In typical conventional aircraft, longitudinal flight model linearization results in transfer functions with two pairs of complex conjugate poles. Consequently, the natural response for these airplanes has two modes in their natural response. The “short period” mode is relatively well damped and has a high-frequency oscillation. The “plugoid mode” is lightly damped and its oscillation frequency is relatively low. For example, in a specific aircraft the transfer function from wing elevator deflection to nose angle (angle of attack) is (McRuer, 1973)

a. Find which of the poles correspond to the short period mode and which to the phugoid mode.

b. Peform a “phugoid approximation” (dominant-pole approximation), retaining the two poles and the zero closest to the; ω-axis.

c. Use MATLAB to compare the step responses of the original transfer function and the approximation.

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O(s) de(s) 26.12(s + 0.0098)(s+1.371) (s? + 8.99 x 10-3s+3.97x 10-3)(s + 4.21s + 18.23)