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
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