  In this paper, we derive a sensor based Nonlinear Dynamic Inversion (NDI)
control law for a nonlinear system with first-order linear actuators, and
compare it to Incremental Nonlinear Dynamic Inversion (INDI), which has gained
popularity in recent years. It is shown that for first-order actuator dynamics,
INDI approximates the corresponding NDI control law arbitrarily well under the
condition of sufficiently fast actuators. If the actuator bandwidth is low
compared to changes in the states, the derived NDI control law has the
following advantages compared to INDI: 1) compensation of state derivative
terms 2) well defined error dynamics and 3) exact tracking of a reference
model, independent of error controller gains in nominal conditions. The
comparison of the INDI control law with the well established control design
method NDI adds to the understanding of incremental control. It is additionally
shown how to quantify the deficiency of the INDI control law with respect to
the exact NDI law for actuators with finite bandwidth. The results are
confirmed through simulation results of the rolling motion of a fixed wing
aircraft.
