DAFTAR ISI
HALAMAN JUDUL ................................................................................... i LEMBAR PENGESAHAN PEMBIMBING ................................................ ii LEMBAR PENGESAHAN DOSEN PENGUJI ............................................ iii HALAMAN PERSEMBAHAN .................................................................... iv HALAMAN MOTTO................................................................................... v KATA PENGANTAR ................................................................................. vii ABSTAKSI .................................................................................................. ix DAFTAR ISI ............................................................................................... x DAFTAR TABEL ....................................................................................... xiii DAFTAR GAMBAR ................................................................................... xiv BAB I PENDAHULUAN ............................................................................ 1 1.1 Latar Belakang ....................................................................................... 1 1.2 Definisi Masalah ..................................................................................... 3 1.3 Batasan Masalah .................................................................................... 3 1.4 Tujuan dan Manfaat ............................................................................... 4 1.5 Sistematika Penulisan ............................................................................. 4 BAB II STUDI PUSTAKA ........................................................................ 6 2.1 Tinjauan pustaka .................................................................................... 6 2.1.1 Analisis Tinjauan Pustaka ............................................................. 7 2.2 Sistem Pengendali................................................................................... 8
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2.2.1 Pengendali Proporsional ................................................................ 12 2.2.2 Pengendali Integral........................................................................ 13 2.2.3 Pengendali Derivatif...................................................................... 15 2.2.4 Pengendali PID ............................................................................. 17 2.2.5 Metode Ziegler-Nichols................................................................. 20 2.3 Logika Fuzzy .......................................................................................... 22 2.4 Sistem Kendali Logika Fuzzy.................................................................. 24 2.4.1 Ruang Input dan Output............................................................... 25 2.4.2 Fuzzifier ...................................................................................... 26 2.4.3 Fuzzy Rule Base.......................................................................... 26 2.4.4 Inference Engine ......................................................................... 29 2.4.5 Defuzzifier ................................................................................. 30 2.5 Persamaan Bernoulli .............................................................................. 31 2.6 Rencana Penelitian.................................................................................. 35 BAB III METODOLOGI .......................................................................... 36 3.1 Pemodelan Matematis Sistem Tangki Air................................................ 37 3.2 Simulasi Sistem dengan Matlab............................................................... 42 3.2.1 Perancangan Simulasi Sistem dengan Matlab Simulink ................. 43 3.2.2 Perancangan Fuzzy Logic Controller (FLC) .................................. 45 3.2.3 Perancangan Kendali PID ............................................................ 47 BAB IV ANALISA DAN PEMBAHASAN SISTEM ................................ 49 4.1 Pengambilan Data .................................................................................. 50 4.1.1 Pengambilan Data Sistem Tangki Air Model Linier........................ 50
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4.1.2 Pengambilan Data Sistem Tangki Air Model Non-linier ................. 53 4.1.3 Perbandingan Respon Sistem Model Linier dan Non-linier............. 55 4.2 Simulasi Sistem Tangki Air dengan Kendali Fuzzy ................................ 55 4.2.1 Simulasi Sistem Tangki Model Linier............................................. 55 4.2.2 Simulasi Sistem Tangki Model Non-linier ...................................... 58 4.3 Simulasi Sistem dengan Kendali PID ..................................................... 61 4.3.1 Simulasi Sistem Tangki Model Linier............................................. 61 4.3.2 Simulasi Sistem Tangki Model Non-linier ...................................... 63 4.4 Simulasi Sistem dengan Kendali PID-Fuzzy ........................................... 66 4.4.1 Simulasi Sistem Tangki Model Linier............................................ 66 4.4.2 Simulasi Sistem Tangki Model Non-linier ..................................... 69 4.5 Perbandingan Kendali Fuzzy, PID, dan PID-Fuzzy .......................... 73 4.6 Pengujian Sistem dengan Perubahan Setpoint................................... 76 4.7 Pengujian Sistem dengan Penambahan Gangguan ............................ 79 BAB V KESIMPULAN DAN SARAN ...................................................... 82 5.1 Kesimpulan ............................................................................................ 82 5.2 Saran ...................................................................................................... 83 DAFTAR PUSTAKA .................................................................................. 84
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DAFTAR TABEL Tabel 2.1 Efek Kontroler (Kp, Ki, Kd) dalam Sistem Loop Tertutup ........... 19 Tabel 2.2 Penalaan Paramater PID dengan Metode Osilasi .......................... 22 Tabel 2.3 Aturan kendali fuzzy.................................................................... 28 Tabel 3.1 FAM untuk Fungsi Keanggotaan Masukan dan Keluaran............. 46 Tabel 4.1 Perbandingan Respon Sistem Linier dan Non-linier ..................... 55 Tabel 4.2 Perbandingan Unjuk Kerja Sistem ............................................... 58 Tabel 4.3 Perbandingan Unjuk Kerja Sistem pada Tangki 2 ........................ 60 Tabel 4.4 Perbandingan Unjuk Kerja Sistem ............................................... 63 Tabel 4.5 Perbandingan Unjuk Kerja Sistem ............................................... 65 Tabel 4.6 Perbandingan Unjuk Kerja Sistem ............................................... 69 Tabel 4.7 Perbandingan Unjuk Kerja Sistem ............................................... 72 Tabel 4.8 Perbandingan Respon dengan Pengendali Berbeda (Linier).......... 73 Tabel 4.9 Perbandingan Respon dengan Model Berbeda.............................. 74 Tabel 4.10 Karakteristik respon sistem terhadap perubahan H2_Set = 0.2m .. 74 Tabel 4.11 Karakteristik respon sistem terhadap perubahan H2_Set = 0.2m .. 76 Tabel 4.12 Karakteristik respon sistem terhadap perubahan H2_Set = 0.3m .. 77 Tabel 4.13 Karakteristik respon sistem terhadap perubahan H2_Set = 0.3m .. 78 Tabel 4.14 Respon sistem dengan penambahan gangguan ............................ 80
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DAFTAR GAMBAR
Gambar 2.1 Pengendali Level Air Berbasis ANFIS .................................... 7 Gambar 2.2 Kurva karakteristik Respon Water Tank .................................. 10 Gambar 2.3 Diagram Blok Kontroler Proposional ...................................... 13 Gambar 2.4 Diagram Blok Kontroler Integral............................................. 14 Gambar 2.5 Diagram Blok Kontroler Derivatif ........................................... 16 Gambar 2.6 Diagram Blok Kontroler PID Struktur Paralel ......................... 18 Gambar 2.7 Kurva Respons Tangga Satuan ............................................... 21 Gambar 2.8 Sistem Untaian Tertutup dengan Alat Kontrol Proporsional..... 21 Gambar 2.9 Kurva Respon Sustain Oscillation ........................................... 21 ~ Gambar 2.10 Fungsi Karakteristik Himpunan Klasik A dan Fuzzy A ......... 24
Gambar 2.11 Struktur Sistem Kendali Logika Fuzzy ................................... 25 Gambar 2.12 Proses Fuzzifikasi................................................................... 26 Gambar 2.13 Grafik Asumsi Respon Sistem Orde 2 .................................... 28 Gambar 2.14 Aliran Fluida dalam Suatu Pipa .............................................. 31 Gambar 2.15 Elemen Zat Cair Bergerak pada Garis Lurus........................... 32 Gambar 2.16 Garis Tenaga dan Tekanan pada Zat Cair ............................... 32 Gambar 2.17 Tangki Terbuka Penampung Fluida ........................................ 34 Gambar 3.1
Diagram Blok Sistem Pengendali Permukaan Air .................. 36
Gambar 3.2
Pemodelan Tangki Air........................................................... 38
Gambar 3.3
Rangkaian Simulasi Tangki Air............................................. 43
Gambar 3.4
Rangkaian Tangki Model Linier ............................................ 43
Gambar 3.5
Rangkaian Tangki Model Non-linier ..................................... 44
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Gambar 3.5
Rangkaian Katup Tangki ....................................................... 44
Gambar 3.6
Masukan fungsi keanggotaan error ....................................... 46
Gambar 3.6
Masukan fungsi keanggotaan d_error.................................... 46
Gambar 3.6
Masukan fungsi keanggotaan keluaran kendali fuzzy ............. 46
Gambar 4.1
Rangkaian Simulasi Sistem pada Simulink ............................ 50
Gambar 4.2
Grafik Tanggapan Sistem ...................................................... 51
Gambar 4.3
Grafik Error Sistem ............................................................... 52
Gambar 4.4
Grafik Perubahan Error Sistem .............................................. 52
Gambar 4.5
Rangkaian Simulasi dengan Sistem Non-linier ..................... 53
Gambar 4.6
Respon Sistem Tangki Air Non-linier................................... 53
Gambar 4.7
Grafik Error Sistem .............................................................. 54
Gambar 4.8 Grafik d_error Sistem ............................................................ 54 Gambar 4.9 Rangkaian Simulasi Sistem dengan Kendali Fuzzy................. 56 Gambar 4.10 Grafik Unjuk Kerja Sistem dengan Kendali Logika Fuzzy...... 57 Gambar 4.11 Rangkaian Sistem Tangki Air Non-linier dengan FLC............ 58 Gambar 4.12 Respon Sistem pada Tangki 1................................................. 59 Gambar 4.13 Respon Sistem Tangki Air Non-linier dengan FLC................. 60 Gambar 4.14 Rangkaian Sistem dengan Kendali PID .................................. 61 Gambar 4.15 Respon Sistem dengan Kendali PID ....................................... 62 Gambar 4.16 Rangkaian Sistem dengan Kendali PID .................................. 63 Gambar 4.17 Respon pada Tangki 1 ............................................................ 64 Gambar 4.18 Respon Sistem dengan Kendali PID ....................................... 65 Gambar 4.19 Rangkaian Sistem dengan Kendali PID-Fuzzy ....................... 66
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Gambar 4.20 Fungsi keanggotaan error ....................................................... 67 Gambar 4.21 Fungsi keanggotaan derror ..................................................... 67 Gambar 4.22 Fungsi keanggotaan output ..................................................... 67 Gambar 4.23 Respon sistem dengan kendali PID-Fuzzy .............................. 68 Gambar 4.24 Rangkaian Sistem dengan Kendali PID-Fuzzy ....................... 69 Gambar 4.25 Fungsi keanggotaan error ....................................................... 70 Gambar 4.26 Fungsi keanggotaan derror ..................................................... 70 Gambar 4.27 Fungsi keanggotaan output ..................................................... 70 Gambar 4.28 Respon pada tangki 1 ............................................................. 71 Gambar 4.29 Respon sistem dengan kendali PID-Fuzzy .............................. 72 Gambar 4.30 Respon sistem dengan masukan h2_set = 0.2m....................... 76 Gambar 4.31 Respon sistem dengan masukan h2_set = 0.3m....................... 77 Gambar 4.32 Respon sistem dengan masukan h2_set = 0.4m....................... 78 Gambar 4.33 Respon Sistem dengan penambahan gangguan ....................... 80
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