universitas brawijayamaulana.lecture.ub.ac.id/files/2012/04/04_fungsi_alih_dan_manipula… ·...
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Eka Maulana, ST, MT, MEng.Electrical Engineering Department
Brawijaya University
Fungsi Alih &Manipulasi Blok Diagram
Matakuliah: Sistem Kontrol Digital
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Topik Pembahasan
Fungsi Alih Sistem (representasi diskrit)
Sistem Loop Terbuka
Tanggapan Waktu Loop Terbuka
Sistem Loop Tertutup
Tanggapan Waktu Sistem Loop Tertutup
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Overview
y(z)e(z) =G(z)
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Sistem Loop Terbuka #1
K
y(z)e(z) = ?
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Sistem Loop Terbuka #2
y(z)e(z) =G1G2(z)
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Contoh [pembuktian]
dan
denganTabel T.Z
Output
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Sistem Loop Terbuka #3
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Contoh [pembuktian]
dan
dan
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Time Response Loop TerbukaTanggapan waktu loop terbuka pada sistem data
tersampling dapat diperoleh dengan mencaritransformasi Z balik dari fungsi output.
Hitung dan gambarkan tanggapan output sistem RC dalam gambardengan periode sampling T=1s
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Solusi [RC]
Fungsi Alih sistem:
Input: Unit Step Fungsi AlihdenganTransformasi Z
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Solusi Response Z [RC]
Tanggapan Output Transformasi Z:
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Pembagian ParsialTanggapan output dapat diperoleh dengan transformasi Z balik
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Tanggapan Output Sistem RCDengan tabel transformasi balik didapatkan:
Tanggapan Output:
Sample Output:
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Sistem dengan ZOH Loop Terbuka
Tentukan tanggapan output sistem jika dalam sistem tersebutdigunakan ZOH dengan input unit step dan unit ramp!
Fungsi Alih sistem G2(s):Fungsi Alih ZOH G1(s):
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Solusi
Transformasi Z
Dg. Pecahan parsial
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Tanggapan
a. Input unit step
Dgn. Metode Pecahan parsial
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Tanggapan Output Sistem
a adalah unit step sistem
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Tanggapan
b. Input unit ramp
Dgn. Metode Long Division
Tanggapan Output:
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Tanggapan Output
Tanggapan Output dengan Input Unit Ramp
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Sistem Loop Tertutup #1
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Solusi Sistem Loop Tertutup #1
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Solusi Sistem Loop Tertutup #1
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Sistem Loop Tertutup #2
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Solusi Sistem Loop Tertutup #2
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Tugas Loop Tertutup #3
Tentukan Fungsi Alih Sistem Berikut
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Time Response Loop TertutupTanggapan waktu loop tetutup pada sistem data
tersampling dapat diperoleh dengan mencaritransformasi Z balik dari fungsi output.
Hitung dan plotkan tanggapan output sistem pada gambar di atasdengan periode sampling T=1s
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Solusi Tanggapan Waktu Loop Tertutup
Tanggapan Output Sistem:
Dimana input:
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Sistem Loop Tertutup #2
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Output Time Response L.Tertutup
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Soal #1
Tentukan tanggapan output sistem dalam gambar jika input adalah unit step dengan fungsi Alih sistem:
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TabelTransformasi Z