nyquist pertemuan ke 6
DESCRIPTION
bahan kuliahTRANSCRIPT
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Analisis Respon Frekwensi
SISTEM KONTROL 2
Pertemuan ke 7
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Introduction
Nyquist Diagram revisited
Nyquist Stability Criterion
Relative Stability
Outlines
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Introduction
✔kita telah mempelajari tentang analisis kestabilan dalam s-domain menggunakan kreteria kestabilan Routh-Hurwitz. ✔sekarang kita akan menerapkan kestabilan lup tertutup (closed loop) system dalam domain frequency.✔metode untuk memperhitungkan kestabilan system lup tertutup (closed-loop system) menggunakan Nyquist diagram.
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System Stability
Introduction
)(1
)()(
sGH
sGsT
Persamaan Karakteristik F(s)
sGH1)s(F
Suatu system lup tertutup (closed-loop system) adalah stabil jika semua pole F(s) berada pada sebelah kiri dari bidang s.
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Nyquist Diagram Revisited
Representasi frekuensi respon dalam grafik, antara lain:Bode diagramsPolar plot (Nyquist Diagram)Log magnitude and phase diagrams (Nichols Diagrams)
kita akan menggunakan diagram Nyquist dari sistem lup terbuka (open-loop system) untuk mengetahui stabilitas dari sistem lup tertutup (closed-loop system).
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Sketch of Nyquist Diagrams
Transfer function dari suatu sistem G(s) dapat didifinisikan dalam domain frequency, sebagai berikut;
)(jX)(R)s(G)j(Gjs
dimana
)j(GRe)(R )j(GIm)(X
Nyquist Diagram Revisited
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polar plot (Nyquist diagram) dari sebuah frequency response dalam transfer function G(j) adalah grafik yang memiliki coordinate bagian real dan imaginary dari G(j)
Sketch of Nyquist Diagrams
Nyquist Diagram Revisited
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Polar Plots
Dalam membuat sket diagram Nyquist, point point dasar adalah sebagai berikut:• Point saat = 0• Point = • Point saat response melewati real axes• Point saat response melewati imaginary axes.
Nyquist Diagram Revisited
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Example
Sketch Nyquist plot dari transfer function berikut:
10s3s1s
500)s(G
Nyquist Diagram Revisited
)(jX)(R
10j3j1j
K500)j(G
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Nyquist Diagram Revisited
Example
The cardinal points:
• = 0
• =
3
50)0(R 0)0(X
0)(R 0)(X
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Nyquist Diagram Revisited
Example
The cardinal points:
• Imaginary axis diagram Nyquist diagram pada imaginary axis, saat
0)(R
379,8)46,1( X
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Nyquist Diagram Revisited
Example
The cardinal points:
• Real axisDiagram Nyquist pada real axis saat
0)(X
874.0)43(R
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Nyquist Diagram Revisited
Completed Nyquist Diagram
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Nyquist Diagram Revisited
Effect of gain K
10s3s1s
K500)s(G
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Nyquist Stability Criterion
Jika system tidak mempunyai pole-pole atau zero-zero open-loop disebelah kanan plane. Closed-loop system adalah stable, jika point -1+j0 terletak disebelah kiri open-loop Nyquist diagram berjalan sepanjang plot dengan arah yang menuju peningkatan frequency.
Simplified Nyquist Stability Criterion
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Nyquist Stability Criterion
Example
Tentukan stabilitas dari sistem berikut
10s3s1s
K500)s(GH
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Example
Nyquist Stability Criterion
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Example
Tentukan stabilitas dari sistem berikut
10s3s
100)s(GH
Nyquist Stability Criterion
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Example
Tentukan range dari K sehingga closed-loop system menjadi stable.
10s3s
K100)s(GH
Nyquist Stability Criterion
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Example
Nyquist Stability Criterion
10s3s1s
K500)s(G
1)s(H
Tentukan range dari K sehingga closed-loop system menjadi stable.
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