Multi-Objective Synthesis of Hybrid Incremental Dynamic Inversion Control Laws Using H-Infinity Loop-Shaping

Nonlinear Dynamic Inversion (NDI) control and its Incremental variant (INDI) provide a conceptually simple and modular control framework, making it an attractive technique for designing flight control laws. By coupling these control architectures with robust control synthesis procedures, the overall approach can systematically ensure compliance with certification-level robustness requirements. In this sense, the H∞ Loop-Shaping Design Procedure (LSDP) is a strong contender as a robust control synthesis approach, as it provides controllers with a priori robust stability guarantees. Therefore, in this study, structured H∞ synthesis based on the H∞ LSDP is used to systematize the development of (I)NDI control laws. This has been made possible by the advent of non-smooth non-convex multi-objective H∞ optimization with MATLAB® systune. Despite the inherently nonlinear nature of (I)NDI-based control laws, local stability and robustness can be assessed using established trim-and-linearize techniques, allowing LTI methodologies to address design trade-offs in alignment with well established practices. Consequently, a linear hybrid Incremental Dynamic Inversion (IDI) control architecture is proposed, combining linear model-based DI with sensor-based IDI to leverage their complementary robustness properties. Model-following requirements are included using a weighting filter, whose parameters are optimized together with the hybrid IDI controller via a co-design approach. The potential of the proposed methodology is assessed in a design case study focused on a digital pitch-rate controller for a simulation model of NASA’s X-29 experimental aircraft. Results demonstrate that the synthesis procedure allows to optimize hybrid IDI controllers with the robustness guarantees associated with the H∞ Loop-Shaping setup while simultaneously allowing to meet performance requirements.