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DESAIN KONTROL PENDULUM TERBALIK
MENGGUNAKAN METODE LINEAR QUADRATIC
REGULATOR
TUGAS AKHIR
Diajukan Untuk Memenuhi Salah Satu Persyaratan Akademik dalam
Menyelesaikan Program Sarjana (S-1) Teknik
Disusun Oleh :
MUHAMAD ROKIM MUSLIM
201110130311045
JURUSAN TEKNIK ELEKTRO
FAKULTAS TEKNIK
UNIVERSITAS MUHAMMADIYAH MALANG
2016
KATA PENGANTAR
Dengan memanjatkan puji syukur kehadirat Allah SWT. Atas rahmat serta
hidayah-Nya sehingga penulis dapat menyelesaikan tugas akhir yang berjudul :
“DESAIN KONTROL PENDULUM TERBALIK MENGGUNAKAN
METODE LINEAR QUADRATIC REGULATOR”.
Dalam mewujudkan semua yang lebih baik, kami selalu berhadapan
dengan segala macam hambatan. Tidak lain halnya dalam pembuatan Laporan
Tugas Akhir ini, banyak hambatan yang harus penulis lewati, tetapi berkat
bantuan dari beberapa pihak akhirnya penulis dapat melampauinya dengan lancar.
Penulis menyadari bahwa didalam penulisan laporan ini tidak terlepas dari
bimbingan dan pengarahan dari para dosen Universitas Muhammadiyah Malang
serta pihak – pihak yang telah tulus ikhlas memberikan bantuan baik secara moril
dan spiritual. Semoga amal kebaikan serta keikhlasan mereka mendapat balasan
setimpal dari Allah SWT.
Penulis menyadari sepenuhnya bahwa dalam penulisan tugasakhir ini
masih banyak kekurangan dan keterbatasan. Oleh karena itu penulis
mengharapkan saran yang membangun agar tulisan ini bermanfaat bagi
perkembangan ilmu pengetahuan dan perkembangan teknologi kedepan.
Malang, 29 April 2016
Muhamad Rokim Muslim
DAFTAR ISI
LEMBAR JUDUL .................................................................................................. i
LEMBAR PERSETUJUAN ................................................................................. ii
LEMBAR PENGESAHAN ................................................................................. iii
LEMBAR PERNYATAAN ................................................................................. iv
ABSTRAK .............................................................................................................. v
ABSTRACT ........................................................................................................... vi
KATA PENGANTAR ......................................................................................... vii
DAFTAR ISI ....................................................................................................... viii
DAFTAR GAMBAR .............................................................................................. x
DAFTAR TABEL ............................................................................................... xii
BAB I PENDAHULUAN ....................................................................................... 1
1.1 Latar Belakang .................................................................................................. 1
1.2 Rumusan Masalah ............................................................................................. 2
1.3 Tujuan ............................................................................................................... 2
1.4 Batasan Masalah ............................................................................................... 2
1.5 Metodelogi Penelitian ....................................................................................... 2
1.6 Sistematika Penulisan ....................................................................................... 2
BAB IILANDASAN TEORI ................................................................................. 4
2.1 Sistem Pendulum Terbalik ................................................................................ 4
2.1.1 GambaranUmum Pendulum Terbalik ................................................... 4
2.1.2 AnalisaMatematisdanPersamaanSistem ................................................ 5
2.1.3 Transfer Function .................................................................................. 8
2.1.4 State - Space .......................................................................................... 9
2.1.5 Persamaan State-Space .......................................................................... 9
2.2 Linear Quadratic Regulator ........................................................................... 11
2.2.1 GambaranUmum Linear Quadratic Regulator ................................... 12
2.2.2 Quadratic Optimal Regulator System ................................................. 13
2.3 Pole Placement ............................................................................................... 16
2.4 State Observer ................................................................................................. 17
2.4.1 Minimum Order Observer ................................................................... 18
BAB III PERANCANGANSISTEM .................................................................. 24
3.1 PerancanganSistem Pendulum Terbalik.......................................................... 24
3.1.1 PerancanganState-Space Pendulum Terbalik ..................................... 24
3.1.2 PerancanganKontrol LQR .................................................................. 26
3.1.3 PerancanganKontrol LQR MenggunakanMetode Pole Placement .... 27
3.1.4 Perancangan Minimum Order Observer ............................................. 29
3.1.5 PerancanganKarakteristikResponSistem ............................................. 31
BAB IV HASIL PERANCANGAN SISTEM .................................................... 32
4.1 HasilPerancangan State – SpacePendulum Terbalik ...................................... 32
4.2 HasilPerancanganKontrol LQR ...................................................................... 34
4.3 HasilPerancanganKontrol LQR MenggunakanMetodePole Placement ......... 47
4.4 HasilPerancanganMinimum Order Observer .................................................. 50
BAB V PENUTUP ................................................................................................ 54
5.1 Kesimpulan ..................................................................................................... 54
5.2 Saran ............................................................................................................... 54
DAFTAR PUSTAKA
LAMPIRAN
DAFTAR PUSTAKA
[1] MohdSyazwiHelmiBin Jashari, Automatic Inverted Pendulum Control
System. Thesis, Universiti Malaysia Pahang, Pahang, 2013.
[2] NetranjeebLenka, Modeling and Controller Design for an Inverted
Pendulum System. Thesis, National Institute of Technology, Rourkela,
2011.
[3] Ogata Katsuhiko. 2002. Madern Control Engineering. Tehran: Aeeizh.
[4] O Sename. 2015. Pole placement control: state space and polynomial
approaches (lecture). France
[5] Reza DwiImami, DesainKontrolInverted Pendulum Dengan Metode
Kontrol Robust Fuzzy, Dissertation, UniversitasDiponegoro.
[6] The “Inverted Pendulum, Analysis, Design and Implementation”, a
collection of MATLAB functions, scripts, and Simulink models, IIEE
Visionaries. Document Version 1.0, developed by Khalil Sultan, B.E. in
Industrial Electronics, Institute of Industrial Electronics Engineering
(IIEE),PCSIR , Karachi, Pakistan, 2003.
[7] University of Michigan, dkk. Inverted Pendulum: System Modeling. 8
januari 2016.
http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulu
m§ion=SystemModeling.
[8] VelchuriSirisha, 2014. A Comparative study of controllers for stabilizing a
Rotary Inverted Pendulum. International Journal of Chaos, Control,
Modelling and Simulation (IJCCMS) Vol.3, No.1/2.
[9] Wikipedia. 26 Desember 2015. https://en.wikipedia.org/wiki/Linear-
quadratic_regulator.
[10] Wikipedia.26 Desember 2015.
https://en.wikipedia.org/wiki/State_observer.
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