PERANCANGAN DAN SIMULASI KONTROLER JST UNTUK …digilib.its.ac.id/public/ITS-Master-12854-Presentation.pdf · 1 Tesis TE 2099 PERANCANGAN DAN SIMULASI KONTROLER JST UNTUK PENGENDALIAN

1

Tesis TE 2099

PERANCANGAN DAN SIMULASI KONTROLER JSTUNTUK PENGENDALIAN GERAKAN HOVERPADA HELIKOPTEROleh

R. Ade Supriyadi2207202203

Bidang Studi Teknik Sistem PengaturanJurusan Teknik ElektroFakultas Teknologi IndustriInstitut Teknologi Sepuluh NopemberSurabaya2010

PembimbingIr. Katjuk Astrowulan MSEEIr. Rusdhianto Effendie AK, M.T.

2

PENDAHULUAN

● Permasalahan– Pembentukan formulasi dinamika sistem gerakan hover– Pengendalian gerakan hover menggunakan metode JST

● Tujuan– Mengembangkan skema serta algoritma pengendalian– Membuat simulasi pengaturan gerakan hover menggunakan JST

● Batasan– Gerakan hover– Jenis pesawat UH-60 dan Lynx

3

MODELLING

● Interaksi antara sub system– Fuselage– Main Rotor– Tail Rotor– Empennage– Fuselage

● Menerapkan body axes– Pusat di central of gravity (c.g)– Titik c.g dapat berpindah

4

KOMPONEN HELIKOPTER

5

BLADE FLAPPING

6

FORCE & MOMENT

7

CONTROL

8

FORCE & MOMENTFormulasi

F = F R F TR F f F tp F fn

M = M R M TR M f M tp M fn

Translasional

u = −wq−vr XM a

− g sin

v = −ur−℘ YM a

− g cossin

w = −vp−uq ZM a

− g coscos

RotationalI xx p = I yy− I zzqr I xz r pq LI yy q = I zz− I xxrp I xz r

2− p2 MI zz r = I xx− I yy pq I xz p−qr N

9

ROTOR UTAMA - 1

ForcesX hw = T 1cw

Y hw = −T 1sw

Z hw = −T

Moments

LH =−N b

2K 1s

M H =−N b

2K 1c

N H = CQ R2R3 I R

10

ROTOR UTAMA - 2

X hw = ∑i=1

N b

∫i=1

R

{− f z−mazbii cosi − f y−ma ybi sini maxbcosi}drb

Y hw = ∑i=1

N b

∫i=1

R

{ f z−mazbiisini− f y−ma ybi cosi ma xbsini}drb

Z hw = ∑i=1

N b

∫i=1

R

f z−mazbmxbiidrb

2C xw

a0 s =X hw

12R2R2 s a0

2C yw

a0 s =Y hw

12R2R2 s a0

2C zw

a0 s =Z hw

12R2R2 s a0

= −2CT

a0 s

11

ROTOR EKOR - 1

Forces & MomentsX T = T T 1cT

Y T = T TZ T = −T T 1sT

LT = hT Y TM T = lTx cgZ T − QT

N T = −lTxcgY T

ThurstT T = CT T

T RT 2RT

2

12

ROTOR EKOR - 2

Y T = T RT 2 sT a0T RT

2 CT Ta0T sT F TCT T =

T TT RT

2RT2

2CT T

a0T sT = *

3 132 zT−0T

2T21sT

*

F T = 1 − 34S fnRT

2

13

FUSELAGE - 1

Forces

X f = 12V f

2 S pC xf f , f

Y f = 12V f

2 S sC yf f , f

Z f = 12V f

2 S pC zf f , f

Moments

L f = 12V f

2 S s l f C lf f , f

M f = 12V f

2 S pCmf f , f

N f = 12V f

2 S sCnf f , f

14

FUSELAGE - 2

Incidence Angle

f = tan−1 wu , 00

f = tan−1 wu , 00

VelocityV f = u2v2w2 , 00V f = u2v2w

2 , 00

Sideslip

f = sin−1 vV f

15

EMPENNAGE

Forces

Z tp = 12V tp

2 S tpC ztp tp ,tp

Y fn = 12V fn

2 S fnC y fn fn , fn

MomentsM tp = l tpxcgZ tpN fn = −l fnxcg Y fn

16

INTEGRASI

17

TRIM ANALYSIS

18

LINIERISASI PERSAMAAN

x = F x ,u , t

dengan: x = { x f , x r , x p , x p}x f = {u , w , q , , v , p , , r}xr = {0 , 1c , 1s , 0 , 1c , 1s }x p = { , Qe , Qe}xc = {0 , 1s , 1c , 0T }u = {0 , 1s , 1c , 0T }

Bentuk Trimx = x e x

19

LINIERISASI PERSAMAAN

x − Ax = Bu t f t

A = ∂F∂ x x=xe dan A = ∂F∂u x=xeX u ≡

X u

Ma

x = Ax Bu dan y = Cx Du

u = −Kxx = Ax−BKx

= A−BK xsehingga didapatkan: det sI−A−BK = 0

20

LINIERISASI PERSAMAAN

Forces

X = X e∂ X∂u

u ∂ X∂w

w ... ∂ X∂0

0 ...

Y = Y e∂Y∂u

u ∂Y∂w

w ... ∂Y∂0

0 ...

Z = Z e∂Z∂u

u ∂ Z∂w

w ... ∂Z∂0

0 ...

Moments

L = Le∂ L∂u

u ∂ L∂w

w ... ∂ L∂0

0 ...

M = M e∂M∂u

u ∂M∂w

w ... ∂M∂0

0 ...

N = N e∂N∂u

u ∂N∂w

w ... ∂N∂0

0 ...

21

LINIERISASI PERSAMAAN

di mana:

∂ X∂u

= X u , ∂ X∂w

= X w , ... , ∂ X∂0

= X 0, ...

∂Y∂u

= Y u , ∂Y∂w

= Y w , ... , ∂Y∂0

= Y 0, ...

∂Z∂u

= Zu , ∂Z∂w

= Z w , ... , ∂Z∂0

= Z 0, ...

∂ L∂u

= Lu , ∂ L∂w

= Lw , ... , ∂ L∂0

= L0, ...

∂M∂u

= M u , ∂M∂w

= M w , ... , ∂M∂0

= M 0, ...

∂ N∂u

= N u , ∂N∂w

= N w , ... , ∂N∂0

= N 0, ...

22

LINIERISASI PERSAMAAN

L ' p =I zz

I xx I zz− I xz2 Lp

I xzI xx I zz− I xz

2 N p

N ' r =I xz

I xx I zz−I xz2 Lr

I xxI xx I zz− I xz

2 N r

k1 =I xz I zz I xx−I yyI xx I zz− I xz

2

k 2 =I zz I zz− I yy I xz

2

I xx I zz− I xz2

k3 =I xx I yy− I xx− I xz

2

I xx I zz− I xz2

23

LINIERISASI PERSAMAAN

A= [X u X w−Qe X q−W e −g cose X vRe X p 0 X rV e

Z uQe Z w Z qU e −g cosesin e Z v−Pe Z p−V e −gsin ecose Z rM u M w M q 0 M v M p−2Pe I xz I yy−Re I xx−I zz I yy 0 M r2Re I xz I yy−Pe I xx−I zz I yy0 0 cose 0 0 0 −a∗cose −sineY u−Re Y wPe Y q −g sin esin e Y v Y pW e g cos ecose Y r−U e

Lu' Lw

' Lq'k 1Pe−k 2Re 0 Lv

' L p' k 1Qe 0 Lr

'−k 2Q e

0 0 sin e tane a sece 0 1 0 cose∗taneN u' N w

' N q' −k 1Re−k3Pe 0 N v

' N p' −k 3Qe 0 N r

'−k1∗Q e

]B= [

X 0X 1s

X 1cX 0T

Z 0Z 1s

Z 1cZ 0T

M 0M 1s

M 1cM 0T

0 0 0 0Y 0

Y 1sY 1c

Y 0T

L0

' L1s

' L1c

' L0T

'

0 0 0 0N 0

N 1sN 1c

N 0T

]C = diag 8,8D = zeros 8,4 (untuk tanpa gangguan)

= rand 8,4 (dengan gangguan acak)

24

STRUKTUR JST

z = f z w1 x dan y= f y w2 z = f y w2 f z w1 x di mana:f z : fungsi aktivasi hidden layerf y : fungsi aktivasi output layerx : vektor masukanz : vektor keluaran dari hidden layer atau masukan ke output layery : vektor keluaran JSTd : vektor keluaran yang diharapkan

25

PEMBELAJARAN JSTBACKPROPAGATION - 1

Aktivasi terhadap input di lapisan keluaran: y _inK = ∑jz jw jK

Error (diminimalkan): E = .5∑K[t k − y k ]

2

Rambatan error: EwJK

= w JK

.5∑K[t k − y k ]

2

= w JK

.5 [tK − f y _inK ]2

= −[ tK − yK ]

wJKf y _inK

= −[ tK − yK ] f ' y _inK

wJK y _inK

= −[ tK − yK] f ' y _inK z J

kemudian ditentukan: K = [ tK − yK ] f ' y _inK

26

PEMBELAJARAN JSTBACKPROPAGATION - 2

Rambatan error untuk hidden unit: Ev IJ

= −∑K[ tk − y k ]

v IJ

y k

= −∑K[ tK − yK ] f ' y _inK

v IJ

y _inK

= −∑KK

v IJ

y _inK

= −∑KK w JK

v IJ

zJ

= −∑KK w JK f ' z _inJ [X I ]

kemudian ditentukan: J = ∑KK wJK f ' z _inJ

27

PEMBELAJARAN JSTBACKPROPAGATION - 3

Update bobot (unit keluaran):

w jk = − Ew jk

= [t k − yk ] f ' y _ink z j= k z j

Update bobot (hidden unit):

vij = − E vij

= f ' z _in j xi∑Kk w jk

= j xi

28

PEMBELAJARAN JSTREINFORCEMENT LEARNING - 1

Non associative Associative

29

PEMBELAJARAN JSTREINFORCEMENT LEARNING - 2

s t = ∑i=1

n

wi t xi t

dimana:x t : stimulus vectorwt : weight vectora t : actionr t : reinforcement signal

30

KOMPONEN SISTEM PENGATURAN

● Dynamic System (DS)● Neural Network Plant Model (NNPM)● Neural Network Inverse Plant Model (NNIPM)● Reference Model (RM)● Neural Network Control (NNC)

31

NNPM

32

NNPMLearning

33

NNIPM

34

NNIPMLearning

35

NNCPengaturan Kecepatan

36

NNCPengaturan Kecepatan (Learning)

37

SIMULINK

38

STATE SPACELYNX

A = [−0.0199 0.0215 0.06674 −9.7837 −0.0205 −0.16 0 0

0.0237 −0.3108 0.0134 −0.7215 −0.0028 −0.0054 0.5208 00.0468 0.0055 −1.8954 0 0.0588 0.4562 0 0

0 0 0.9985 0 0 0 0 0.05320.0207 0.0002 −0.1609 0.038 −0.0351 −0.684 9.7697 0.0995

0.03397 0.0236 −2.6449 0 −0.2715 −10.976 0 −0.02030 0 −0.0039 0 0 1 0 0.0737

0.0609 0.0089 −0.4766 0 −0.0137 −1.9367 0 −0.2743]

eigenvalue−160.19−95.223−28.794−10.246−1.83342.4181i−1.8334−2.4181i−2.09432.1627i−2.0943−2.1627i

B = [6.9417 −9.286 2.0164 0

−93.918 −0.002 −0.0003 00.9554 26.401 −5.7326 0

0 0 0 0−0.3563 −2.0164 −9.2862 3.677

7.0476 −33.212 −152.95 −0.73580 0 0 0

17.305 −5.9909 −27.591 −9.9111]

K = [ 0.057008 −0.98156 0.010214 0.080449 0.024821 0.0072675 0.10755 0.16457−0.97104 −0.076202 0.76276 3.5465 −0.20677 −0.1789 −1.0062 −0.086259

0.22057 −0.061367 −0.16283 −0.85137 −0.89605 −0.82133 −4.1481 −0.433170.021632 −0.13598 0.0032034 −0.12965 0.3785 0.12534 0.43583 −0.8794]

39

HASIL SIMULASI - 1

Kontrol

40

HASIL SIMULASI - 2

Kecepatan

41

HASIL SIMULASI - 3

Rate

42

HASIL SIMULASI - 4

Euler

43

HASIL PEMBELAJARAN - 1

tTARGET

NNIPM LEARNING

0.0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.3 0.0115 0.0010 0.0011 0.0004 0.0086 0.0120 0.0008 0.0017 0.0009 0.0084 0.0009 0.00020.4 0.0210 0.0016 0.0039 0.0012 0.0048 0.0213 0.0015 0.0038 0.0015 0.0047 0.0004 0.00010.5 0.0399 0.0031 0.0062 0.0030 0.0184 0.0410 0.0027 0.0058 0.0041 0.0179 0.0017 0.00050.6 0.0544 0.0040 0.0086 0.0052 0.0112 0.0551 0.0038 0.0084 0.0058 0.0109 0.0010 0.00030.7 0.0737 0.0056 0.0101 0.0078 0.0204 0.0749 0.0052 0.0097 0.0090 0.0198 0.0018 0.00060.8 0.0882 0.0068 0.0112 0.0104 0.0123 0.0889 0.0066 0.0109 0.0112 0.0119 0.0011 0.00030.9 0.1052 0.0085 0.0113 0.0131 0.0173 0.1062 0.0082 0.0109 0.0142 0.0169 0.0016 0.00051.0 0.1174 0.0098 0.0112 0.0155 0.0102 0.1180 0.0096 0.0110 0.0161 0.0099 0.0009 0.00021.1 0.1307 0.0113 0.0105 0.0178 0.0131 0.1314 0.0110 0.0102 0.0186 0.0128 0.0011 0.00031.2 0.1399 0.0124 0.0098 0.0197 0.0076 0.1403 0.0122 0.0097 0.0201 0.0074 0.0006 0.0002

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .19.8 0.1973 0.0155 0.0143 0.0284 0.0029 0.1970 0.0156 0.0141 0.0285 0.0029 0.0004 0.000019.9 0.1973 0.0156 0.0142 0.0285 0.0029 0.1970 0.0157 0.0140 0.0286 0.0029 0.0004 0.000020.0 0.1973 0.0157 0.0141 0.0286 0.0029 0.1970 0.0158 0.0139 0.0287 0.0029 0.0004 0.0000

ΔθT

Δ emθ

0θ

1sθ

1cθ

0Te

mθ

0θ

1sθ

1cθ

0Te

m

44

HASIL PEMBELAJARAN - 2

tKONTROL

NNC LEARNING

0.0 0.0000 -0.0001 -0.0001 -0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.00000.1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.3 0.0000 0.0000 0.0000 0.0000 0.0061 0.0120 0.0008 0.0017 0.0009 0.0000 0.0122 0.00000.4 0.0120 0.0008 0.0017 0.0009 0.0048 0.0212 0.0015 0.0038 0.0015 0.0000 0.0095 0.00010.5 0.0212 0.0015 0.0038 0.0015 0.0101 0.0410 0.0027 0.0058 0.0041 0.0000 0.0201 0.00000.6 0.0410 0.0027 0.0058 0.0041 0.0072 0.0551 0.0038 0.0084 0.0058 0.0000 0.0145 0.00000.7 0.0551 0.0038 0.0084 0.0058 0.0101 0.0749 0.0052 0.0097 0.0090 0.0000 0.0201 0.00000.8 0.0749 0.0052 0.0097 0.0090 0.0071 0.0889 0.0066 0.0109 0.0112 0.0000 0.0143 0.00000.9 0.0889 0.0066 0.0109 0.0112 0.0088 0.1062 0.0082 0.0109 0.0141 0.0000 0.0176 0.00011.0 0.1062 0.0082 0.0109 0.0142 0.0060 0.1180 0.0096 0.0110 0.0161 0.0000 0.0120 0.00001.1 0.1180 0.0096 0.0110 0.0161 0.0069 0.1314 0.0110 0.0102 0.0186 0.0000 0.0137 0.00001.2 0.1314 0.0110 0.0102 0.0186 0.0046 0.1403 0.0122 0.0097 0.0201 0.0000 0.0091 0.0000

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .19.8 0.1970 0.0155 0.0142 0.0284 0.0001 0.1970 0.0156 0.0141 0.0285 0.0000 0.0002 0.000019.9 0.1970 0.0156 0.0141 0.0285 0.0001 0.1970 0.0157 0.0140 0.0286 0.0000 0.0002 0.000020.0 0.1970 0.0157 0.0140 0.0286 0.0001 0.1970 0.0158 0.0139 0.0287 0.0000 0.0002 0.0000

ΔθK

ΔθTKθ

0θ

1sθ

1cθ

0Te

uθ

0θ

1sθ

1cθ

0Te

u

45

PENGEMBANGAN PEMBELAJARAN

46

KESIMPULAN

1. Osilasi sekitar 5% terhadap nilai target yang diinginkan.

2. Arsitektur NNC dan teknik pembelajaran sangat berpengaruh pada waktu dan hasil pembelajarannya.

3. Pembelajaran NNC dengan prinsip reinforcment learning membutuhkan waktu proses yang lebih lama dari pada dengan cara penerapan invers dan backpropagasi.

4. Pembelajaran menggunakan reinforcment learning, dapat dilakukan dengan cara menerapkan struktur pohon, di mana dapat dicari nilai local minimum dan global minimum.

5. Penerapan LQR (sebagai linier feedback) atau dalam penerapannya sebagai Stability Augmentation System, memberikan hasil yang baik.

6. Pembelajaran NNPM dan NNIPM dilakukan secara on-line agar ketidakpastian pada dinamika sistem dapat segera diketahui, sehingga NNC dapat segera beradaptasi.

47

SARAN PENGEMBANGAN

1. Simulasi dikembangkan menjadi beberapa bentuk, berdasarkan arsitektur JST dan model dynamic system, serta metode pembelajaran JST.

2. Hasil dari penerapan JST mungkin dapat dibandingkan berdasarkan metode misalnya PID dan Fuzzy, atau berdasarkan jenis dinamika sistem (Lynx, UH60, atau lainnya).

3. Data yang diperoleh dari referensi ditelaah lebih lanjut pada plant sebenarnya.

4. Menyertakan analisa dan pembahasan peralatan yang digunakan pada plant sebenarnya, seperti hidraulic, motor, sensor, INS, serta lainnya.

5. Menyertakan analisa untuk penangannan disturbance dan noise yang dapat terjadi pada peralatan.

6. Perbandingan secara lebih mendalam dalam pencarian nilai sinyal kontrol optimal dengan memodelkan dalam bentuk graf atau struktur pohon dan kemudian menggunakan algoritma djikstra atau algoritma pencarian breadth-first search atau depth-first search maupun modifikasinya.

48

DAFTAR PUSTAKA

[B01] Donald McLean, “Automatic Flight Control System”, Prentice Hall International, 1990.

[B02] Steven M. LaValle, “Planning Algorithms”, Cambridge University Press, University of Illinois, USA, 2006.

[B03] Katsuhiko Ogata, “Discrete Time Control System”, Prentice Hall, USA, 1995.

[B04] Robert Grover Brown and Patrick Y. C Hwang, “Introduction To Random Signals And Applied Kalman Filtering”, 3th Edition, John Wiley & Sons, USA, 1997.

[B05] Richard C. Dorf and Robert H. Bishop, “Modern Control Systems”, 9th Edition, Prentice Hall, USA, 2001.

[B06] Frank L. Lewis, “Applied Optimal Control & Estimation”, Prentice Hall International, USA, 1992.

[B07] Ken Dutton and Steve Thompson and Bill Barraclough, “The Art of Control Engineering”, Addison-Wesley, USA, 1997.

[B08] Howard Anton, “Aljabar Linier Elementer (Alih Bahasa)”, Erlangga, Indonesia, 1987.

[I01] Nikos Drakos, “Computer Based Learning Unit”, University of Leeds, Internet, 1996.

[I02] E. de Weerdt and Q.P. Chu and J.A. Mulder, “Neural Network Aerodynamic Model Identification for Flight Control Reconfiguration”, Delft University of Technology, Department of Control and Simulation, GB Delft, Netherlands.

[I03] Kevin J. Walchko and Michael C. Nechyba and Eric Schwartz and Antonio Arroyo, “Embedded Low Cost Inertial Navigation System”, University of Florida, Gainesville.

[I04] Fahad A Al Mahmood, “Constructing & Simulating a Mathematical Model of Longitudinal Helicopter Flight Dynamics”.

[I05] Luca Vigan`o and Gianantonio Magnani, “Acausal Modelling of Helicopter Dynamics for Automatic Flight Control Applications”, Politecnico di Milano Dipartimento di Elettronica ed Informazione (DEI) Via Ponzio, Milano, Italy.

49

DAFTAR PUSTAKA

[I06] Kathryn B. Hilbert, “A Mathematical Model of the UH-60 Helicopter”, Aeromechanics Laboratory, U.S. Army Research and Technology Laboratories-AVSCOM NASA, California, USA.

[I07] S. K. Kim & D. M. Tilbury, “Mathematical Modeling and Experimental Identification of an Unmanned Helicopter Robot with Flybar Dynamics”, Department of Mechanical Engineering University of Michigan, USA.

[I08] M. D. Takahashi, “A Flight-Dynamic Helicopter, Mathematical Model with a Single, Flap-Lag-Torsion Main Rotor”, NASA, USA, 1990.

[I09] Wikipedia, The free encyclopedia, Internet.

[I10] Richard E. McFarland, “a Standard Kinematic Model for Flight Simulation at NASA-AMES”, California, USA.

[I11] Martin T. Hagan and Howar B. Demuth, “Neural Networks for Control”, School of Electrical & Computer Engineering Oklahoma State University & Electrical Engineering Department University of Idaho.

[I12] George Saikalis and Feng Lin, “Adaptive Neural Network Control by Adaptive Interaction”, Hitachi America Ltd. & Wayne State University, USA.

[I13] J. Andrew Bagnell and Jeff G. Schneider, “Autonomous Control Using Reinforcement Learning”.

[I14] Thomas S. Alderete, “Simulator Aero Model Implementation”, NASA Ames Research Center, Moffett Field, California, USA.

[I15] Joseph B. Mueller and Michael A. Paluszeky (Princeton Satellite Systems, Princeton) and Yiyuan Zhaoz (University of Minnesota, Minneapolis), “Development of an Aerodynamic Model and Control Law Design for a High Altitude Airship”, American Institute of Aeronautics and Astronautics, USA.

[I16] Gabriel M. Hoffmann and Haomiao Huang and Steven L. Waslander and Claire J. Tomlin, “Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment, Navigation and Control Conference and Exhibit”, AIAA Guidance, Hilton Head, South Carolina, USA, 2007.

50

IMU

51

TERIMA-KASIH