As the roll mode initially migrates to the left, and
as the complex q(s) zeros migrate towards the break-in
point, a fundamental question of interest is the
following: "Where is the roll mode relative to the breakin
point at the break-in gain value, i.e., to the left or
right, and why?" Eqs. (17)-( 18) (Rule 2) can be utilized
to determine the system gain at reversal (k= 1.6).
Additionally, standard sketching rules for the q(s)
migration yield the gain at break-in (k= 2.9). Event
sequence would suggest the roll mode is to the right of
the break-in point. The resulting real axis zero "traps"
the roll mode, pushes it towards the origin, and leaves
the dutch-roll mode to move off towards --. The
opposite scenario, where the roll mode is to the left of
the break-in occurrence and is pushed off towards --
followed by a dutch-roll break-in to the real axis, can be
ruled out. Dutch-roll break-in on the real axis would
violate the phase requirement in Eq. (16) (Rule 3).
Information of this sort could provide basis for
controller modification to illicit further improvement