Dynamic Modeling PDR Dynamic Modeling Preliminary Design Review for Vehicle and Avionics October 17, 2000 Presented By: Christopher Peters …and that’s cool Team DR2 Chris Curtis Loren Garrison Jeff Rodrian Mark Blanton

Dynamic Modeling PDR Presentation Outline: General Dynamic Model Buildup Component Description Mathematical/Physical Approach Methods Results Conclusion Progress Plan

Gain Selector and Feedback sign implementation Dynamic Modeling PDR General Dynamic Model Buildup for YAW-Feedback Loop Transmitter Pilot Rudder Input δrc(Volts) Aircraft Model Dutch Roll Approx. + δr r Receiver Servo + - kr Gain Selector and Feedback sign implementation Washout Filter Rate Gyro

Dynamic Modeling PDR Component Description Transmitter Receiver Servo Block Diagram Dynamic Model Simulation Airplane Dynamic Model for Yaw Feedback Non-Linear vs. Linear Dutch-Roll Approximation For small dihedral effect, mainly sideslipping and yawing Gain Selector Washout Filter Rate Gyro

Dynamic Modeling PDR Simulink Servo Model Not Specified FUTABA Model Actual model determined by testing, hopefully soon…

Dynamic Modeling PDR Mathematical/Physical Approach General Transfer Function for Dutch-Roll Approximation: Terms Described in Subsequent Slides

Dynamic Modeling PDR Lateral-Directional, Dimensional Stability Derivatives Lateral Acceleration per Unit Sideslip Angle Lateral Acceleration per Unit Yaw Rate Lateral Acceleration per Unit Rudder Angle Yaw Angular Acceleration per Unit Sideslip Angle Yaw Angular Acceleration per Unit Yaw Rate Yaw Angular Acceleration per Unit Rudder Angle Dynamic Pressure

Dynamic Modeling PDR Lateral-Directional, Dimensional Stability Derivative Coefficients

Dynamic Modeling PDR Lateral-Directional, Dimensional Stability Derivatives and Coefficients… Continued: [rad-1] DR2 C182 MP-X5 Cyβ -0.30 -0.31 -0.34 Cyr 0.22 0.21 0.32 Cyδr 0.194 0.187 0.24 Cnβ 0.108 0.065 0.16 Cnr -0.079 -0.099 4.84 Cnδr -0.073 -0.066 -0.11

Dynamic Modeling PDR Lateral-Directional, Dimensional Stability Derivatives and Coefficients… Continued: Yβ = -9.09 ft/s2 Yr = 1.07ft/s Yδr = 5.88 ft/s2 Nβ = 5.87 s-2 Nr = -0.69 s-1 Nδr = -3.96 s-2 All Evaluated at ρ= 2.335e-03slugs/ft3 (600ft) and Vloi = 24 ft/s Difficult to compare to other values do to dependency on Vloi

Dynamic Modeling PDR Transfer Function, Damping Ratio and Natural Damped Frequency: Open Loop (OL) Numerator Constant Coefficient 0

Dynamic Modeling PDR Constant Coefficient:

Dynamic Modeling PDR Stability Analysis Closed Loop (CL)

Dynamic Modeling PDR Stability Analysis (CL)

Dynamic Modeling PDR Washout Filter Depends on Selection of Feedback Implementation Might not be needed For Destabilizing Effects To Visualize Dutch Roll Mode Might be needed If Rate Gyro is supposed to stabilize Aircraft Depends on Roll/Yaw Effects Very Simple T.F.: s/(s+c), c = 1,2,3

Dynamic Modeling PDR Rate Gyro No Specifications yet… BUT We still have a week left…

Dynamic Modeling PDR Progress Plan Improve Current Values as Design continues to improve Analyze Pitch and Roll Dynamic Models Complete Stability and Control Analysis Simulate Components and Aircraft to obtain A PRIORI Model Compare Results to Mark Peters’ Analysis