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Frequency, radts
Fig. 6.11     Longitudinal frequency response of the general a\riation airplane: angle of
attack.
     The frequency response of Ga displays the infiuence of frequency both at short-
period and phugoid frequencies. The IGrrl remains nearly constant at low values of
frequency but displays somewhat complex behavior around COph. Such a behavior
is due to a pole-zero cancellation (close proxim/ty of pole and zero) in the transfer
function Ga. The frequency response of Go also displays a similar and complex
behavior'around the phugoid frequency that is characteristic of lightly damped
systems. Furthermore, around the short-period frequency, the phase angle of Go is
close to 90 deg, which is a characteristic feature of second- order systems. We may
recall that,  for a second-order system, when o)  :  COn, the phaserangle is 90 deg
for all values of C. The magnitude crossover frequency for Gu and Go is about
2.0 rad/s. Therefore, a human pilot with a bandwidth of 4 rad/s can have a good
control over the angle of attack and pitch angle.
6.3 Lateral-DirectionaIResponse
  Equations (4.461-4.463) based on small disturbances in lateral directional
degrees of freedom can be expressed as
ddp=( bC., ,:-B)[Cy,aAp+Cy4A4+bICypp
           - (mi  - biCyr)r + Cy8,A8o + C).8r A8r]                        (6.168)
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL          565
                                                                                                                                                             
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