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Given the two-input and two-output system below R, G, h H G G. and the following subsystems' transfer functions G(S) = - G4(S) = s 4 G2(S) S +2 10 G.SE s(s + 25) 7 10 G3(s) s(s+5) H(S) = s(s + 3) 7 G5(S) H(S) S + 7 S + 7 the find following closed-loop transfer functions G(S) = C(s)/R1(s), Gz(s) = C2(s)/R1(s), G3(s) = C(s)/R2(s), and G4(s) = C2(s)/R2(s). Analyze the step responses of subsystems G(s), G2(s), G3(s), and G.S. 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 "phugoid 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 e(s) 8.(s) 26.12(s + 0.0098) (s + 1.371) (52 + 8.99 x 10-3s + 3.97 x 10-3)(2 + 4.21s + 18.23) Which pair of poles causes the phugoid mode? Which pair causes the short mode? Determine the damping ratios and natural frequencies for each mode. b Characterize the step response of this system. Decompose the response into the short mode response and phugoid mode response. Comment on each, and its relation to the location of the poles. Given the two-input and two-output system below R, G, h H G G. and the following subsystems' transfer functions G(S) = - G4(S) = s 4 G2(S) S +2 10 G.SE s(s + 25) 7 10 G3(s) s(s+5) H(S) = s(s + 3) 7 G5(S) H(S) S + 7 S + 7 the find following closed-loop transfer functions G(S) = C(s)/R1(s), Gz(s) = C2(s)/R1(s), G3(s) = C(s)/R2(s), and G4(s) = C2(s)/R2(s). Analyze the step responses of subsystems G(s), G2(s), G3(s), and G.S. 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 "phugoid 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 e(s) 8.(s) 26.12(s + 0.0098) (s + 1.371) (52 + 8.99 x 10-3s + 3.97 x 10-3)(2 + 4.21s + 18.23) Which pair of poles causes the phugoid mode? Which pair causes the short mode? Determine the damping ratios and natural frequencies for each mode. b Characterize the step response of this system. Decompose the response into the short mode response and phugoid mode response. Comment on each, and its relation to the location of the poles