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PENGETAHUAN DASAR 

SISTEM KENDALI 

Marwan Effendy, S.T., M.T., Ph.D.

2019

 

Pengetahuan Dasar Sistem Kendali Penulis Marwan Effendy, S.T., M.T., Ph.D. Reviewer Dr. Waluyo Adi Siswanto Dr. Ubaidillah Layout & Desain Cover Ali Himawan ISBN 978-602-361-216-1 Cet. I, September 2019 Copyright©2019 Hak Cipta pada penulis dan dilindungi Undang-Undang

Penerbit Muhammadiyah University Press Gedung I Lantai 1 Sayap Utara Universitas Muhammadiyah Surakarta  Jl. A. Yani Yani Tromol Tromol Pos Pos 1 Kartasura Surakarta 57102 Jawa Tengah - Indonesia Telp : (0271) 717417 ext. 2172 Email : [email protected]

 

KATA PENGANTAR

  ‫ا‬  󰙎 �  󰙎 󰙎‫ع‬ ‫م‬ 󰙎󰙄    󰙎 󰙎 ‫و󰙎ب‬ 󰙎  󐙄‫ا‬ ‫ة‬ 󰙎‫ح‬  󰙎‫ور‬ 󰙎  ‫يك‬ 􀙄  ‫󰙃ته‬  Puji syukur Alhamdulillah dengan rahmat-Nya penulis  berhasil  berhas il men menyeles yelesaikan aikan pembuata pembuatan n buku ajar berjudul “Pengetahuan Dasar Sistem Kendali”. Buku ajar ini ditulis dan disusun berdasarkan catatan kuliah dan pengalaman mengajar mata kuliah Teknik Pengaturan di Jurusan Teknik Mesin UMS sejak tahun 1997.  Hand-ou  Hand-outt  materi perkuliahan ini kemudian dikembangkan oleh penulis untuk mengikuti workshop “ Applied  di UMS” dalam rangka mempersiapkan buku ajar pada  Approach di  Approach tahun 2010 dengan narasumber dari UNS. Setelah jeda dalam kurun beberapa tahun, akhirnya buku ini bisa diselesaikan melalui program buku ajar yang difasilitasi oleh LPPI-UMS tahun 2018 dan berhasil diterbitkan pada tahun 2019. Buku edisi pertama ini disajikan dalam sembilan bab, yakni diawali dari 1. Pengantar sistem kendali dan otomasi, 2. Istilahistilah dalam sistem kendali, 3. Komponen sistem kendali, 4. Dasar-dasar matematika sistem kendali, 5. Fungsi alih sistem kendali, 6. Model matematika fisik fi sik sistem kendali, 7. Karakteristik sistem kendali, 8. Kestabilan sistem kendali, dan 9. Sistem kendali proporsional, integral dan diferensial (PID controler controler). ). Isi buku ini masih sederhana, namun sangat membantu dalam memahami pengetahuan dasar teknik pengendalian di tingkat sarjana, serta  bagi pengampu pengampu yang mengajar mengajar bidang terkait. Ucapan terima kasih kepada: LPPI-UMS yang telah memfasilitasi proses proses pembuatan buku ajar ini, Muhammadiy Muhammadiyah ah University Press yang membantu penerbitannya, Dr. Waluyo Adi Siswanto (UMS) dan Dr. Ubaidillah (UNS) atas “review “ review”, ”, masukan maupun saran-sarannya, serta seluruh rekan-rekan sejawat di UMS atas kontribusi pemikiran dan dukungannya selama pembuatan karya yang masih sederhana ini.

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Penulis menyadari bahwa karya kecil ini masih terbatas sumber-sumber informasinya, sehingga masukan dan sumbangan pemikiran akan diterima dengan lapang hati dalam rangka perbaikan isi tulisan buku ini. Kritik dan saran bisa disampaikan melalui email: Marwan.Eff[email protected]. Akhirnya, selamat membaca dan mempelajarinya! Semoga  bermanfaat bagi anda.

 󰙎 󰙎  󰙎    󰙎  󰙎 󰙎 󰙎 󰙎 󰙎    󰙎  󰙎  󰙎 ‫󰙃ته‬  �‫وب‬ 󐙄‫ا‬ ‫ورحة‬ ‫يك‬ 􀙄 ‫ع‬ ‫󰙄م‬   ‫او‬ Penulis

Marwan Effendy Effendy,, ST. ST. MT. Ph.D.

iv 

 

DAFTAR DAFT AR ISI

Kata Peng Pengantar antar ................. .................................. ................................... ................................... ......................... ........ iii Daftar Isi ............... ................................. ................................... .................................. ................................... ...................... v Daftar Gambar ................. .................................. ................................... ................................... ......................... ........ xiii Daftar Tabel ................ ................................. ................................... ................................... ............................... .............. xix BAB I .......... 1 PENGANTAR PENGANT AR SISTEM SI STEM KEND KENDALI ALI DAN OTOMASI .......... A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... 1 B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. 1 C. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... 2 D. Materi..................................................................................... Materi..................................................................................... 3 1.1. Teknik Kendali dan Teknik Otomasi ................ ........................ ........ 4 1.2. Definisi Definisi Sistem Kendali .................. ................................... ............................ ........... 4 1.3. Mengapa Instrumentasi Diperlukan dalam Pengendalian? Peng endalian? ................ .................................. ................................... ............................ ........... 8 1.4. Peng Pengelompokan elompokan Sistem Kendali ............... ................................ ................. 10 1.4.1. Sistem Sistem Kendali Manual dan Otomatis ........... 10 1.4.2. Sistem Kendali Simpal Terbuka dan Tertutup 12

1.4.3. Sistem kendali kontin kontinyu yu dan diskontin diskontinyu yu ..... 1.4.4. Sistem Sistem kendali servo dan regulator ................ 1.5. Peng Pengaplikasian aplikasian Sistem Kendali................. .................................. ................. 1.6. Orientasi pengendalian/ pengontrolan ................. ..................... E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ...

16 18 19 21 24 25 25 26 27

 v 

 

BAB II ............... ...... ISTILAH-ISTILAH DALAM SISTEM KENDALI ......... A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. C. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... D. Materi..................................................................................... Materi..................................................................................... 2.1. Istilah-Ist Istilah-Istilah ilah Umum dalam Sistem Pengendalian.. 2.2. Kom Komponen-Kom ponen-Komponen ponen Sistem Kendali Otomatis... 2.3. Sistem Kendali Kendali Simpal Tertutu ertutup p dan Bagian  Bagiannyaa................ Bagianny ................................. .................................. ................................... ...................... 2.4. Fenomena Sistem Kendali dan Diagram Baloknya 2.4.1. Sistem kendali simpal terbuka ................ ........................ ........ 2.4.2. Sistem Kendali Simpal Tertutup................. ...................... .....

2.5. Kelebihan dan dan Kekurangan Kekurangan Sistem Sistem Kendali Simpal Tertutup................ ................................. .................................. ................................... ....................... ..... E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ...

29 29 29 30 31 31 42 45 47 49 50 51 51 51 52 53 54

BAB III KOMPONEN SISTEM KENDALI ................................... .................. ......................... ........ A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. C. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... D. Materi..................................................................................... Materi..................................................................................... 3.1. Plant ................ ................................. ................................... ................................... ............................ ........... 3.2. Kontroler (Controller ) .................. ................................... ............................... .............. 3.3. Aktuator ................. .................................. .................................. ................................... ...................... 3.3.1. Aktuator elektrik .................. ................................... ............................ ...........

55 55 55 56 56 57 57 66 67

3.3.2. ................................. ................ ............................ ........... 3.3.3. Aktuator Aktuator mekanik pneumatik ................................... ................. ....................... ..... 3.3.4. Aktuator hidrolik ................. .................................. ............................ ...........

72 73 74

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3.4. Sensor dan Tranduser .................. ................................... ............................... .............. 3.4.1. Spesifikasi sensor dan tranduser .................. ...................... 3.4.2. Klasifikasi Klasifikasi sensor dan tranduser ................ ..................... ..... 3.5. Pendeteksi Galat (Error Detector ) ............... ............................. .............. E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ... BAB IV DASAR-DASAR MATEMATIKA SISTEM KENDALI ....... A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... .....

B. C. D.

Deskripsi Singkat ................ .................................. ................................... ............................... .............. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... Materi..................................................................................... Materi..................................................................................... 4.1. Bilangan Kom Kompleks pleks................. .................................. ................................... ...................... 4.2. Persamaan Persamaan Diferensial ................. .................................. ............................... .............. 4.2.1. Persa Persamaan maan diferensial linear ................ ........................... ........... 4.2.2. Persa Persamaan maan diferensial non-linear ................. ..................... 4.3. Polinomial ................. ................................... ................................... .................................. ................. 4.4. Transformasi Transformasi Laplace ................ ................................. .................................. ................. 4.4.1. Teorema Teorema transformasi Laplace....................... Laplace........................... 4.4.2. Transformasi Transformasi Laplace balik ................ .............................. .............. 4.4.3. Ur Uraian aian pecahan parsial jika F(s) melibatkan pole berbeda ............... ................................ ................................... ....................... ..... 4.4.4. Ur Uraian aian pecahan parsial jika F(s) melibatkan pole bernilai sama ................. .................................. ............................ ........... 4.4.5. Ur Uraian aian pecahan parsial jika F(s) melibatkan pole kompleks kompleks konyugasi konyugasi................ ................................. ................. 4.4.6. Pengg Penggunaan unaan MATLAB MATLAB untuk menguraikan

75 76 77 86 88 89 89 90 91

93 93 93 94 95 95 96 97 98 98 99 103 105 107 109 110

pecahan parsial ................ ................................. .................................. ................. 112 4.5. Matrik ........................................................................... 115 4.5.1. Matrik segitiga ................. .................................. .................................. ................. 118

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4.5.2. Matrik diagonal .................. ................................... ............................... .............. 118 4.5.3. Matrik simetris................. .................................. .................................. ................. 119 4.5.4. Matrik satuan ................ ................................. ................................... ...................... 119 4.5.5. Tr anpose ................................... .................. .............. 4.5.6. Tranpose Minor danmatrik kofaktor kofakto r ............................ ........... ............................... ............................... .............. 4.5.7. Determinan matriks ................. .................................. ......................... ........ 4.5.8. Adjoint matrik.................. ................................... .................................. ................. 4.5.9. Invers Invers matrik ................. .................................. ................................... ...................... E. Rangkuman ................. .................................. ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................ .................................. ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ...

120 120 121 126 128 130 130 130 133 134

BAB V FUNGSI ALIH SISTEM KENDALI.........................................  ......................................... A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. C. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... D. Materi..................................................................................... Materi..................................................................................... 5.1. Diagram Blok/ Ko Kotak tak................ ................................. .................................. ................. 5.1.1. Diagram blok susunan seri ................ .............................. ..............

135 135 135 136 137 137 138

5.1.2. Diagram blok susunan paralel ................ ........................ ........ 5.1.3. Sistem kendali loop tertutup ................ ........................... ........... 5.1.4. Sistem kendali loop tertutup tertutup dengan gangguan ................. .................................. ................................... .......................... ........ 5.1.5. Bentuk kanonik sistem kendali umpanbalik 5.1.6. Sistem umpanbalik satuan ................. ............................... .............. 5.1.7. Atur Aturan an aljabar diagram blok dan penggunaannya penggunaann ya .................. ................................... ............................... ..............

139 139 142 144 145 146

5.1.8. Sistem SISO, SIMO dan dan MIMO MIMO .................. ....................... ..... 150 5.2. Diagram Aliran Siny Sinyal al (Signal Flow Graph) ........... 153 5.2.1. Istilah-is Istilah-istilah tilah dalam diagram aliran siny sinyal al .... 153 5.2.2. Hukum Mason ................. .................................. .................................. ................. 155

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5.3. Transformasi Diagram Blok ke Diagram Aliran Aliran Sinyal ............................................................................ 158 5.4. Aplikasi MATLAB MATLAB untuk Menentukan Fungsi Fungsi

E. F.

Alih Blok ................. .................................. ................................... .................... 5.4.1.Diagram Sistem kendali simpal terbuka simpal (Open loop .. control system) ................................................. 5.4.2. Sistem kendali umpan umpan balik satuan ................ 5.4.3. Sistem kendali simpal simpal tertutup dengan umpan balik ............... ................................ ................................... ....................... ..... 5.4.4. Sistem kendali jaring jaring tertutup dengan umpan balik balik banyak banyak loop loop ................ ................................. ................. Rangkuman.................. ................................... ................................... ................................... ...................... ..... Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... ..............

160 160 161 162 162 165 165

G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... 166 H. Tugas ................. ................................... ................................... .................................. .................................. ................. 172 I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ... 173 BAB VI ........... MODEL MATEMATIKA FISIK SISTEM KENDALI ......... A. Kom Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. C. Peta Konsep.................. ................................... .................................. ................................... ....................... .....

D.

Materi..................................................................................... Materi ..................................................................................... 6.1. Sistem mekanis..................... mekanis...................................... ................................... ....................... ..... 6.1.1. Sistem mekanika translasi............... ................................ ................. 6.1.2. Sistem mekanika rotasi ................. ................................... ...................... 6.2. Sistem susunan roda gigi gigi............................................ ............................................ 6.3. Sistem hidrolik ............... ................................. ................................... ............................ ........... 6.3.1. Pompa dan motor motor hidrolik................. ............................... ..............

175 175 175 176 176 179 180 182 184 187 188

6.3.2. Valv Valvee hidrolik ................ ................................. ................................... ...................... 191 6.3.3. Aktuator linier hidrolik ................ .................................. ...................... 193 6.4. Sistem Liquid-Level  ................................................... 196 6.4.1. Sistem liquid-level sa  satu tu tangki tangki ................ ........................ ........ 197 6.4.2. Sistem liquid-level dua tangki ................ ........................ ........ 199

ix 

 

6.5. Sistem Pneumatik ................ ................................. ................................... ....................... ..... 201 6.5.1. Pneumatik ......................................................... 201 6.5.2. Aktuator pneumatik ............................. ............ ............................ ........... 202 6.6. Sistem termal ............... ................................. ................................... ............................... .............. E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ...

204 207 207 208 209 209

BAB VII KARAKTERISTIK SISTEM KENDALI  ................................ 211

A. B. C. D.

Kompetensi Dasar dan Indikator ............... Kompetensi ................................. ....................... ..... Deskripsi Singkat ................ .................................. ................................... ............................... .............. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... Materi..................................................................................... Materi..................................................................................... 7.1. Karakteristik Respon Waktu ............... ................................. ....................... ..... 7.2. Karakteristik Sistem Orde Satu................. .................................. ................. 7.2.1. Tanggapan sistem orde satu terhadap input step ................ ................................. .................................. ................................... ...................... 7.2.2. Tanggapan sistem orde satu terhadap input ramp ................ .................................. ................................... .................................. ................. 7.2.3. Tanggapan sistem orde satu terhadap input impuls ................ .................................. ................................... ............................... .............. 7.2.4. Karakteristik tanggapan tanggapan sistem sistem orde satu satu ..... 7.3. Karakteristik Sistem Orde Dua ................. .................................. ................. 7.3.1. Karakteristik tanggapan tanggapan sistem orde dua (under-damped) .................. ................................... ............................... ..............

211 211 212 212 213 215 215 218 219 220 221 224

7.3.2. Karakteristik tanggapan tanggapan sistem orde dua (critically damped) ................. ................................... .......................... ........ 227 7.3.3. Karakteristik tanggapan tanggapan sistem orde dua E. F.

(over-damped).................. ................................... .................................. ................. 227 Rangkuman.................. ................................... ................................... ................................... ...................... ..... 228 Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. 228

 x 

 

G. Soal-soal ................ ................................. .................................. ................................... ............................. ........... 228 H. Tugas ................. ................................... ................................... .................................. .................................. ................. 229 I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ... 230 BAB VIII ................ ......................... ........ KESTABILAN SISTEM KENDALI ................................. Kompetensi petensi Dasar dan Indikator ............... ................................. ....................... ..... A. Kom B. Deskripsi Singkat ................ .................................. ................................... ............................... .............. C. Peta Konsep.................. ................................... .................................. ................................... ....................... ..... D. Materi..................................................................................... Materi..................................................................................... 8.1. Definisi Kesta Kestabilan bilan............... ................................ ................................... ....................... ..... 8.2. Kestabilan sistem ........................................................

8.3. Kriteria kestabilan Hurwitz ................ .................................. ....................... ..... 8.4. Kriteria kestabilan Routh................ ................................. ............................ ........... 8.5. Kasus-Kasus Khusus pada Kriteria Kriteria Kestabilan Kestabilan Routh ................. .................................. .................................. ................................... .......................... ........ 8.5.1. Kasus dengan suku-suku nol pada kolom pertama ................. ................................... ................................... ............................ ........... 8.5.2. Kasus dengan suku-suku nol pada kolom pertama dan yang sebaris ............... ................................ ................. 8.6. Kriteria Kestabilan Kestabilan Pecah Pecahan an Kontinyu Kontinyu................. ...................... ..... 8.7. Aplikasi Kriteria Kestabi Kestabilan lan ................ .................................. ....................... ..... E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-Soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan ................ .................................. ................................... .................................. .................... ...

231 231 231 232 232 232 235 239 245 248 248 250 253 257 258 258 259 262 262

BAB IX KENDALI KEND ALI PROPORSIONAL, PROPORSIO NAL, INTEGRAL DAN DIFERENSIAL (PID CONTROLLER) ................................... ................. ...................... 265

A. B. C.

Kompetensi Dasar dan Indikator ............... Kompetensi ................................. ....................... ..... 265 Deskripsi Singkat ................ .................................. ................................... ............................... .............. 265 Peta Konsep.................. ................................... .................................. ................................... ....................... ..... 266

 xi

 

D.

Materi..................................................................................... Materi..................................................................................... 9.1. Kendali Proporsional ................ ................................. .................................. ................. 9.2. Kendali Integral ................ ................................. ................................... .......................... ........ 9.3. Kendali Proporsional-Integral ............... ................................. ...................... 9.4. Kendali Proporsional-Diferensial................ .............................. .............. 9.5. Kendali Proporsional-Integral-Diferensial .............. E. Rangkuman.................. ................................... ................................... ................................... ...................... ..... F. Pertany ertanyaan aan Kunc Kuncii ................ .................................. ................................... ............................... .............. G. Soal-soal ................. .................................. .................................. ................................... ............................. ........... H. Tugas ................. ................................... ................................... .................................. .................................. ................. I. Daftar Bacaan Tambahan .................. ................................... .................................. .................

266 268 269 271 272 274 276 277 277 278 279

DAFT AFTAR AR PUSTAKA PUSTAKA................. ................................... ................................... .................................. ................. 280 INDEKS ................. ................................... ................................... .................................. ................................... ...................... 282 GLOSARIUM GLOS ARIUM ................. .................................. ................................... ................................... ............................ ........... 287

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DAFTAR DAFT AR GAMBAR GA MBAR

Gambar 1.1 Gambar 1.2 Gambar 1.3 Gambar 1.4 Gambar 1.5 Gambar 1.6 Gambar 1.7 Gambar 1.8 Gambar 1.9 Gambar 1.10 Gambar 1.11 Gambar 1.12 Gambar 1.13 Gambar 1.14 1.14 Gambar 1.15 Gambar 1.16 Gambar 2.1 Gambar 2.2

Robot .................. Robot ................................... .................................. .................................. ................. Gambaran sistem pengendalian................ ........................ ........ Indra peraba untuk pengukuran............... ....................... ........ Sistem pengendalian ketinggian cairan secara manual ................. ................................... ................................... ............................... .............. Sistem pengendalian ketinggian cairan secara otomatis................................................................. Diagram blok sistem kendali jelajah kendaraan Sistem kendali putaran motor simpal terbuka Diagram blok sistem kendali temperatur setrika listrik................. ................................... ................................... ...................... ..... Sistem kendali putaran motor simpal tertutup Kendali sistem pengendalian kontin kontinyu yu ............ Kendali sistem pengendalian digital ................ Sistem pengendalian servo ................ ................................. ................. Sistem pengendalian regulator ............... .......................... ........... Sistem kendali kecepatan idle ............................ ................. ........... Respon transien sistem pengendalian .............. Respon transien sistem kendali roda cetak ( printwheel  printwheel)) ...................... .............................................. ........................................ ................ Pesaw esawat at terbang A380 ................ ................................. ......................... ........ Sistem pencernaan pada manusia.....................

5 6 9 11 12 13 13 15 15 16 18 18 19 21 22 24 32 32

Gambar 2.3 Gambar 2.4 Gambar 2.5 Gambar 2.6

Diagram blok ............... ................................ ................................... ....................... ..... Continuous StirredStirred-T Tank Reactor (CSTR) ........ Diagram blok CSTR ................ ................................. ............................ ........... Diagram blok variabel CSTR ............... ............................. ..............

33 34 35 36

Gambar 2.7 Gambar 2.8 Gambar 2.9

Sistem kendali simpal terbuka ............... .......................... ........... Sistem kendali simpal tertutup ................. ......................... ........ Sistem pengendalian ny nyala ala api kompo komporr gas ....

36 37 38

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Gambar 2.10 Sistem pengendalian level cairan secara secara otomatis................................................................. Gambar 2.11 Sistem kendali kontin kontinyu yu ................. ................................... ...................... Gambar 2.12 Sistem kendali digital ................ ................................. ......................... ........ Gambar 2.13 Diagram blok sistem kendali .................. ............................. ........... Gambar 2.14 Sistem kendali simpal tertutup ................. ......................... ........ Gambar 2.15 Diagram blok arah berjalan ................. ............................... .............. Gambar 2.16 Diagram blok orang mengambil barang .......... Gambar 2.17 Diagram blok arah mobil ............... ................................. ...................... Gambar 2.18 Diagram blok metabolisme tubuh ................. .................... ... Gambar 2.19 Diagram blok kendali engine-speed..................  .................. Gambar 2.20 Diagram blok kendali simpal terbuka .............. Gambar 2.21 Sistem kendali gov governor ernor ................. ................................... ...................... Gambar 3.1 Sistem kendali loop tertutup dengan kontroler pada lintasan maju............... ............................. .............. Gambar 3.2 Feed-forward control pada pengaturan aliran .... Gambar 3.3 Sistem kendali loop tertutup dengan kontroler pada lintasan umpan balik ............... Gambar 3.4 Feedback controller pada pengaturan aliran....... Gambar 3.5 Sistem kendali loop tertutup disusun seri dengan kontroler .................. ................................... ............................... .............. Gambar 3.6 Gambar 3.7 Gambar 3.8

Sistem kendali sistem loop tertutup dengan model following model ................ ......................  following controller  controller .................................. Kontroler mekanik sistem kemudi ................ ................... ... Sistem kemudi hidrolik ................ ................................. ...................... .....

39 40 41 43 46 48 48 48 49 49 49 50 59 59 60 60 60 61 62 63

Gambar 3.9 Gambar 3.10 Gambar 3.11 Gambar 3.12 Gambar 3.13 Gambar 3.14 Gambar 3.15 Gambar 3.16 Gambar 3.17

Kontroler proporsional hidrolik................ ........................ ........ Sistem elektrik pada power window kendaraan Dental handpiece dengan sistem pneumatik ..... Robott di industri perakitan otomo Robo otomotif tif ................ Solenoid linier ................. .................................. ................................... ...................... Katup solenoid................ ................................. ................................... ...................... Rangkaian DCDC-chopper chopper  ................. ................................... ....................... ..... Inverter Inv erter ................. ................................... ................................... ............................... .............. Aktuator motor DC ................. .................................. ............................ ...........

63 64 65 66 68 69 70 71 73

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Gambar 3.18 Aktuator pneumatik .................. ................................... ......................... ........ Gambar 3.19 Aktuator hidrolik ................. .................................. ............................... .............. Gambar 3.20 Gambar 3.21 Gambar 3.22 Gambar 3.23 Gambar 3.24 Gambar 3.25 Gambar 3.26 Gambar 3.27 Gambar 3.28 Gambar 3.29 Gambar 4.1 Gambar 4.2 Gambar 4.3 Gambar 4.4 Gambar 5.1 Gambar 5.2 Gambar 5.3

Sensor potensiometer rotari ................. ............................... .............. Sensor pelampung................ ................................. ............................... .............. Sensor ultrasonik .................. ................................... ............................... .............. Takometer ............... ................................. ................................... ............................ ........... Pengukur tekanan ................ ................................. ............................... .............. Bimetal ................. ................................... ................................... ............................... .............. Ther mokopel ................ Thermokopel .................................. ................................... ...................... ..... Error detector  detector ................. .................................. ................................... ....................... ..... Summing amplifier................................................. amplifier................................................. ................. ........ Non-inverting Non-in verting summing amplifier amplifier  ......................... Bidang kom kompleks pleks S .................. ................................... ............................ ........... Bidang kom kompleks pleks F(s) ................ ................................. ......................... ........ Rangkaian RLC ............... ................................ ................................... ...................... Pendulum sederhana ................. .................................. ......................... ........ Diagram blok satu penguatan ................ ........................... ........... Diagram blok dua penguatan................. ............................ ........... Diagram blok satu penguatan hasil penggabungan penggabung an ................ ................................. ................................... ...................... Gambar 5.4 Diagram blok dua penguatan paralel .............. Gambar 5.5 Diagram blok satu penguatan hasil penggabungan penggabung an ................ ................................. ................................... ...................... Gambar Gam bar 5.6 Sistem pengendalian loop tertutup umpan

74 74 78 79 80 81 82 83 86 86 87 88 96 96 97 98 138 138 138 139 139

 bal ik pos  balik positi itiff ........................................................................................................ 140 Gambar Gam bar 5.7 Sistem pengendalian loop tertutup umpan  balik  bal ik ne negati gatiff ...................................................................................................... 141 Gambar 5.8 Sistem pengendalian loop tertutup dengan gangguan ................ .................................. ................................... ............................ ........... 142 Gambar Gam bar 5.9 Sistem pengendalian Gambar 5.8 dengan 143 Gambar Gam bar 5.1 5.100 U(s)=0 Sistem ............................................................. pengendalian Gambar 5.8 dengan R(s)=0 ............................................................. 143 Gambar Gamb ar 5.11 Bentu Bentuk k kanon kanonik ik sistem kend kendali ali umpan umpanbalik balik 144

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Gam Gambar bar 5.1 5.122 Sistem umpanbalik satuan ...... ............ ............ ............ ......... ... 146 Gambar Gam bar 5.1 5.133 Diagram blok dengan dua loop yang saling  ber singgu  bersin ggunga ngan n .............................................................................................. Gambar Gam bar 5.1 5.144 Diagram blok kasus Gambar 5.13 ..... ........... ........... ..... Gambar Gam bar 5.1 5.155 Diagram blok perubah perubahan an Gambar 5.14 ..... ....... .. Gambar 5.16 Diagram blok kendali dengan dengan dua masukan dan dua keluaran.................. ................................... ............................... .............. Gamb Ga mbar ar 5. 5.17 17 Diagram aliran sin sinyal yal ................................... Gambar Gam bar 5.1 5.188 Bagian-bagi Bagian-bagian an diagram aliran sinyal ...... ........... ..... Gamb Ga mbar ar 5. 5.19 19 Simpul tiruan................................................. Gambar Gam bar 5.2 5.200 Diagram aliran sinyal dengan loop lebih dari satu ......................................................... Gambar Gam bar 5.2 5.211 Diagram aliran sinyal dengan satu loop ..... Gambar Gam bar 5.2 5.222 Diagram aliran sinyal dengan loop lebih dari satu ......................................................... Gamb Ga mbar ar 5. 5.23 23 Diagram blok ................................................. Gamb Ga mbar ar 5. 5.24 24 Diagram aliran sin sinyal yal .................................. Gamb Ga mbar ar 5. 5.25 25 Diagram blok multi-loop ............................. Gambar 6.1 Fenomena gerak................. .................................. .................................. ................. Gambar 6.2 Model matematika hukum Newton ................. Gambar 6.3 Sistem suspensi mobil................ ................................. ......................... ........ Gambar 6.4 Gambar 6.5 Gambar 6.6

146 148 149 151 153 153 154 155 156 157 158 159 163 177 179 180

Sistem mekanika translasi ................. .................................. ................. 181 Diagram blok sistem mekanika translasi ......... 182 Sistem mekanika rotasi ................. .................................. ...................... ..... 183

Gambar 6.7 Gambar 6.8 Gambar 6.9 Gambar 6.10 Gambar 6.11 Gambar 6.12

Diagram blok sistem mekanika rotasi ............. Susunan roda gigi gigi................................................ ................................................ Skema susunan gear gear............................................ ............................................ Diagram blok diagram sistem gear ................ .................... Konstruksi Kons truksi sistem transmisi hidrolik ............... Diagram blok transmisi hidrolik .................. ....................... .....

184 184 185 187 188 191

Gambar 6.13 Gambar 6.14 Gambar 6.15 Gambar 6.16

Karakteristik val Karakteristik valve ve hidrolik ................ .............................. .............. Diagram blok val valve ve hidrolik ............................. ..................... ........ Aktuator linear hidrolik ......................... ....... ............................. ........... Diagram blok aktuator hidrolik .................... ... .................... ...

192 193 194 195

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Gambar 6.17 Penguat hidrolik ................ ................................. .................................. ................. 195 Gambar 6.18 Diagram blok penguat hidrolik................. ......................... ........ 196 Gambar 6.19 Sistem liquid-level s  satu atu tangki .......................... .................. ........ Gambar 6.20 Diagram blok sistem liquid-level satu tangki pada Gambar 6.19................. .................................. ............................... .............. Gambar 6.21 Sistem liquid-level dua tangki .................. .......................... ........ Gambar 6.22 Diagram blok sistem liquid-level dengan dua tangki Gambar 6.21 ................. .................................. ............................ ........... Gambar 6.23 Sistem pneumatik ................. .................................. ............................... .............. Gambar 6.24 6.24 Diagram blok blok sistem sistem pneumatik pneumatik pada Gambar 6.23 ................. .................................. ................................... ....................... .....

197

Gambar pneumatik ................................... .................. ......................... Gambar 6.25 6.26 Aktuator 6.26 Diagram b blok lok aktuator aktuator pneumatik pada ........ Gambar 5.25 ................. .................................. ................................... ....................... ..... Gambar 6.27 Sistem termal................ .................................. ................................... ...................... ..... Gambar 6.28 Diagram blok sistem termal pada Gambar 6.27 Gambar 7.1 Sistem orde satu................. .................................. .................................. ................. Gambar 7.2 Respon transien sistem orde satu terhadap input step dengan K=1 ................. .................................. ...................... ..... Gambar 7.3 Respon transien sistem orde satu terhadap input step dengan K≠1 ................. .................................. ...................... .....

203

Gambar 7.4

199 200 200 201 202

204 205 207 215 216 217

Respon transien sistem orde satu dengan input ramp ................. ................................... ................................... ......................... ........ 219

Gambar 7.5 Gambar 7.6 Gambar 7.7 Gambar 7.8 Gambar 8.1 Gambar 8.2 Gambar 8.3 Gambar 8.4 Gambar 8.5 Gambar 8.6

Respon transien sistem orde satu dengan input impuls ................. .................................. ................................... ....................... ..... Sistem orde dua ................. .................................. .................................. ................. Respon transien sistem orde dua ................. ...................... ..... Respon transien orde dua under-damped under-damped  ......... ........... Sistem stabil dan tidak stabil .................. ............................. ........... Respon sistem stabil ................ ................................. ............................ ........... Respon sistem tak stabil ................. ................................... ...................... Sistem stabil............... ................................. ................................... ......................... ........ Sistem tidak stabil............................ stabil.............................................. ...................... Respon sistem kendali dan kedudukan pole pada bidang-s....................................................... bidang-s.......................................................

220 221 223 224 233 234 235 235 236 238

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Gambar 8.7 Gambar 8.8 Gambar 8.9 Gambar 8.10 Gambar 8.11 Gambar 9.1 Gambar 9.2 Gambar 9.3

Determinan Hurwitz ................ .................................. .......................... ........ Tabulasi Routh atau susunan Routh [5] ........... Kedudukan pole-pole contoh 8.9 ................. ...................... ..... Kedudukan pole-pole contoh 8.10 ................. .................... ... Diagram blok sistem kendali .................. ............................. ........... Diagram kotak kotak sistem kendali ................ ........................... ........... Diagram kotak kotak kendali proporsional (P) ......... Diagram kotak kendali proporsional dalam alih Laplace ............... ................................. ................................... ......................... ........ Diagram kotak kendali integral (I)............... (I).................... ..... Diagram kotak kendali integral dalam alih

240 245 252 253 257 267 268

Laplace ................. ................................... ................................... ............................... .............. Gambar 9.6 Diagram kotak kendali proporsional-integral (PI) ................ ................................. .................................. ................................... ....................... ..... Gambar 9.7 Diagram kotak kendali proporsional-integral dalam alih Laplace .................. ................................... ............................ ........... Gambar 9.8 Diagram kotak kendali proporsionaldiferensial (PD) ............... ................................ ................................... ...................... Gambar 9.9 Diagram kotak kendali proporsionaldiferensial ............... ................................. ................................... ............................ ........... Gambar 9.10 Diagram kotak kendali proporsionalintegral-diferensial (PID)................ ................................. .................... ... Gambar 9.11 Diagram kotak kotak kendali kendali PID dalam alih

271

Gambar 9.4 Gambar 9.5

269 270

271 272 273 274 275

Laplace ................. ................................... ................................... ............................... .............. 276

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DAFTAR TABEL

Tabel 4.1 Tabel 5.1. Tabel 5.2.

Tabel transformasi Laplace [4] ................. ............................... .............. 102 Tranformasi diagram blok [1] ............... ................................ ................. 147 Transformas ransformasii diagram blok ke diagra diagram m sinyal.... 159