Commonalities between robust hybrid incremental nonlinear dynamic inversion and proportional-integral-derivative flight control law design

Incremental Nonlinear Dynamic Inversion (INDI) has received substantial interest in the recent years as a nonlinear flight control law design methodology that features inherent robustness against bare airframe aerodynamic variations. However, systematic studies into the robust design benefits of INDI-based control over the classical divide-and-conquer philosophy have been scarce. To bridge this gap, this paper compares the setup of hybrid INDI with a standard industry benchmark that is based on two-degree-of-freedom gain-scheduled proportional-integral-derivative control. This is done on an architectural basis and in terms of achievable robust stability and performance levels with respect to a common set of design requirements. To this end, a non-smooth, multi-objective $H_{\infty }$-synthesis algorithm is used that incorporates mixed parametric and dynamic uncertainties in the design objective and constraints. It is shown that close similarities exist between hybrid INDI design and gain-scheduled PID control, which leads to virtually equivalent robustness and performance outcomes in both linear time-invariant and linear time-varying contexts. It is therefore concluded that the main benefit of the hybrid INDI does not lie in improved robustness properties per se, but in the opportunity to perform modular robust design in an implicit model-following context. Specifically, this implies that the areas of flying qualities, robustness, and nonlinear implementation are directly visible and accessible in the control law structure.