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MATLABのBODEが離散と連続で一致しない

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現象メモ

連続プラントとそれを離散化したプラントのBODE線図が結構一致しないという問題です。
高周波部分が合わないというのはわかりますが,何故か低周波部分が合わないです。

なにか見落としているのかな。。。

sysc = tf([1 2 1 1 2],[1 2 1 2 2 2 1 2 1]);
Tsys = 1000e-6;
sysd = c2d(sysc,Tsys,'tustin');
sysc2t = d2c(sysd,'tustin');
sysc2z = d2c(sysd,'zoh');

figure(1)
bode(sysc,sysd)
legend('c','d')
figure(2)
bode(sysc,sysc2t)
legend('c','c2')
figure(3)
bode(sysc2t,sysc2z)
legend('c2t','c2z')

グラフ

Fig1:青が連続,赤がTustinで離散化したやつ。
image.png

Fig2:青が連続,赤が離散化したプラントを再度d2cで連続に戻したやつ。
image.png

Fig3:青がTustinでd2cしたもの,赤がZohでd2cしたもの。
image.png

考察

どうもc2dとd2cは逆変換の対応にないらしい(Fig2)。
離散化したプラントをd2cしたもののBode線図と離散プラントのBode線図は似通っているので連続化の処理のせいと思われるがなんでだろう?

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