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

3. Control Surface Sizing Historical Data: Cessna Skywagon ( Historical Data: Cessna Skywagon (Roskam Part II P.261) Elevator: S e =0.45 ft 2 C e = 0.45C ht The elevator will span the entire length of the horizontal tail. Flaperon: S f =0.4 ft 2 C f =0.245MAC Inboard flaperon location = 0.7683ft from aircraft centerline. Outboard flaperon location = 2.765ft from aircraft centerline. Rudder: S r =0.172 ft 2 C r = 0.375C vt The rudder will span the entire length of the vertical tail.

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

5. C L vs. α

6. Trim Diagram 1

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

8. Trim Diagram 2

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

10. Stability And Control Derivatives Stability Stability Longitudinal Static Stability Longitudinal Static Stability C mα =-1.6265 Usually negative Usually negative Weathercock Stability Weathercock Stability C nβ =0.10193 typically 0.06 to 0.2 typically 0.06 to 0.2 Dihedral Effect Dihedral Effect C lβ =-0.0753 typically -0.09 to -0.3 typically -0.09 to -0.3  Control  Pitch, elevator size C mδe =-2.6408 C mδe =-2.6408 typically -1 to -2 typically -1 to -2  Yaw and/or roll, rudder size C nδr =-0.1002 C nδr =-0.1002 typically -0.06 to -0.12 typically -0.06 to -0.12  Roll, flaperon size C lδa =0.285 C lδa =0.285 typically 0.05 to 0.2 typically 0.05 to 0.2

11. Modal Parameters Open Loop Phugoid mode Phugoid mode Damping Ratio: 0.495 Damping Ratio: 0.495 Natural Frequency: 0.2582 rad/sec Natural Frequency: 0.2582 rad/sec Short Period mode Short Period mode Damping Ratio: 0.934 Damping Ratio: 0.934 Natural Frequency: 13.248 rad/sec Natural Frequency: 13.248 rad/sec Dutch Roll mode Dutch Roll mode Damping Ratio: 0.2014 Damping Ratio: 0.2014 Natural Frequency: 8.355 rad/sec Natural Frequency: 8.355 rad/sec Roll mode Roll mode Time Constant: 0.75 sec Time Constant: 0.75 sec Spiral mode Spiral mode Time Constant: 81.89 sec 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 Nominal Gain: -0.11 Dutch Roll closed loop Dutch Roll closed loop Damping Ratio: 0.841 Damping Ratio: 0.841 Natural Frequency: 10.9 rad/sec Natural Frequency: 10.9 rad/sec

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

14. Transfer Functions Aircraft and Servo Transfer Function Servo Transfer Function Aircraft 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 Closed Loop Poles for Yaw Rate feedback to Rudder

16. Installation of the Rate Gyro Static Test 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 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?