Dynamics & Control PDR 2

1. Dynamics & Control PDR 2 Purdue University AAE 451 Fall 2006 Team 4 Eparr Tung (in my) Tran Matt Dwarfinthepantssky Nazim Haris Mohammad Ishak (no, it’s true) Matt Losshismanhood Mark (sometimes w/ a k) Koch Ravi Patel aka Epar Leader Ki-Bom(ber) Kim Andrew Lockheed Martin

2. Overview • Control Surface Sizing • Trim Diagram • Modal Parameters • Dutch Roll Feedback Block Diagram • Transfer Functions • Root Locus of Control System • Setting Rate Gyro Gain

3. Control Surface Sizing • 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. • Flaperon: Sf=0.4 ft2 Cf=0.245MAC Inboard flaperon location = 0.7683ft from aircraft centerline. Outboard flaperon location = 2.765ft from aircraft centerline. • Rudder: Sr=0.172 ft2 Cr= 0.375Cvt The rudder will span the entire length of the vertical tail.

4. Trim Diagram 1 Procedure • Calculations (Roskam p. 205)

5. CL vs. α

6. Trim Diagram 1

7. Trim Diagram 2 Procedure • Calculations (Roskam, Brandt p.111)

8. Trim Diagram 2

9. Trim Diagram Conclusion • Horizontal Stabilizer Incidence Angle • -1o • Max Elevator Deflection Angle • -15o

10. Stability And Control Derivatives • Control • Pitch, elevator size 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 • Stability • 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

11. Modal ParametersOpen Loop • Phugoid mode • Damping Ratio: 0.495 • Natural Frequency: 0.2582 rad/sec • Short Period mode • Damping Ratio: 0.934 • Natural Frequency: 13.248 rad/sec • Dutch Roll mode • Damping Ratio: 0.2014 • Natural Frequency: 8.355 rad/sec • Roll mode • Time Constant: 0.75 sec • Spiral mode • Time Constant: 81.89 sec Calculation Reference: Modern Control Engineering Ogata pg.231 Closed loop poles were obtained from Flat Earth.

12. Dutch Roll Feedback Block Diagram • Nominal Gain: -0.11 • Dutch Roll closed loop Damping Ratio: 0.841 Natural Frequency: 10.9 rad/sec

13. Futaba S-148 Servo Subsystem D&C Source Book

14. Transfer Functions Aircraft and Servo Transfer Function Aircraft Transfer Function Servo Transfer Function Rate Gyro Transfer Function Control Law Transfer Function

15. Root Locus of Control System • Closed Loop Poles for Yaw Rate feedback to Rudder

16. Installation of the Rate Gyro • 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.

17. Setting the Rate Gyro Gain • 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.

18. Questions?