Fa2004 16.3331210 Now have a coupled situation that is quite interesting Forces on the aircraft change with altitude(h)because height langes the gust velocity Changes in the forces on the aircraft impact the height of the airplane since both 0 and a will change Analyze the coupling by looking at the longitudinal equations Lu w q h T h=[00001]x=Ch with controls fixed(zero and input u = AT+Bu( 1)ug= Ar+ Bu d A c +mBu(, 1ChI d A+Bu(, 1Cr dynamics have been modified because of the coupling between the change in altitude and the change in forces(with ug) Closed this loop on the b747 dynamics to obtain du Phugoid poles 0-0.0033士0.0672i 0.08-0.0014±0.1150 0.1500002±01442i 020.0014±01619 Clearly this coupling is not good, and an unstable phugoid mode is to be avoided during landing operations� � � Fall 2004 16.333 12–10 • Now have a coupled situation that is quite interesting – Forces on the aircraft change with altitude (h) because height changes the gust velocity – Changes in the forces on the aircraft impact the height of the airplane since both θ and α will change. • Analyze the coupling by looking at the longitudinal equations � �T x = u w q θ h h = 0 0 0 0 1 x = Chx with controls fixed (zero) and input ug x˙ = Ax + ˜ ˜ Bw(:, 1) ˜ Bw(:, 1)ug = Ax + ˜ duh dh du = Ax˜ ˜ + Bw(:, 1)Chx � dh du = A˜ + B˜w(:, 1)Ch x dh ⇒ dynamics have been modified because of the coupling between the change in altitude and the change in forces (with ug). • Closed this loop on the B747 dynamics to obtain du Phugoid Poles dh 0 0.08 0.15 0.2 ­0.0033 ± 0.0672i ­0.0014 ± 0.1150i 0.0002 ± 0.1442i 0.0014 ± 0.1619i – Clearly this coupling is not good, and an unstable Phugoid mode is to be avoided during landing operations