boiler xpress 1 final presentation april 26, 2001

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