This paper presents a sampled-data form of the recently reformulated incremental nonlinear dynamic inversion (INDI) applied for robust spacecraft attitude control. INDI is a combined model- and sensor-based approach mostly applied for attitude control that only requires an accurate control effectiveness model and measurements of the state and some of its derivatives. This results in a reduced dependency on exact knowledge of system dynamics which is known as a major disadvantage of model-based nonlinear dynamic inversion controllers. However, most of the INDI derivations proposed in the literature assume a very high sampling rate of the system and its controller while also not explicitly considering the available sampling time of the digital control computer. Neglecting the sampling time and its effect in the controller derivations can lead to stability and performance issues of the resulting closed-loop nonlinear system. Therefore, our objective is to bridge this gap between continuous-time, highly sampled INDI formulations and their discrete, lowly sampled counterparts in the context of spacecraft attitude control where low sampling rates are common. Our sampled-data reformulation allows explicit consideration of the sampling time via an approximate sampled-data model in normal form widely known in the literature. The resulting sampled-data INDI control is still robust up to a certain sampling time since it remains only sensitive to parametric uncertainties. Simulation experiments for this particular problem demonstrate the bridge considered between INDI formulations which allows for low sampling control rates.@en

Previous results reported in the robotics literature show the relationship between time-delay control (TDC) and proportional-integral-derivative control (PID). In this paper, we show that incremental nonlinear dynamic inversion (INDI) — more familiar in the aerospace community — are in fact equivalent to TDC. This leads to a meaningful and systematic method for PI(D)-control tuning of robust nonlinear flight control systems via INDI. We considered a reformulation of the plant dynamics inversion which removes effector blending models from the resulting control law, resulting in robust model-free control laws like PI(D)-control.

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