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&section=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.