Actuator modelling for attitude control using incremental nonlinear dynamic inversion

Abstract

Recently, the concept of incremental nonlinear dynamic inversion has seen an increasing adoption as an attitude control method for a variety of aircraft configurations. The reasons for this are good stability and robustness properties, moderate computation requirements and low requirements on modelling fidelity. While previous work investigated the robust stability properties of incremental nonlinear dynamic inversion, the actual closed-loop performance may degrade severely in the face of model uncertainty. We address this issue by first analysing the effects of modelling errors on the closed-loop performance by observing the movement of the system poles. Based on this, we analyse the neccessary modelling fidelity and propose simple modelling methods for the usual actuators found on small-scale electric aircraft. Finally, we analyse the actuator models using (flight) test data where possible.

Stabilization of the vertical take-off of a rigid flying wing for an airborne wind energy system

“…This is critical mainly concerning the pitch moment, as the elevons have to compensate the pitch moment induced by the aerodynamic forces on Fig. 5 Wing elements of the flying wing, not scaled [11] Fig. 6 Polar of the airfoil the entire wing.…”

“…Due to the slipstream, the inflow speed at the wing located behind the propeller is increased, following Eq. (1), resulting from the Bernoulli-equations along a streamline [11]:…”

Flight Path and Flight Dynamic Analysis of the Starting Procedure of a Flying Wing for an Airborne Wind Energy System

“…The wing is separated into elements with similar aerodynamic characteristics. The presence of elevons modify the aerodynamic coefficients, while the slipstream of the propellers have influence on the airflow of the wing, see also [6,12]. For each element, the 2D polar of the airfoil is used to calculate under consideration of inflow, propeller slipstream and elevon deflection the forces and moments acting on the center of gravity.…”

Synthesis of Control Law Based on Nonlinear Dynamic Inversion for Supersonic Aircraft in Presence of Noise and Uncertainties

“…[21] The incremental NDI controller has a practical issue of requiring actuator feedback, which in reality cannot be obtained. The authors suggest to use system identification of actuator model, and use a pseudo model as in [22]. The requirement of angular acceleration measurements is another problem which needs to be practically resolved as filtering a differentiated signal adds a time delay, which can impact overall performance.…”

“…) where, 𝑦𝑦 𝑇𝑇 = [𝛼𝛼, 𝜗𝜗, 𝑉𝑉]state vector𝑢𝑢 𝑇𝑇 = [𝑉𝑉, 𝜔𝜔 𝑧𝑧 ] -control vectorThe full observation model is defined as follows:𝑍𝑍 1 (𝑡𝑡 𝑖𝑖 ) = 𝛼𝛼(𝑡𝑡 𝑖𝑖 ) + 𝜀𝜀 𝛼𝛼 (𝑡𝑡 𝑖𝑖 ) (21) 𝑍𝑍 2 (𝑡𝑡 𝑖𝑖 ) = 𝜗𝜗(𝑡𝑡 𝑖𝑖 ) + 𝜀𝜀 𝜗𝜗 (𝑡𝑡 𝑖𝑖 ) (22) 𝑍𝑍 3 (𝑡𝑡 𝑖𝑖 ) = 𝑉𝑉(𝑡𝑡 𝑖𝑖 ) + 𝜀𝜀 𝑉𝑉 (𝑡𝑡 𝑖𝑖 ) (23) 𝑍𝑍 4 (𝑡𝑡 𝑖𝑖 ) = 𝜔𝜔 𝑧𝑧 (𝑡𝑡 𝑖𝑖 ) + 𝜀𝜀 𝜔𝜔 𝑧𝑧 (𝑡𝑡 𝑖𝑖 )(24)where, 𝑧𝑧 𝑇𝑇 = [𝑍𝑍 1 (𝑡𝑡 𝑖𝑖 ), 𝑍𝑍 2 (𝑡𝑡 𝑖𝑖 ), 𝑍𝑍 3 (𝑡𝑡 𝑖𝑖 )]sate vector In the scope of this research work, the observation model is represented by(22) …”