Tesis TE 2099
PERANCANGAN DAN SIMULASI KONTROLER JST UNTUK PENGENDALIAN GERAKAN HOVER PADA HELIKOPTER Oleh R. Ade Supriyadi 2207202203 Pembimbing Ir. Katjuk Astrowulan MSEE Ir. Rusdhianto Effendie AK, M.T. Bidang Studi Teknik Sistem Pengaturan Jurusan Teknik Elektro Fakultas Teknologi Industri Institut Teknologi Sepuluh Nopember Surabaya 2010
1
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
2
MODELLING
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●
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 3
KOMPONEN HELIKOPTER
4
BLADE FLAPPING
5
FORCE & MOMENT
6
CONTROL
7
FORCE & MOMENT Formulasi F M
= =
F R F TR F f F tp F fn M R M TR M f M tp M
fn
Translasional X − g sin Ma Y v˙ = −ur−℘ − g cos sin Ma Z w˙ = − vp−uq − g cos cos Ma
u˙
= − wq−vr
Rotational I xx p˙ = I yy − I zz qr I xz r˙ pq L I yy q˙ = I zz− I xx rp I xz r 2 − p2 M I zz r˙ = I xx − I yy pq I xz p˙ −qr N 8
ROTOR UTAMA - 1
Forces X hw = T 1cw Y hw = −T 1sw Z hw = −T Moments LH MH NH
−N b = K 1s 2 −N b = K 1c 2 ˙ = C Q R2 R 3 I R
9
ROTOR UTAMA - 2 Nb
R
X hw =
∑ ∫ {− f z −ma zb i i cosi − f y−ma yb i sin i ma xb cos i }dr b
Y hw
{ f z −ma zb i i sin i − f y −ma yb i cosi ma xb sin i }dr b ∑ ∫ i =1
=
i =1 i=1 Nb R
Nb
Z hw
=
2 C xw a0 s 2 C yw a0 s 2 C zw a0 s
i=1 R
∑ ∫ f z−ma zbm xb i i dr b i =1 i=1
=
X hw
1 2 2 R R s a 0 2 Y hw = 1 R2 R 2 s a 0 2 Z hw = 1 R2 R 2 s a 0 2
2CT = − a0 s
10
ROTOR EKOR - 1
Forces & Moments X T = T T 1cT YT = TT Z T = −T T 1sT
LT MT NT
= hT Y T = l T x cg Z T − QT = −l T x cg Y T
Thurst T T = C T T R T 2 R 2T T
11
ROTOR EKOR - 2
2
2 T
Y T = T R T sT a 0 R T
CT
T
a0 sT
FT
T
CT = T
TT T RT 2 R2T
2CT
T
a0 sT T
FT
z −0 T * * 3 = 1 3 2 2 2 1s T
T
T
3 S fn = 1− 4 R 2T
12
FUSELAGE - 1 Forces 1 2 V f S p C xf f , f 2 1 2 = V f S s C yf f , f 2 1 = V 2f S p C zf f , f 2
Xf
=
Yf Zf
Moments Lf M Nf
1 2 V f S s l f C lf f , f 2 1 2 = V f S p C mf f , f 2 1 = V 2f S s C nf f , f 2 =
f
13
FUSELAGE - 2 Incidence Angle w f = tan−1 u −1 w f = tan u
,
0 0
,
0 0
Velocity V
f
=
u2v 2w 2
,
0 0
V
f
=
u v w
,
0 0
2
2
2
Sideslip f
= sin−1
v Vf
14
EMPENNAGE Forces Z tp Y fn
1 2 V tp S tp C z tp , tp 2 1 2 = V fn S fn C y fn , fn 2 =
tp
fn
Moments M tp = l tp x cg Z tp N fn = −l fn x cg Y fn
15
INTEGRASI
16
TRIM ANALYSIS
17
LINIERISASI PERSAMAAN x˙ = F x , u , t dengan: x = { x f , xr , x p , x p } xf = {u , w , q , , v , p , , r} x r = { 0 , 1c , 1s , 0 , 1c , 1s } x p = { , Q e , Q˙ e } x c = { 0 , 1s , 1c , 0T } u = { 0 , 1s , 1c , 0T } Bentuk Trim x = xe x
18
LINIERISASI PERSAMAAN x˙ − Ax = Bu t f t A =
Xu
∂F ∂x
dan x=x e
A =
∂F ∂u
x=x e
Xu ≡ Ma
x˙ =
Ax Bu
dan
y = Cx Du
u = −Kx x˙ = Ax− BKx = A− BK x sehingga didapatkan: det sI − A− BK = 0
19
LINIERISASI PERSAMAAN Forces X Y Z
∂X ∂X ∂X u w ... 0 ... ∂u ∂w ∂ 0 ∂Y ∂Y ∂Y = Ye u w ... 0 ... ∂u ∂w ∂ 0 ∂Z ∂Z ∂Z = Ze u w ... 0 ... ∂u ∂w ∂ 0 =
Xe
Moments L M N
∂L ∂L ∂L u w ... 0 ... ∂u ∂w ∂ 0 ∂M ∂M ∂M = Me u w ... 0 ... ∂u ∂w ∂ 0 ∂N ∂N ∂N = Ne u w ... 0 ... ∂u ∂w ∂ 0 =
Le
20
LINIERISASI PERSAMAAN di mana: ∂X ∂u ∂Y ∂u ∂Z ∂u ∂L ∂u ∂M ∂u ∂N ∂u
=
= Yu = Zu
=
Lu
= Mu =
∂X ∂w ∂Y , ∂w ∂Z , ∂w
Xu ,
Nu
∂L ∂w ∂M , ∂w ∂N , ∂w ,
=
= Yw = Zw
=
Lw
= Mw =
∂X ∂ 0 ∂Y , ... , ∂ 0 ∂Z , ... , ∂ 0
X w , ... ,
Nw
∂L ∂ 0 ∂M , ... , ∂ 0 ∂N , ... , ∂ 0 , ... ,
=
X
= Y
0
= Z
0
=
0
L
0
= M =
N
0
0
,
...
,
...
,
...
,
...
,
...
,
... 21
LINIERISASI PERSAMAAN
L' p
=
N 'r =
k1 =
I zz I xx I zz − I I xz
2 xz
I xx I zz −I
2 xz
Lp Lr
I xz I xx I zz− I I xx
2 xz
I xx I zz− I
2 xz
Np Nr
I xz I zz I xx −I yy I xx I zz− I 2xz 2
k2 = k3 =
I zz I zz − I yy I xz 2
I xx I zz− I xz I xx I yy − I xx − I 2xz I xx I zz− I 2xz
22
LINIERISASI PERSAMAAN
[ [ ]
Xu Z u Qe Mu 0 A= Y u −Re ' Lu 0 N
X w−Qe Zw Mw 0 Y wP e ' Lw 0
' u
X Z M B= 0 Y 0
0
0
0
'
L 0 N
N
X Z M 0 Y
1s
1s
0
1s
1s
1s
0
' q
1s
−g cose −g cos e sin e 0 0 −g sin esin e 0 a sece
N −k 1 Re− k 3 P e 0
X Z M 0 Y
1c
1c
'
L 0 N
' w
X q −W e Z q U e Mq cose Yq ' L q k 1 Pe−k 2 Re sin e tane
0T
0T
1c
1c
'
L 0 N
X Z M 0 Y
0T
X v R e Z v−P e Mv 0 Yv ' Lv 0 N
C = D = =
' v
Xp Z p −V e M p −2 Pe I xz I yy − Re I xx −I zz I yy 0 Y p W e ' L pk 1 Q e 1 ' p
N − k 3 Qe
0 − g sin ecose 0 − a∗cose g cos e cose 0 0 0
X r V e Zr M r 2 R e I xz I yy− Pe I xx −I zz I yy −sine Y r −U e ' L r −k 2 Q e cose ∗tan e ' r
N −k1∗Q e
diag 8,8 zeros 8,4 (untuk tanpa gangguan) rand 8,4 (dengan gangguan acak)
0T
'
1c
1c
L 0 N
0T
0T
23
]
STRUKTUR JST
z = f z w1 x dan y = f y w 2 z = f y w 2 f z w 1 x di mana: f z : fungsi aktivasi hidden layer f y : fungsi aktivasi output layer x : vektor masukan z : vektor keluaran dari hidden layer atau masukan ke output layer y : vektor keluaran JST d : vektor keluaran yang diharapkan
24
PEMBELAJARAN JST BACKPROPAGATION - 1 Aktivasi terhadap input di lapisan keluaran: y _in K =
∑j z j w jK
Error (diminimalkan): E = .5 ∑ [t k − y k ]2 K
Rambatan error: E 2 = .5 ∑ [t k − y k ] w JK w JK K 2 = .5 [t K − f y _in K ] w JK = −[ t K − y K ] f y _in K w JK = −[ t K − y K ] f ' y _in K y _in K w JK = −[ t K − y K ] f ' y _in K z J kemudian ditentukan: K = [ t K − y K ] f ' y _in K 25
PEMBELAJARAN JST BACKPROPAGATION - 2 Rambatan error untuk hidden unit: E = − ∑ [t k − y k ] yk v IJ v K IJ = − ∑ [t K − y K ] f ' y _in K K
y _in K v IJ
y _in K v IJ K w JK z v IJ J
= − ∑ K K
= −∑ K
= − ∑ K w JK f ' z _in J [ X I ] K
kemudian ditentukan: J =
∑ K K
w JK f ' z _in J
26
PEMBELAJARAN JST BACKPROPAGATION - 3 Update bobot (unit keluaran): E w jk = − w jk = [t k − y k ] f ' y _in k z j = k z j Update bobot (hidden unit): E v ij = − v ij = f ' z _in j x i ∑ k w jk K
= j xi
27
PEMBELAJARAN JST REINFORCEMENT LEARNING - 1
Non associative
Associative
28
PEMBELAJARAN JST REINFORCEMENT LEARNING - 2
n
s t =
∑ wi t xi t i=1
dimana: x t : wt : a t : r t :
stimulus vector weight vector action reinforcement signal
29
KOMPONEN SISTEM PENGATURAN ●
Dynamic System (DS)
●
Neural Network Plant Model (NNPM)
●
Neural Network Inverse Plant Model (NNIPM)
●
Reference Model (RM)
●
Neural Network Control (NNC)
30
NNPM
31
NNPM Learning
32
NNIPM
33
NNIPM Learning
34
NNC Pengaturan Kecepatan
35
NNC Pengaturan Kecepatan (Learning)
36
SIMULINK
37
STATE SPACE LYNX
[ [
−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 0 0.0468 0.0055 −1.8954 0 0.0588 0.4562 0 0 0 0 0.9985 0 0 0 0 0.0532 A = 0.0207 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 −0.0203 0 0 −0.0039 0 0 1 0 0.0737 0.0609 0.0089 −0.4766 0 −0.0137 −1.9367 0 −0.2743 6.9417 −9.286 2.0164 0 −93.918 −0.002 −0.0003 0 0.9554 26.401 −5.7326 0 0 0 0 0 B = −0.3563 −2.0164 −9.2862 3.677 7.0476 −33.212 −152.95 −0.7358 0 0 0 0 17.305 −5.9909 −27.591 −9.9111
[
]
eigenvalue −160.19 −95.223 −28.794 −10.246 −1.83342.4181i −1.8334−2.4181i −2.09432.1627i −2.0943−2.1627i
]
0.057008 −0.98156 0.010214 0.080449 0.024821 0.0072675 0.10755 0.16457 0.76276 3.5465 −0.20677 −0.1789 −1.0062 −0.086259 K = −0.97104 −0.076202 0.22057 −0.061367 −0.16283 −0.85137 −0.89605 −0.82133 −4.1481 −0.43317 0.021632 −0.13598 0.0032034 −0.12965 0.3785 0.12534 0.43583 −0.8794
] 38
HASIL SIMULASI - 1 Kontrol
39
HASIL SIMULASI - 2 Kecepatan
40
HASIL SIMULASI - 3 Rate
41
HASIL SIMULASI - 4 Euler
42
HASIL PEMBELAJARAN - 1 TARGET NNIPM
t 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 . . . 19.8 19.9 20.0
LEARNING
θ0
θ1s
θ1c
θ0T
em
θ0
θ1s
θ1c
θ0T
em
0.0000 0.0000 0.0000 0.0115 0.0210 0.0399 0.0544 0.0737 0.0882 0.1052 0.1174 0.1307 0.1399 . . . 0.1973 0.1973 0.1973
0.0000 0.0000 0.0000 0.0010 0.0016 0.0031 0.0040 0.0056 0.0068 0.0085 0.0098 0.0113 0.0124 . . . 0.0155 0.0156 0.0157
0.0000 0.0000 0.0000 0.0011 0.0039 0.0062 0.0086 0.0101 0.0112 0.0113 0.0112 0.0105 0.0098 . . . 0.0143 0.0142 0.0141
0.0000 0.0000 0.0000 0.0004 0.0012 0.0030 0.0052 0.0078 0.0104 0.0131 0.0155 0.0178 0.0197 . . . 0.0284 0.0285 0.0286
0.0000 0.0000 0.0000 0.0086 0.0048 0.0184 0.0112 0.0204 0.0123 0.0173 0.0102 0.0131 0.0076 . . . 0.0029 0.0029 0.0029
0.0000 0.0000 0.0000 0.0120 0.0213 0.0410 0.0551 0.0749 0.0889 0.1062 0.1180 0.1314 0.1403 . . . 0.1970 0.1970 0.1970
0.0000 0.0000 0.0000 0.0008 0.0015 0.0027 0.0038 0.0052 0.0066 0.0082 0.0096 0.0110 0.0122 . . . 0.0156 0.0157 0.0158
0.0000 0.0000 0.0000 0.0017 0.0038 0.0058 0.0084 0.0097 0.0109 0.0109 0.0110 0.0102 0.0097 . . . 0.0141 0.0140 0.0139
0.0000 0.0000 0.0000 0.0009 0.0015 0.0041 0.0058 0.0090 0.0112 0.0142 0.0161 0.0186 0.0201 . . . 0.0285 0.0286 0.0287
0.0000 0.0000 0.0000 0.0084 0.0047 0.0179 0.0109 0.0198 0.0119 0.0169 0.0099 0.0128 0.0074 . . . 0.0029 0.0029 0.0029
ΔθT
Δ em
0.0000 0.0000 0.0000 0.0009 0.0004 0.0017 0.0010 0.0018 0.0011 0.0016 0.0009 0.0011 0.0006 . . . 0.0004 0.0004 0.0004
0.0000 0.0000 0.0000 0.0002 0.0001 0.0005 0.0003 0.0006 0.0003 0.0005 0.0002 0.0003 0.0002 . . . 0.0000 0.0000 0.0000 43
HASIL PEMBELAJARAN - 2 KONTROL NNC
t 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 . . . 19.8 19.9 20.0
LEARNING
θ0
θ1s
θ1c
θ0T
eu
θ0
θ1s
θ1c
θ0T
eu
0.0000 0.0000 0.0000 0.0000 0.0120 0.0212 0.0410 0.0551 0.0749 0.0889 0.1062 0.1180 0.1314 . . . 0.1970 0.1970 0.1970
-0.0001 0.0000 0.0000 0.0000 0.0008 0.0015 0.0027 0.0038 0.0052 0.0066 0.0082 0.0096 0.0110 . . . 0.0155 0.0156 0.0157
-0.0001 0.0000 0.0000 0.0000 0.0017 0.0038 0.0058 0.0084 0.0097 0.0109 0.0109 0.0110 0.0102 . . . 0.0142 0.0141 0.0140
-0.0001 0.0000 0.0000 0.0000 0.0009 0.0015 0.0041 0.0058 0.0090 0.0112 0.0142 0.0161 0.0186 . . . 0.0284 0.0285 0.0286
0.0001 0.0000 0.0000 0.0061 0.0048 0.0101 0.0072 0.0101 0.0071 0.0088 0.0060 0.0069 0.0046 . . . 0.0001 0.0001 0.0001
0.0000 0.0000 0.0000 0.0120 0.0212 0.0410 0.0551 0.0749 0.0889 0.1062 0.1180 0.1314 0.1403 . . . 0.1970 0.1970 0.1970
0.0000 0.0000 0.0000 0.0008 0.0015 0.0027 0.0038 0.0052 0.0066 0.0082 0.0096 0.0110 0.0122 . . . 0.0156 0.0157 0.0158
0.0000 0.0000 0.0000 0.0017 0.0038 0.0058 0.0084 0.0097 0.0109 0.0109 0.0110 0.0102 0.0097 . . . 0.0141 0.0140 0.0139
0.0000 0.0000 0.0000 0.0009 0.0015 0.0041 0.0058 0.0090 0.0112 0.0141 0.0161 0.0186 0.0201 . . . 0.0285 0.0286 0.0287
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 . . . 0.0000 0.0000 0.0000
ΔθK
ΔθTK
0.0002 0.0000 0.0000 0.0122 0.0095 0.0201 0.0145 0.0201 0.0143 0.0176 0.0120 0.0137 0.0091 . . . 0.0002 0.0002 0.0002
0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 . . . 0.0000 0.0000 0.0000 44
PENGEMBANGAN PEMBELAJARAN
45
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.
46
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.
47
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.
48
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.
49
IMU
50
TERIMA-KASIH
51
