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┃ ┃ ┃.~f.....,:......-.... - ┃__-- ┃
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┃ ┃ ┃ ┃ '........N........"'- ┃
┣━┻━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫ ┃
┃ ┃ .....:......,.........: ┃~ ┃
┃ ┃ . . . . ... . . . . .. . . . - . . . . . . ┃~ ┃
┃ ┃ I ┃ I ┃
┗━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━┛
o 5 10
15 20 25 30
Time, s
Fig. 6.55 Unit-step response of the pitch displacement autopilot for the general avi-
atlion airplane.
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 623
6.6 Summarlt .
In this chapter, we have studied the longitudinal and lateral-directional responses
of the airplane. The longitudinal response of a statically stable airplane consists
of two distinct modes, the short-period mode and the phugoid mode. The lateral-
direction motion comprises roll~subsidence mode, the Dutch-roll oscillation, and
the spiral modes. Accordingly, we obtained simplified transfer functions and state-
space models to study these modes individually. These simplified transfer functions
were found to be of considerable help in designing the fiight control systems.
For a statically unstable airplane, the usual short-period and phugoid modes
do not exist. Instead, we have two exponential modes and an oscillatory mode.
The oscillatory mode is called the third oscillatory mode that has short-period-like
damping and phugoidlike frequency. Because of static instability, at least one of
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