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.

This paper introduces and investigates several methods of filtering and delay synchronization in incremental control law structures. It is shown that proper filter and delay synchronization is of great importance for both the performance and stability of the control laws. It is derived how to synthesize complementary filters in case of sensor dynamics, sensor delays and internal control law filtering such as roll-off filters and notch filters. The complementary filters are compared to common synchronization approaches previously applied in incremental control laws. It is shown that the proposed methods are beneficial for Multiple Input Multiple Output (MIMO) systems in case that different delays and filtering is present in the different measurement signals. In case of strongly coupled input effectiveness, the synchronization on the actuator feedback may become even unstable, where the complementary filter approach recovers the design closed-loop behavior. In addition, it is derived how to initialize the complementary filters for a transient-free engagement in non-steady-state conditions. The results are compared in simulation with a roll rate control law for a fixed wing aircraft.

Many control allocation algorithms require the calculation of (pseudo)inverses of control effectiveness matrices, also referred to as a [ ] matrix, which for nonlinear systems might change over time. Such cases would require an online calculation of the respective inverses. Storage of all possible, offline precalculated inverses might exceed available memory sizes in common aircraft applications. This is especially relevant for systems with a high number of control effectors, like novel aircraft configurations. Several control allocation algorithms exist that require updates of the matrix to be inverted, the considered example being Redistributed Scaled Pseudoinverse. Within the Redistributed Scaled Pseudoinverse algorithm, the control allocation problem is solved iteratively by sequentially removing the columns of the [ ] matrix that belong to saturated effectors. An approach using the Sherman–Morrison formula is presented in this study, which calculates the inverses based on recursive updates. This proposed approach has the following advantages over conventional Redistributed Scaled Pseudoinverse algorithm: reduced computational load and ease of protection against run-time errors. These make it a candidate for use in the context of safety-critical applications. The approach gives promising results and shows significant decrease of computational time. However, specific numerical challenges require additional investigations.

The use of non-piloted eVTOL aircraft in non-segregated airspace requires reliable and deterministic automatic flight guidance systems for the aircraft to remain predictable to all the users of the airspace and maintain a high level of safety. In this paper we present a 3D trajectory generation module based on clothoid transition segments in the horizontal plane and high order polynomial transition segments in the vertical plane. The expressions of the coefficients of the polynomial are derived offline are used to generate the trajectory online, making the system capable of running in real time without requiring enormous computational power. For the horizontal plane, we focus on the flyby transition, and therefore present a thorough analysis of the flyby geometry and the limitations linked to this geometry and the construct of three-segment trajectory generation around a fixed turn rate. We present feasible solutions for these limitations, and show simulation results for the combined horizontal and vertical plane concepts, allowing the system to generate complex 3D trajectories.

Using electric vertical takeoff and landing (eVTOL) aircraft for urban air mobility requires a high level of maneuverability and tracking accuracy from the flight guidance systems. This can be achieved by constructing a high-order desired trajectory, in order to provide jerk-level feedforward commands and acceleration-level relative kinematics. In this paper, we perform a noise analysis on a trajectory system where relative kinematics are computed numerically, and we show the resulting noise effects. We then present an analytical alternative which improves the noise sensitivity. Additionally, we develop a smoothing strategy for obtaining a high-order parametrization of a trajectory designed with low-order clothoid curves. The methods presented in the paper are tested and validated in closed-loop simulations and through flight tests on a 700 kg medical-evacuation eVTOL aircraft. The results of these tests are presented and discussed.