for wings-level equilibrium flight. The longitudinal moving
mass reference signal is
r
x = Kpγeγ + Kiγ Zt0t eγ(τ)dτ + Kdγe˙γ.
The channel from lateral mass position rpy to turn rate
ψ ˙ is non-minimum phase, with a single zero in the right
half plane. In principle, this non-minimum phase zero limits
performance (closed-loop bandwidth). In practice, though,
closing the loop from turn rate to lateral mass location
is quite effective, provided the performance limitations are
acknowledged in control parameter selection. Let eψ ˙(t) =
ψ ˙d − ψ ˙(t), where ψ ˙d is the desired turn rate. The lateral
moving mass control signal is
r
y = Kp ˙
ψ
e ˙
ψ + Kiψ ˙ Zt0t eψ ˙(τ)dτ + Kdψ ˙ e˙ψ ˙.
With the glide path and turn rate PID controllers so defined,
the first step is to tune these controllers for the linearized
system dynamics. Having done so, the next step is to retune the controllers as necessary for the nonlinear dynamics
through simulation.