Dynamics & Control PDR 2
Purdue University
AAE 451
Fall 2006
Team 4 Eparr
Tung (in my) Tran
Mark (sometimes w/ a k) Koch
Matt Dwarfinthepantssky
Ravi Patel aka Epar Leader
Nazim Haris Mohammad Ishak (no, it’s true)
Ki-Bom(ber) Kim
Matt Losshismanhood
Andrew Lockheed Martin
Overview
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Control Surface Sizing
Trim Diagram
Modal Parameters
Dutch Roll Feedback Block Diagram
Transfer Functions
Root Locus of Control System
Setting Rate Gyro Gain
Control Surface Sizing
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Historical Data: Cessna Skywagon (Roskam Part II P.261)
Elevator: Se=0.45 ft2 Ce= 0.45Cht
The elevator will span the entire length of the horizontal tail.
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Flaperon: Sf=0.4 ft2 Cf=0.245MAC
Inboard flaperon location = 0.7683ft from aircraft centerline.
Outboard flaperon location = 2.765ft from aircraft centerline.
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Rudder: Sr=0.172 ft2 Cr= 0.375Cvt
The rudder will span the entire length of the vertical tail.
Se
 0.45
Sh
Sa
 0.10
S
Sr
 0.44
Sv
Trim Diagram 1 Procedure
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Calculations (Roskam p. 205)
CL  CL 0  CL   CLe  e
0  C m0 
dCm
C L  C me  e
dC L
Cm
dCm
Static Margin  SM  

 x ac  x cg
dCL
CL
CM cg  CM ac  CL ( x cg  x ac )  CM ac  CL ( SM )
C me  Cme 
Cm
CL
CLe
C m  Cm0 
Cm
CL
CL0
CL vs. α
Trim Diagram 1
Trim Diagram 2 Procedure
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Calculations (Roskam, Brandt p.111)
CL  CL 0  CL   CLih ih  CLe  e
0  C m0 
dCm
C L  C mih ih  C me  e
dC L
C mih  Cmih 
Cm
 tail stall 
h
CL
 ih   0
d
1
d
stall
CLih
Cmi  CL hV h
h
h
Trim Diagram 2
Trim Diagram Conclusion
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Horizontal Stabilizer Incidence Angle
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o
-1
Max Elevator Deflection Angle
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-15o
Stability And Control Derivatives
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Stability
Control
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Longitudinal Static
Stability
Cmα=-1.6265
Usually negative
Weathercock Stability
Cnβ=0.10193
typically 0.06 to 0.2
Dihedral Effect
Clβ=-0.0753
typically -0.09 to -0.3
Pitch, elevator size
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Cmδe=-2.6408
typically -1 to -2
Yaw and/or roll, rudder size
Cnδr=-0.1002
typically -0.06 to -0.12
Roll, flaperon size
Clδa=0.285
typically 0.05 to 0.2
Modal Parameters
Open Loop
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Phugoid mode
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Damping Ratio: 0.495
Natural Frequency: 0.2582 rad/sec
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Short Period mode
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Damping Ratio: 0.934
Natural Frequency: 13.248 rad/sec
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Dutch Roll mode
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Damping Ratio: 0.2014
Natural Frequency: 8.355 rad/sec
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Roll mode
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Time Constant: 0.75 sec
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Spiral mode
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Time Constant: 81.89 sec
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Calculation Reference:
Modern Control
Engineering Ogata pg.231
Closed loop poles were
obtained from Flat Earth.
n    jd
2

 
n
2
Dutch Roll Feedback Block Diagram
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Nominal Gain: -0.11
Dutch Roll closed loop
Damping Ratio: 0.841
Natural Frequency: 10.9 rad/sec
Futaba S-148 Servo Subsystem
Futaba S-148 Servo Linear Model
1
950
surface command
s+40
1
s
Transfer Fcn
Integrator
Sum
D&C Source Book
1
surface deflection
Transfer Functions
Aircraft and Servo
Transfer Function
 69673( s  8.355)( s ^ 2  0.4425s  1.161)
( s  8.369)( s  0.07673)( s ^ 2  3.368s  69.79)( s ^ 2  40s  950)
Aircraft Transfer
Function
 73.3431( s  8.354)( s ^ 2  0.4426s  1.161)
( s  8.366)( s  0.07672)( s ^ 2  3.367 s  69.81)
Servo Transfer
Function
950
s^2 + 40 s + 950
Rate Gyro
Transfer Function
1
Control Law
Transfer Function
 0.1
Root Locus of Control System
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Closed Loop Poles for Yaw Rate feedback to Rudder
Installation of the Rate Gyro
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Static Test
The gear switch on the radio controller will be used to turn the feedback control
system on and off.
Up position on the gear switch will be used for no feedback control. The rate gyro
should work properly inputting no rudder deflection.
Down position on the gear switch will activate the feedback control. Yawing the
aircraft should give a rudder deflection in the direction to counter the yaw motion.
If the rudder deflection is in the wrong direction switch the rev setting on the gyro.
Setting the Rate Gyro Gain
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Dynamic Test
Perform a flight test:
The pilot will need to have an additional person help with the control of the gear switch in
case the feedback control system causes the aircraft to be uncontrollable.
The handling qualities of the aircraft will be determined by the pilot and the feedback gain
will be adjusted accordingly.
This iterative process continues until the handling qualities are determined satisfactory.
Questions?