Microsoft Word – Course Project
Fall 2020 AV 201 Flight Dynamics
Course Project
Given a simplified aircraft dynamic model, complete the following tasks:
(a) Build a nonlinear simulation model using MATLAB/Simulink;
(b) Select appropriate values of altitude and speed, find the corresponding trimmed point;
(c) Find the linearized model at the trimmed point;
(d) Set the trimmed point as the initial condition, assume appropriate control surface
inputs, conduct linear and nonlinear simulations, and compare the simulation results.
Please submit a written report including but not limited to the following information:
(a) Linear and nonlinear simulation results and discussions;
(b) MATLAB codes, including m-files and Simulink block diagrams.
Parameters of the aircraft:
Aerodynamic forces and moments:
Xa XaF C qS Ya YaF C qS Za ZaF C qS
Rolla L a
L C qSb a NN C qSb
Engine forces and moments:
XTF T 0YTF 0ZTF
0TL 0TM 0TN
Total force and moment coefficients:
( , ) ( )
2 Q
Xa X e X
cQ
C C C
V
( , , ) ( )
2 Q
Za Z e Z
cQ
C C C
V
2
( ) 1 0.19 ( )
57.3 25 2 Q
e
Z Z
cQ
C C
V
( , , ) ( ) ( )
2 R P
Ya Y a r Y Y
b
C C C R C P
V
0.02 0.021 0.86 ( ) ( )
20 30 2 R P
a r
Y Y
b
C R C P
V
,( , ) ( ) ( )
2 Q
Ma M e M Za cg ref cg
cQ
C C C C x x
V
, 20 , 30
( , ) ( , ) ( , )
20 30
+ ( ) ( )
2
o o
Roll Roll Roll a Roll r
Roll RollR P
a r
L a L L L
L L
C C C C
b
C R C P
V
, 20 , 30
,
( , ) ( , ) ( , )
20 30
+ ( ) ( ) ( )
2
o o
a r
R P
a r
Na N N N
N N Ya cg ref cg
C C C C
b c
C R C P C x x
V b
Lookup tables:
QX
C
RY
C
PY
C
QZ
C
RollR
LC RollPL
C
QM
C
RN
C
PN
C
-10
-5
0
5
10
15
20
25
30
35
40
45
-0.2670
-0.1100
0.3080
1.3400
2.0800
2.9100
2.7600
2.0500
1.5000
1.4900
1.8300
1.2100
0.8820
0.8520
0.8760
0.9580
0.9620
0.9740
0.8190
0.4830
0.5900
1.2100
-0.4930
-1.0400
-0.1080
-0.1080
-0.1880
0.1100
0.2580
0.2260
0.3440
0.3620
0.6110
0.5290
0.2980
-0.2270
-8.8000
-25.8000
-28.9000
-31.4000
-31.2000
-30.7000
-27.7000
-28.2000
-29.0000
-29.8000
-38.3000
-35.3000
-0.1260
-0.0260
0.0630
0.1130
0.2080
0.2300
0.3190
0.4370
0.6800
0.1000
0.4470
-0.3300
-0.3600
-0.3590
-0.4430
-0.4200
-0.3830
-0.3750
-0.3290
-0.2940
-0.2300
-0.2100
-0.1200
-0.1000
-7.2100
-5.4000
-5.2300
-5.2600
-6.1100
-6.6400
-5.6900
-6.0000
-6.2000
-6.4000
-6.6000
-6.0000
-0.3800
-0.3630
-0.3780
-0.3860
-0.3700
-0.4530
-0.5500
-0.5820
-0.5950
-0.6370
-1.0200
-0.8400
0.0610
0.0520
0.0520
-0.0120
-0.0130
-0.0240
0.0500
0.1500
0.1300
0.1580
0.2400
0.1500
( , )X eC
oe
o
-24 -12 0 12 24
-10
-5
0
5
10
15
20
25
30
35
40
45
-0.0990
-0.0810
-0.0810
-0.0630
-0.0250
0.0440
0.0970
0.1130
0.1450
0.1670
0.1740
0.1660
-0.0480
-0.0380
-0.0400
-0.0210
0.0160
0.0830
0.1270
0.1370
0.1620
0.1770
0.1790
0.1670
-0.0220
-0.0200
-0.0210
-0.0040
0.0320
0.0940
0.1280
0.1300
0.1540
0.1610
0.1550
0.1380
-0.0400
-0.0380
-0.0390
-0.0250
0.0060
0.0620
0.0870
0.0850
0.1000
0.1100
0.1040
0.0910
-0.0830
-0.0730
-0.0760
-0.0720
-0.0460
0.0120
0.0240
0.0250
0.0430
0.0530
0.0470
0.0400
( )ZC
o ( )ZC
-10
-5
0
5
10
15
20
25
30
35
40
45
0.7700
0.2410
-0.1000
-0.4160
-0.7310
-1.0530
-1.3660
-1.6460
-1.9170
-2.1200
-2.2480
-2.2290
( , )M eC
oe
o
-24 -12 0 12 24
-10
-5
0
5
10
15
20
25
30
35
40
45
0.2050
0.1680
0.1860
0.1960
0.2130
0.2510
0.2450
0.2380
0.2520
0.2310
0.1980
0.1920
0.0810
0.0770
0.1070
0.1100
0.1100
0.1410
0.1270
0.1190
0.1330
0.1080
0.0810
0.0930
-0.0460
-0.0200
-0.0090
-0.0050
-0.0060
0.0100
0.0060
-0.0010
0.0140
0
-0.0130
0.0320
-0.1740
-0.1450
-0.1210
-0.1270
-0.1290
-0.1020
-0.0970
-0.1130
-0.0870
-0.0840
-0.0690
-0.0060
-0.2590
-0.2020
-0.1840
-0.1930
-0.1990
-0.1500
-0.1600
-0.1670
-0.1040
-0.0760
-0.0410
-0.0050
( , )
RollL
C ( , ) ( , )
Roll RollL L
C C
o
o
0 5 10 15 20 25 30
-10
-5
0
5
10
15
20
25
30
35
40
45
0
0
0
0
0
0
0
0
0
0
0
0
-0.0010
-0.0040
-0.0080
-0.0120
-0.0160
-0.0220
-0.0220
-0.0210
-0.0150
-0.0080
-0.0130
-0.0150
-0.0030
-0.0090
-0.0170
-0.0240
-0.0300
-0.0410
-0.0450
-0.0400
-0.0160
-0.0020
-0.0100
-0.0190
-0.0010
-0.0100
-0.0200
-0.0300
-0.0390
-0.0540
-0.0570
-0.0540
-0.0230
-0.0060
-0.0140
-0.0270
0
-0.0100
-0.0220
-0.0340
-0.0470
-0.0600
-0.0690
-0.0670
-0.0330
-0.0360
-0.0350
-0.0350
0.0070
-0.0100
-0.0230
-0.0340
-0.0490
-0.0630
-0.0810
-0.0790
-0.0600
-0.0580
-0.0620
-0.0590
0.0090
-0.0110
-0.0230
-0.0370
-0.0500
-0.0680
-0.0890
-0.0880
-0.0910
-0.0760
-0.0770
-0.0760
( , )NC ( , ) ( , )N NC C
o
o
0 5 10 15 20 25 30
-10
-5
0
5
10
15
20
25
30
35
40
45
0
0
0
0
0
0
0
0
0
0
0
0
0.0180
0.0190
0.0180
0.0190
0.0190
0.0180
0.0130
0.0070
0.0040
-0.0140
-0.0170
-0.0330
0.0380
0.0420
0.0420
0.0420
0.0430
0.0390
0.0300
0.0170
0.0040
-0.0350
-0.0470
-0.0570
0.0560
0.0570
0.0590
0.0580
0.0580
0.0530
0.0320
0.0120
0.0020
-0.0460
-0.0710
-0.0730
0.0640
0.0770
0.0760
0.0740
0.0730
0.0570
0.0290
0.0070
0.0120
-0.0340
-0.0650
-0.0410
0.0740
0.0860
0.0930
0.0890
0.0800
0.0620
0.0490
0.0220
0.0280
-0.0120
-0.0020
-0.0130
0.0790
0.0900
0.1060
0.1060
0.0960
0.0800
0.0680
0.0300
0.0640
0.0150
0.0110
-0.0010
, 20
( , )o
Roll aL
C
o
o
-30 -20 -10 0 10 20 30
-10
-5
0
5
10
15
20
25
30
35
40
45
-0.0410
-0.0520
-0.0530
-0.0560
-0.0500
-0.0560
-0.0820
-0.0590
-0.0420
-0.0380
-0.0270
-0.0170
-0.0410
-0.0530
-0.0530
-0.0530
-0.0500
-0.0510
-0.0660
-0.0430
-0.0380
-0.0270
-0.0230
-0.0160
-0.0420
-0.0530
-0.0520
-0.0510
-0.0490
-0.0490
-0.0430
-0.0350
-0.0260
-0.0160
-0.0180
-0.0140
-0.0400
-0.0520
-0.0510
-0.0520
-0.0480
-0.0480
-0.0420
-0.0370
-0.0310
-0.0260
-0.0170
-0.0120
-0.0430
-0.0490
-0.0480
-0.0490
-0.0430
-0.0420
-0.0420
-0.0360
-0.0250
-0.0210
-0.0160
-0.0110
-0.0440
-0.0480
-0.0480
-0.0470
-0.0420
-0.0410
-0.0200
-0.0280
-0.0130
-0.0140
-0.0110
-0.0100
-0.0430
-0.0490
-0.0470
-0.0450
-0.0420
-0.0370
-0.0030
-0.0130
-0.0100
-0.0030
-0.0070
-0.0080
, 30
( , )o
Roll rL
C
o
o
-30 -20 -10 0 10 20 30
-10
-5
0
5
10
15
20
25
30
35
40
45
0.0050
0.0170
0.0140
0.0100
-0.0050
0.0090
0.0190
0.0050
0
-0.0050
-0.0110
0.0080
0.0070
0.0160
0.0140
0.0140
0.0130
0.0090
0.0120
0.0050
0
0.0040
0.0090
0.0070
0.0130
0.0130
0.0110
0.0120
0.0110
0.0090
0.0080
0.0050
0
0.0050
0.0030
0.0050
0.0130
0.0130
0.0110
0.0120
0.0110
0.0090
0.0080
0.0050
0
0.0050
0.0030
0.0050
0.0150
0.0140
0.0130
0.0130
0.0120
0.0110
0.0110
0.0100
0.0080
0.0080
0.0070
0.0030
0.0210
0.0110
0.0100
0.0110
0.0100
0.0090
0.0080
0.0100
0.0060
0.0050
0
0.0010
0.0230
0.0100
0.0110
0.0110
0.0110
0.0100
0.0080
0.0100
0.0060
0.0140
0.0200
0
, 20
( , )o
aN
C
o
o
-30 -20 -10 0 10 20 30
-10
-5
0
5
10
15
20
25
30
35
40
45
0.0010
-0.0270
-0.0170
-0.0130
-0.0120
-0.0160
0.0010
0.0170
0.0110
0.0170
0.0080
0.0160
0.0020
-0.0140
-0.0160
-0.0160
-0.0140
-0.0190
-0.0210
0.0020
0.0120
0.0160
0.0150
0.0110
-0.0060
-0.0080
-0.0060
-0.0060
-0.0050
-0.0080
-0.0050
0.0070
0.0040
0.0070
0.0060
0.0060
-0.0110
-0.0110
-0.0100
-0.0090
-0.0080
-0.0060
0
0.0040
0.0070
0.0100
0.0040
0.0100
-0.0150
-0.0150
-0.0140
-0.0120
-0.0110
-0.0080
-0.0020
0.0020
0.0060
0.0120
0.0110
0.0110
-0.0240
-0.0100
-0.0040
-0.0020
-0.0010
0.0030
0.0140
0.0060
-0.0010
0.0040
0.0040
0.0060
-0.0220
0.0020
-0.0030
-0.0050
-0.0030
-0.0010
-0.0090
-0.0090
-0.0010
0.0030
-0.0020
0.0010
, 30
( , )o
rN
C
o
o
-30 -20 -10 0 10 20 30
-10
-5
0
5
10
15
20
25
30
35
40
45
-0.0180
-0.0520
-0.0520
-0.0520
-0.0540
-0.0490
-0.0590
-0.0510
-0.0300
-0.0370
-0.0260
-0.0130
-0.0280
-0.0510
-0.0430
-0.0460
-0.0450
-0.0490
-0.0570
-0.0520
-0.0300
-0.0330
-0.0300
-0.0080
-0.0370
-0.0410
-0.0380
-0.0400
-0.0400
-0.0380
-0.0370
-0.0300
-0.0270
-0.0240
-0.0190
-0.0130
-0.0480
-0.0450
-0.0450
-0.0450
-0.0440
-0.0450
-0.0470
-0.0480
-0.0490
-0.0450
-0.0330
-0.0160
-0.0430
-0.0440
-0.0410
-0.0410
-0.0400
-0.0380
-0.0340
-0.0350
-0.0350
-0.0290
-0.0220
-0.0090
-0.0520
-0.0340
-0.0360
-0.0360
-0.0350
-0.0280
-0.0240
-0.0230
-0.0200
-0.0160
-0.0100
-0.0140
-0.0620
-0.0340
-0.0270
-0.0280
-0.0270
-0.0270
-0.0230
-0.0230
-0.0190
-0.0090
-0.0250
-0.0100
Engine model (Engine thrust force ( , , )a TT M h )
The relationship between the power and throttle:
64.94
217.38 1
0.77
0.7
7 8
7
1 .3
T
T
T
T
If
P
If
P
The relationship between the thrust force and power:
max
50
/ 50
50
50 / 50
idle mil idle
mil mil
If P
T T T T P
If P
T T T T P
Idle thrust levels ( , )idle aT M h
h
Ma 0 10000 20000 30000 40000 50000
0
0.2
0.4
0.6
0.8
1.0
1060
635
60
-1020
-2700
-3600
670
425
25
-710
-1900
-1400
880
690
345
-300
-1300
-595
1140
1010
755
350
-247
-342
1500
1330
1130
910
600
-200
1860
1700
1525
1360
1100
700
Military thrust levels ( , )mil aT M h
h
Ma 0 10000 20000 30000 40000 50000
0
0.2
0.4
0.6
0.8
1.0
12680
12680
12610
12640
12390
11680
9150
9150
9312
9839
10176
9848
6200
6313
6610
7090
7750
8050
3950
4040
4290
4660
5320
6100
2450
2470
2600
2840
3250
3800
1400
1400
1560
1660
1930
2310
Maximum thrust levels max ( , )aT M h
h
Ma 0 10000 20000 30000 40000 50000
0
0.2
0.4
0.6
0.8
1.0
20000
21420
22700
24240
26070
28886
15000
15700
16860
18910
21075
23319
10800
11225
12250
13760
15975
18300
7000
7323
8154
9285
11115
13484
4000
4435
5000
5700
6860
8642
2500
2600
2835
3215
3950
5057