULTS:
#+begin_example
[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
Resetting value of Gamma min based on D_11, D_12, D_21 terms
Test bounds: 0.1000 < gamma <= 1050.0000
Test bounds: 0.3223 <= gamma <= 1000
gamma hamx_eig xinf_eig hamy_eig yinf_eig nrho_xy p/f
1.050e+03 2.8e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
525.050 2.8e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
262.575 2.8e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
131.337 2.8e+01 2.4e-07 4.1e+00 -1.0e-13 0.0000 p
65.719 2.8e+01 2.4e-07 4.1e+00 -9.5e-14 0.0000 p
32.909 2.8e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
16.505 2.8e+01 2.4e-07 4.1e+00 -1.0e-13 0.0000 p
8.302 2.8e+01 2.4e-07 4.1e+00 -7.2e-14 0.0000 p
4.201 2.8e+01 2.4e-07 4.1e+00 -2.5e-25 0.0000 p
2.151 2.7e+01 2.4e-07 4.1e+00 -3.8e-14 0.0000 p
1.125 2.6e+01 2.4e-07 4.1e+00 -5.4e-24 0.0000 p
0.613 2.3e+01 -3.7e+01# 4.1e+00 0.0e+00 0.0000 f
0.869 2.6e+01 -3.7e+02# 4.1e+00 0.0e+00 0.0000 f
0.997 2.6e+01 -1.1e+04# 4.1e+00 0.0e+00 0.0000 f
1.061 2.6e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
1.029 2.6e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
1.013 2.6e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
1.005 2.6e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
1.001 2.6e+01 -3.1e+04# 4.1e+00 -3.8e-14 0.0000 f
1.003 2.6e+01 -2.8e+05# 4.1e+00 0.0e+00 0.0000 f
1.004 2.6e+01 2.4e-07 4.1e+00 -5.8e-24 0.0000 p
1.004 2.6e+01 2.4e-07 4.1e+00 0.0e+00 0.0000 p
gamma X>=0 Y>=0 rho(XY)<1 p/f
1.795e+01 1.4e-07 0.0e+00 1.481e-16 p
2.406e+00 1.4e-07 0.0e+00 3.604e-15 p
8.806e-01 -3.1e+02 # -1.4e-16 7.370e-19 f
1.456e+00 1.4e-07 0.0e+00 1.499e-18 p
1.132e+00 1.4e-07 0.0e+00 8.587e-15 p
9.985e-01 1.4e-07 0.0e+00 2.331e-13 p
9.377e-01 -7.7e+02 # -6.6e-17 3.744e-14 f
9.676e-01 -2.0e+03 # -5.7e-17 1.046e-13 f
9.829e-01 -6.6e+03 # -1.1e-16 2.949e-13 f
9.907e-01 1.4e-07 0.0e+00 2.374e-19 p
9.868e-01 -1.6e+04 # -6.4e-17 5.331e-14 f
9.887e-01 -5.1e+04 # -1.5e-17 2.703e-19 f
9.897e-01 1.4e-07 0.0e+00 1.583e-11 p
Limiting gains...
9.897e-01 1.5e-07 0.0e+00 1.183e-12 p
9.897e-01 6.9e-07 0.0e+00 1.365e-12 p
Gamma value achieved: 1.0036
Best performance (actual): 0.9897
#+end_example
We then define the high pass filter $H_1 = 1 - H_2$. The bode plot of both $H_1$ and $H_2$ is shown on figure [[fig:hinf_filters_results]].