Answer Happy

Please assume Uo = 176(fps), g = 32.2(fps^2) and theta_o
= 0 no need to convert to SI
G1. The following are the dimensional derivatives of longitudinal motion for the Navion aircraft: (Xu + XP) -0.0451, Xa 6.384, XSE 0, XT = 0.0117; (Zu + Zp.) = -0.3697, Za = -356.29, Za = 0, ZE = –28.17; (1) (M, + MP) = 0.0, Ma = -8.795, Ma = -0.909, Mg = -2.0767, ME = -11.189; If you feel some derivatives you need have been omitted, it because they are too small to report and can be safely assumed to be zero. Let the states and control be: x = 0 u = α A - {F} δE ST) (2) Note that you might want to replace SE + -8E in the polynomial-matrix format to achieve proper convention (that a downward elevator deflection leads to a positive pitching moment). (a) Plot the open-loop poles of longitudinal dynamics. Identify the damping ratio and natural frequency for the short-period and phugoid modes. (b) It is desired to improve the phugoid response by increasing its damping ratio. As mentioned in class, a way to do this is to provide a pitch attitude feedback via a proportional controller as follows: U1 = Estick - K20 (3) Draw the root-locus of the closed-loop poles with the above SAS in the loop. Determine the gain, Ke that increases the phugoid damping ratio to five times its original value. (c) What happens to zeros of the a(s)/(-8E(s)) transfer function upon turning on the pitch- feedback SAS proposed above? i. For both _386. a() and a(s) plot the pole-zero distribution, preferably on a single graph. Do you think there is a "potential for problem” in terms of cancellation of the phugoid mode poles with zeros? -8E() open loop - ES) cl. loop