boiler xpress 1 final presentation april 26, 2001 kacie burtonkevin dahya kerem koraymellisa glaser...
TRANSCRIPT
Boiler Xpress 1Final Presentation
April 26, 2001
Kacie Burton Kevin DahyaKerem Koray Mellisa GlaserWael Nour Tanya Tuinstra
Project Objective
Write a MATLAB computer program for dynamic modeling and control system design of fixed wing aircraft
Use Boiler Xpress geometry, mass, and aerodynamic data Produce stability and control derivatives Determine 4th order TF, Q(s)/E(s), R(s)/R(s), and P(s)/A(s) Determine 12th order TF, Q(s)/E(s), R(s)/R(s), and P(s)/A(s) Design 3 stability augmentation systems
Pitch rate feedback to elevator to increase of Short Period mode Yaw rate feedback to rudder to increase of Dutch Roll mode Roll rate feedback to aileron to decrease time constant of roll mode
How we did it… Modified Cessna182.m to apply to the
BoilerXpress Calculated control derivatives using Jan Roskam,
Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes
4th order transfer functions: BoilerXpressLatSC.m BoilerXpressLongSC.m Plotted root loci
12th order transfer functions and step responses: FlatEarth.mdl and FlatEarthAnal.m
How we did it… Modified DesignPitch.m, DesignYaw.m,
and DesignRoll.m to use Boiler Xpress 4th order transfer functions Varied control gain, K, to achieve design
damping ratio Used 6th order transfer functions from
DesignPitch.m, DesignYaw.m, and DesignRoll.m to determine n for design damping ratio
Control Derivative Constants
Lifting Force: CLO=0.95 CL=4.9174 CL’=0.3333 CLq=5.3879
Side Force: CyO=0 Cy=-0.0484 CyA=0 CyR=0.0353 Cyp=-0.0056 CyR=0.7080
Reference Positions: xbarac=0.3412 xbarcg=0.3412
Control Derivative Constants
Pitching Moment: CmO=-0.0400 Cm=-1.8448 Cm’=-0.6329 Cmq=-2.9935
Rolling Moment: Clo=0 Cl=-0.0331 ClA=0.8000 ClR=0 Clp=-0.1500 ClR=0.2467
Yawing Moment: Cno=0 Cn=0.1100 CnA=-0.1203 CnR=-0.1280 Cnp=-0.1233 CnR=-0.7214
Universal Block Diagram
TransferFunction
Gaink
input output+
-
4th Order Transfer Functions
Pitch:
Yaw:
Roll:
375.32688.0448.3869.5
1447.121.576.13495.27
)(
)(234
23
ssss
Esss
s
sQ
e
3076.0458.3911.2806.2
6.11513.137.916.49
)(
)(234
23
ssss
sss
s
sR
R
3076.0458.3911.2806.2
178827492875
)(
)(234
23
ssss
sss
s
sP
A
12th Order Transfer Functions
)678.16602.0)(5292.04735.0)(6988.6)(07163.0)(23.1)(244.2)(217.5(
)2549.0()1()1()3254.0(
)(
)(223
2442
ssssEssssss
ssss
s
sQ
e
)678.16602.0)(5288.04728.0)(6988.6)(07159.0)(231.1)(244.2)(193.5(
)2548.0()1()1()3251.0(
)(
)(223
2442
ssssEssssss
ssss
s
sR
R
)678.16602.0)(5289.04729.0)(6988.6)(07159.0)(231.1)(244.2)(195.5(
)2548.0()1()1()3251.0(
)(
)(223
2442
ssssEssssss
ssss
s
sP
A
Pitch:
Yaw:
Roll:
-6 -5 -4 -3 -2 -1 0 1 2 3-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Real Axis
Imag
Axi
s
Root Locus for Q(s)/E(s)
Root Locus for R(s)/R(s)
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1.5
-1
-0.5
0
0.5
1
1.5
Real Axis
Imag
Axi
s
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2-1.5
-1
-0.5
0
0.5
1
1.5
Real Axis
Imag
Axi
sRoot Locus for P(s)/A(s)
Output from BoilerXpressLongSC.m
0 20 40 60 80 100 120 140 160 180 200-10
-5
0
5x 10
21
time(sec)
u(f
t/se
c)
Note lightly damped phugoid mode
0 20 40 60 80 100 120 140 160 180 200-2
0
2
4
6x 10
21
time(sec)
alp
ha(
deg
)
0 20 40 60 80 100 120 140 160 180 200-5
0
5
10x 10
21
time(sec)
q(d
eg/s
ec)
0 20 40 60 80 100 120 140 160 180 200-5
0
5
10
15x 10
21
time(sec)
thet
a(d
eg)
Note lightly damped phugoid mode
Step elevator response, Boiler Xpress, cruise configuration
Output from BoilerXpressLongSC.m
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
0
1
2
time(sec)
u(f
t/se
c)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1.5
-1
-0.5
0
time(sec)
alp
ha(
deg
)
Note highly damped short period mode
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1
time(sec)
q(d
eg/s
ec)
Note highly damped short period mode
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2
-1.5
-1
-0.5
0
time(sec)
thet
a(d
eg)
Step elevator response, Boiler Xpress, cruise configuration
Q(s)/E(s) from FlatEarth.m
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02
-0.01
0
0.01
0.02
time (sec)
Q (
rad
/sec)
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.08
-0.06
-0.04
-0.02
0
time (sec)
theta
(ra
d)
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
time (sec)
alp
ha (
rad
)
linear sim nonlinear sim
Time response comparison for elevator input. Flat Earth Model, Boiler Xpress
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.05
-0.04
-0.03
-0.02
-0.01
0
time (sec)
R (
rad
/sec)
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.1
-0.08
-0.06
-0.04
-0.02
0
time (sec)
psi
(rad
)
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.08
-0.06
-0.04
-0.02
0
0.02
time (sec)
beta
(ra
d)
linear sim nonlinear sim
Time response comparison for rudder input. Flat Earth Model, Boiler Xpress
R(s)/R(s) from FlatEarth.m
P(s)/A(s) from FlatEarth.m
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
time (sec)
P (
rad
/sec
)
Time response comparison for aileron input. Flat Earth Model, Boiler Xpress
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
time (sec)
ph
i (ra
d)
linear sim nonlinear sim
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
50
100
150
200
time (sec)
Y (
ft)
linear sim nonlinear sim
Pitch Stability Augmentation System
Incorporated Boiler Xpress and Cessna 182 transfer functions into DesignPitch.m for system comparison
Adjusted gains to meet following criteria -1.3<K<1.3 = 0.707
For K=0.2885, =0.707 Damping objective met for pitch
stability
Pitch Stability Augmentation System
Used 6th order transfer function from DesignPitch.m to determine n for design damping ratio
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Real Axis
Ima
g A
xis
Root Locus Q(s)/DeltaE(s) for Improved System
Pitch Root Locus
Yaw Stability Augmentation System
Incorporated Boiler Xpress and Cessna 182 transfer functions into DesignYaw.m for system comparison
Adjusted gains to meet following criteria -1.3<K<1.3 = 0.26
For K=0.35, =0.261 Damping objective met for yaw stability
Yaw Stability Augmentation System
Used 6th order transfer function from DesignYaw.m to determine n for design damping ratio
-80 -60 -40 -20 0 20 40 60 80
-60
-40
-20
0
20
40
60
Real Axis
Ima
g A
xis
Root Locus R(s)/DeltaR(s) for Improved System
Yaw Root Locus
Roll Stability Augmentation System
Incorporated Boiler Xpress and Cessna 182 transfer functions into DesignRoll.m for system comparison
Adjusted gains to meet following criteria -1.3<K<1.3 T = 0.1
For K=0.0001, T=0.05 Damping objective not met for roll
stability
Roll Stability Augmentation System
Used 6th order transfer function from DesignRoll.m to determine n for design damping ratio
-100 -50 0 50
-60
-40
-20
0
20
40
60
Real Axis
Ima
g A
xis
Root Locus P(s)/DeltaA(s) for Improved System
Roll Root Locus
Results Pitch Stability Augmentation System
K=0.2885, n=0.305 rad/sec, =0.707
Yaw Stability Augmentation System K=0.35, n=25 rad/sec, =0.261
Roll Stability Augmentation System K=0.0001, n=31 rad/sec, =0.65 T=0.05
Conclusions Stability and control derivatives found for
Boiler Xpress 4th and 12th order transfer functions
determined for Boiler Xpress Desired damping ratio met for pitch and yaw
cases within gain limits; roll case did not meet design time constant
Corresponding natural frequencies were found for each case
Purpose is to achieve stable system by adding a control system