Question

In the state-space model form for an aircraft, the Dutch roll motion can be approximated using the following equations Assume the coefficients in the above state-space model have the following numerical values: N0.34 s-1 U1 154 fus = 5.236 ft/s2 Ya -7.8 ft/s2 N, =-0.616 s-2 y,-2.47 ft/s (a) Determine the Dutch roll eigenvalues (b) Dtermine the damping ratio and undamped natural frequency of the Dutch roll mode (c) Draw a pole-zero map of the system and provide pitctorial representation of the undamped natural frequency and the damping ratio on this map. (d) Provide a sketch of the expected response of the system if it is subjected to a unit step input of the control surface indicated in the above equation

Answer 1

NA NY plugging Yn--F8ft/s. Nr..。.34 Is a-44ft/s ul=154ft/sec Yr= 5,2.36 Pt/s 'o, 64. -o, 34, ] ashere A- 0506936 o 64 34 :[ o veeigen values as foll ous -64 to34 25-0141 个undampec) o 2.5 lc) Pole zerv plot: SA wn LI

Ys)- Ta king Laplace (212) ST-Ajxlo3 1 χ(s) = (st-A)-) BU ls) やlugging values of A, B & LI (s) 추 Henc

Transfer function element poles: s0.2-0.781025i (simple pole) s0.20.781025 i (simple pole) Less time Unit step response plot -0.2 -0.4 -0.6 -0.8 Bode plot 0 一 -100 -150 00 1000 10 10

Transfer function element poles s0.2-0.781025i (simple pole) s~-0.2 +0.78 1025i simple pole) Less ti Unit step response plot: 0.1 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 Bode plot: 0 -10 20 -30 10 0.01

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