Nonlinear Dynamic Inversion with Actuator Dynamics: An Incremental Control Perspective

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 roll motion of a fixed-wing aircraft.