SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s...
Transcript of SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s...
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SISTEM
KONTROL
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TUJUAN DARI SISTEM KONTROL
Regulation
Trajectory following
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Konsep Pengendalian
Mencapai suatu set point (titik yang
diinginkan) 𝑥𝑠𝑒𝑡 Dilakukan dengan mengatur
input(masukan) 𝑢 sehingga tercapai set
point
Pada saat mencapai set point maka
𝑒 (𝑒𝑟𝑟𝑜𝑟) = 0.
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Sejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed
control of a steam engine.
1920s Minorsky worked on automatic controllers for steering ships.
1930s Nyquist developed a method for analyzing the stability of controlled systems
1940s Frequency response methods made it possible to design linear closed-loop control systems
1950s Root-locus method due to Evans was fully developed
1960s State space methods, optimal control, adaptive control and
1980s Learning controls are begun to investigated and developed.
Present and on-going research fields. Recent application of modern control theory includes such non-engineering systems such as biological, biomedical, economic and socio-economic systems
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Sejarah
James Watt Governor Control
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STRATEGI KONTROL
Open loop control
Feedforward control
Feedback contol
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Studi Kasus
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Open Loop Control
Paling sederhana
Untuk memperoleh ketinggian air tertentu
dilakukan dengan mengatur besar
kecilnya bukaan katup
Apabila terjadi perubahan laju keluar
tidak dapat diantisipasi
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Block Diagram Open Loop
Control
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Feedforward Control
Modifikasi dari sistem kendali open loop
Yang diukur adalah perubahan laju
keluar (gangguan)
Perubahan laju keluar digunakan sebagai
acuan seberapa besar bukaan katup
Tidak dapat mengatasi gangguan yang
tidak terukur.
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Block Diagram Feedforward
Control
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Feedback Control
Pengukuran dilakukan langsung pada
ketinggian air dalam tangki
Dapat mengatasi gangguan yang tidak
terukur atau tidak termodelkan
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Block Diagram Feedback
Control
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Pengendalian Sistem
Sederhana
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Intuisi Dibalik Pengendalian
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Kendali Kecepatan atau
Percepatan
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Kendali Bang-Bang
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Kendali Bang-Bang Saat
Bekerja
• Optimal untuk mencapai set point
• Tidak baik untuk berada di dekat titik tersebut
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Kendali Proporsional
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Contoh: Kendali Kecepatan
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Kerja Kendali Proportional
• Menaikkan gain akan mencapai set point lebih cepat
• Dapat menyebabkan overshoot dan bahkan ketidak stabilan
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Stabilitas
Perilaku pada 𝑡 tak hingga
Suatu model adalah
Tak stabil respons bebas menuju tak hingga
Stabil respons bebas menuju ke nol
Stabilitas netral kasus perbatasan
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Step Respon Criteria
Percentage overshoot
Decay ratio
Rise time
Settling time
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Steady State Error
Misal ada gangguan kontinyu
𝑥 = 𝐹 𝑥, 𝑢 + 𝑑
Kendali P tidak dapat mempertahankan
𝑒 = 0
Mengapa??
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Steady State Error
Misal ada gangguan kontinyu
𝑥 = 𝐹 𝑥, 𝑢 + 𝑑
Kendali P tidak dapat mempertahankan
𝑒 = 0
Bila 𝑢𝑏 didefinisikan sebagai 𝐹(𝑥𝑠𝑒𝑡, 𝑢𝑏) = 0
Maka 𝐹(𝑥𝑠𝑒𝑡, 𝑢𝑏) + 𝑑 ≠ 0
Harus adaptasi 𝑢𝑏 ke gangguan 𝑑
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Mengadaptasi Kendali
Kadang satu kendali tidak cukup
Diperlukan kendali pada suatu waktu
yang berbeda
𝑢 = 𝑘𝑝𝑒 + 𝑢𝑏 𝑢𝑏 = 𝑘𝑖𝑒 dimana 𝑘𝑖 << 𝑘𝑝
Ini dapat menghilangkan steady state
eror
mengapa?
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Mengadaptasi Kendali
Kadang satu kendali tidak cukup
Diperlukan kendali pada suatu waktu yang berbeda
𝑢 = 𝑘𝑝𝑒 + 𝑢𝑏 𝑢𝑏 = 𝑘𝑖𝑒 dimana 𝑘𝑖 << 𝑘𝑝
Ini dapat menghilangkan steady state eror
Karena pengendali yang lebih pelan mengadaptasi 𝑢𝑏
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Kendali Integral
Kendali yang adaptive 𝑢𝑏 = 𝑘𝑖𝑒 artinya
𝑢𝑏 = 𝑘𝑖 0
𝑡
𝑒𝑑𝑡 + 𝑢𝑏
Sehingga
𝑢 𝑡 = 𝑘𝑝𝑒 𝑡 + 𝑘𝑖 0
𝑡
𝑒𝑑𝑡 + 𝑢𝑏
Disebut dengan kendali proportional
integral
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Kendali Derivative
Damping friction adalah gaya yang
melawan gerak, proportional terhadap
kecepatan
Mencegah overshoot dengan kendali
damping𝑢 = 𝑘𝑝𝑒 + 𝑘𝑑 𝑒
Estimasi derivative dari hasil pengukuran
adalah rentan, dan memperbesar noise
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Kerja Kendali Derivative
• Damping mengisolasi overshoot dan osilasi
• Tetapi rentan terhadap noise
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Efek Kendali Derivative
Berbagai nilai damping tanpa noise
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Derivative Memperbesar Noise
Ini menjadi masalah apabila control
output tergantung pada slope (gain
tinggi)
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Kendali PID
Kombinasi dengan pembobotan bagian
Proportional, Integral, dan Derivative
𝑢 𝑡 = 𝑘𝑝𝑒 𝑡 + 0
𝑡
𝑘𝑖𝑒 𝑡 +𝑘𝑑 𝑒(𝑡)
Kendali PID adalah tumpuan pada
industri kendali. Tuning tidak sederhana.
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Kerja Kendali PID
Perilaku baik tergantung pada tuning yang baik
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Eksplorasi Tuning Kendali PID
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Habituation
Kendali integral mengadaptasi gangguan 𝑢𝑏
Habituation mengadapatasi set point 𝑥𝑠𝑒𝑡 untuk mencegah agar sinyal kendali tidak
terlalu tinggi dan membahayakan
Kedua adaptasi menurunkan steady state error
𝑢 = 𝑘𝑝𝑒 + 𝑢𝑏
𝑥𝑠𝑒𝑡 = +𝑘ℎ𝑒 dimana 𝑘ℎ << 𝑘𝑝
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Tuning Ziegler-Nichols
Respons open-loop terhadap unit step
d adalah deadtime. T time constant
process
K adalah gain process
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Tuning Kendali PID
PID dideskripsikan sebagai
𝑢 𝑡 = 𝑘𝑝𝑒 𝑡 + 0
𝑡
𝑘𝑖𝑒 𝑡 + 𝑘𝑑 𝑒(𝑡)
Bentuk standar lainnya
𝑢 𝑡 = 𝑃 𝑒 𝑡 + 𝑇𝑖 0
𝑡
𝑒 𝑡 + 𝑇𝑑 𝑒(𝑡)
Ziegler-Nichols menyatakan
𝑃 =1,5𝑇𝑑𝐾𝑑
, 𝑇𝑖 = 2,5𝑑, 𝑇𝑑 = 0,4𝑑
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Ziegler-Nichols Close Loop
Hentikan kendali D dan I (murni P)
Beri perubahan step pada set point
Ulang mengatur gain kendali sehingga
memperoleh gain yang stabil
Gain ini adalah ultimate gain 𝑘𝑢 Periodanya adalah ultimate period 𝑃𝑢
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Tuning Closed-loop Z-N PID
Bentuk standar PID adalah
𝑢 𝑡 = 𝑃 𝑒 𝑡 + 𝑇𝑖 0
𝑡
𝑒 𝑡 + 𝑇𝑑 𝑒(𝑡)
Untuk kendali PI
𝑃 = 0,45𝑘𝑢, 𝑇𝑖 =𝑃𝑢1,2
Untuk kendali PID
𝑃 = 0,6𝑘𝑢, 𝑇𝑖 =𝑃𝑢2, 𝑇𝑑 =
𝑃𝑢8