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:
F C qS Xa Xa
F C qS Ya Ya
F C qS Za Za
Na CNqSb
La CLRollaqSb
Engine forces and moments:
FTF0F0 XT YT ZT
LT 0 MT 0 NT 0
Total force and moment coefficients:
CXa CX (,e) cQ CX () 2V Q
CZaCZ(,,e)cQCZ () 2V Q
Q
C()1 20.19e cQC ()
ZZ 57.3 25 2V
C C (, , ) b C ()RC ()P
YaYar2VY Y RP
0.020.021a 0.86r b C ()RC ()P RP
20302VY Y
CMa CM(,e)cQCM ()CZa(xcg,ref xcg) 2V Q
CLRolla CLRoll (,)CL , 20o (,)a CL
, 30o (,)r r 30
Roll a 20 + b C ()RC ()P
Roll
2V LRoll R
C C (,)C
LRoll P (,)a C
(,)r N,r 30o 30
Na N
+2V CN ()RCN ()PCYa(xcg,ref xcg)b
N,a 20o
20
bc
RP
Lookup tables:
CXQ
CYR
CYP
CZQ
CLRollR
CLRollP
CMQ
CNR
CNP
-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
CX (,e)
o e
o
-10 -5 0 5
10
15
20
25
30
35
40
45
-24
-12
0
12
24
-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
CZ ()
o
CZ ()
-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
CM (,e)
o e
o
-10 -5 0 5
10
15
20
25
30
35
40
45
-24
-12
0
12
24
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
CLRoll (,) CLRoll (,) CLRoll (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
0
5
10
15
20
25
30
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
CN (,) CN (,) CN (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
0
5
10
15
20
25
30
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
CLRoll,a20o (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
-30
-20
-10
0
10
20
30
-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
CLRoll ,r 30o (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
-30
-20
-10
0
10
20
30
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
CN,a20o (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
-30
-20
-10
0
10
20
30
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
CN,r 30o (,)
o o
-10 -5 0 5
10
15
20
25
30
35
40
45
-30
-20
-10
0
10
20
30
-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 T(Ma,h,T )) The relationship between the power and throttle:
If T 0.77
P 64.94T
If T 0.77 P217.38T 117.38
The relationship between the thrust force and power: If P50
TTidle Tmil TidleP/50 If P50
T Tmil Tmax Tmil P50/50 Idle thrust levels Tidle (Ma ,h)
Military thrust levels Tmil (M a , h)
Maximum thrust levels Tmax (Ma ,h)
h Ma
0 0.2 0.4 0.6 0.8 1.0
0
10000
20000
30000
40000
50000
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
h Ma
0 0.2 0.4 0.6 0.8 1.0
0
10000
20000
30000
40000
50000
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
h Ma
0 0.2 0.4 0.6 0.8 1.0
0
10000
20000
30000
40000
50000
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