SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s...

41
SISTEM KONTROL

Transcript of SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s...

Page 1: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

SISTEM

KONTROL

Page 2: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

TUJUAN DARI SISTEM KONTROL

Regulation

Trajectory following

Page 3: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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.

Page 4: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 5: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Sejarah

James Watt Governor Control

Page 6: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

STRATEGI KONTROL

Open loop control

Feedforward control

Feedback contol

Page 7: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Studi Kasus

Page 8: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 9: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Block Diagram Open Loop

Control

Page 10: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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.

Page 11: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Block Diagram Feedforward

Control

Page 12: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Feedback Control

Pengukuran dilakukan langsung pada

ketinggian air dalam tangki

Dapat mengatasi gangguan yang tidak

terukur atau tidak termodelkan

Page 13: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Block Diagram Feedback

Control

Page 14: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Pengendalian Sistem

Sederhana

Page 15: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Intuisi Dibalik Pengendalian

Page 16: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kendali Kecepatan atau

Percepatan

Page 17: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kendali Bang-Bang

Page 18: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kendali Bang-Bang Saat

Bekerja

• Optimal untuk mencapai set point

• Tidak baik untuk berada di dekat titik tersebut

Page 19: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kendali Proporsional

Page 20: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Contoh: Kendali Kecepatan

Page 21: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kerja Kendali Proportional

• Menaikkan gain akan mencapai set point lebih cepat

• Dapat menyebabkan overshoot dan bahkan ketidak stabilan

Page 22: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 23: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Step Respon Criteria

Percentage overshoot

Decay ratio

Rise time

Settling time

Page 24: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked
Page 25: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Steady State Error

Misal ada gangguan kontinyu

𝑥 = 𝐹 𝑥, 𝑢 + 𝑑

Kendali P tidak dapat mempertahankan

𝑒 = 0

Mengapa??

Page 26: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 27: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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?

Page 28: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 29: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 30: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 31: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kerja Kendali Derivative

• Damping mengisolasi overshoot dan osilasi

• Tetapi rentan terhadap noise

Page 32: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Efek Kendali Derivative

Berbagai nilai damping tanpa noise

Page 33: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Derivative Memperbesar Noise

Ini menjadi masalah apabila control

output tergantung pada slope (gain

tinggi)

Page 34: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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.

Page 35: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Kerja Kendali PID

Perilaku baik tergantung pada tuning yang baik

Page 36: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Eksplorasi Tuning Kendali PID

Page 37: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 38: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

Tuning Ziegler-Nichols

Respons open-loop terhadap unit step

d adalah deadtime. T time constant

process

K adalah gain process

Page 39: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 40: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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

Page 41: SISTEM KONTROL - mesin.itb.ac.id Kontrol 2013.pdfSejarah Sistem Kontrol 18th Century James Watt’s centrifugal governor for the speed control of a steam engine. 1920s Minorsky worked

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