Dynamic Modeling PDR 17 October 2000 Keith R

Dynamic Modeling PDR 17 October, 2000 Keith R. Hout Patrick Dempsey Bridget Fitzpatrick

Loop Closure Description § Rate feedback in the pitch axis § Objective: To vary the damping ratio of the short period mode § Short Period Mode § Describes airplane pitch response to elevator inputs § Characterized by near constant velocity and oscillations in angle of attack and pitch angle § Tends to be highly damped for flight conditions such as ours § I. e. ~0. 7 < ξ < ~1

Loop Closure Description § Block Diagram TX RX Pilot inputs elevator command Pilot + Aircraft Servo +/ - ? Servo converts voltage to elevator deflection Pitch Rate Gyro Sign of feedback gain is chosen to stabilize or destabilize the mode

Dynamic Models § Servo Model § 2 nd Order Approximation § Frequency and damping ratio are still unknown and are to be obtained from testing

Dynamic Models § Pitch Rate Gyro § 2 nd Order Approximation § Gyro frequency and damping ratio still needed, are to be obtained from testing

Dynamic Models § Aircraft Transfer Function § Short Period Approximation § 2 nd Order - Flight speed

Dynamic Models § Longitudinal Dimensional Stability Derivatives § SM=0. 18 Equation Units Description Value [(rad/s 2)/rad] Pitch angular acceleration due to elevator deflection -16. 07 [(ft/s 2)/rad] Vertical acceleration due to elevator deflection -13. 61 [(rad/s 2)/(rad/s)] Pitch angular acceleration -1. 87 due to rate of change of α [(rad/s 2)/rad] Pitch angular acceleration due to α -14. 12 [(ft/s 2)/rad] Vertical acceleration due to α -186. 82 [(rad/s 2)/(rad/s)] Pitch angular acceleration due to pitch rate -5. 14

Dynamic Models §Longitudinal Non-Dimensional Stability Derivatives §SM=0. 18 Equation Description Δ Pitching moment coefficient due to elevator deflection Δ Lift coefficient due to elevator deflection Value[rad-1] SID 5 (MPX 5) -0. 81 (-1. 15) 0. 30 (0. 42) Δ Pitching moment coefficient with α -0. 71 (-1. 13) Δ Pitching moment coefficient due to rate of change of α -3. 11 (-3. 59) Δ Pitching moment coefficient due to pitch rate -8. 54 (-10. 57)

Dynamic Models §Damping Ratio and Natural Frequency §SM=0. 18 §Mode is very highly damped

Root Locus

Dynamic Models §Tasks Remaining §Complete transfer function models for remaining elements of block diagram §Obtain parameters for the servo and gyro §Construct equivalent transfer function for entire loop and obtain a root locus §Determine gain magnitude and sign to achieve either a higher or lower damping ratio §Determine the exact method the pilot will use to implement the feedback gain §i. e. what channel will be used to switch the gyro gain from off to nominal