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IMAV 2018-Original Research Article International Journal of Micro Air Vehicles Attitude control of tiltwing aircraft using Volume 11: 1–12 ! The Author(s) 2019 a wing-fixed coordinate system and Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1756829319861370 incremental nonlinear dynamic inversion journals.sagepub.com/home/mav F Binz , T Islam and D Moormann Abstract In this paper, we present a novel concept for robustly controlling the attitude of tiltwing aircraft. Our main contribution is the introduction of a wing-fixed coordinate system for angular acceleration control, which forms the basis of a simple and robust attitude controller. Using the wing-fixed coordinate system allows us to describe the actuator effectivity using simple approximations based on the current operating conditions of the aircraft. Coupled with a robust angular rate control concept, which does not rely on an accurate aerodynamic model, we present a controller stabilizing the entire flight envelope of a tiltwing aircraft. The underlying angular acceleration controller uses the concept of Incremental Nonlinear Dynamic Inversion (INDI) to achieve robustness against aerodynamic uncertainties. The resulting controller is evaluated in both simulation studies and flight tests. Keywords Attitude control, tiltwing, INDI Received 8 February 2019; accepted 15 April 2019 Introduction tilt angle of 0, the ailerons primarily include a rolling A key goal in the design of many unconventional air- moment, as in a conventional airplane. In between the craft types is the combination of efficient forward flight hover and forward flight configurations the ailerons with vertical take-off and landing (VTOL) capabilities. include both a rolling and a yawing moment. Besides One solution to this problem is the concept of a tiltwing the change in direction of the actuator-induced aircraft. These aircraft fly like a conventional airplane moments, the transition between hover and forward in forward flight and achieve VTOL capabilities by flight is further characterized by potentially highly tur- tilting the entire wing upwards to hover. bulent airflow behind the main wing. This complicates To stabilize the aircraft in both hover and forward the design of high-fidelity aerodynamic models, which flight, several actuators are needed. The aircraft con- are needed for many advanced control schemes. sidered here is depicted in Figure 1 and features the Because of these properties, controller design for tilt- following actuators for attitude control: asymmetric wing aircraft still presents a challenging problem. thrust of the main motors, ailerons, elevator and In light of these properties, our main contribu- thrust of the auxiliary motor. Table 1 shows the prima- tions are: ry moments induced by each actuator during hover and • forward flight and the corresponding tilt angle. Table 1 We observe that the moments induced by the actua- hints at a central problem in the design of attitude tors only change direction w.r.t. the body-fixed controllers of tiltwing aircraft: the moments induced by the asymmetric thrust and ailerons change direction between hover and forward flight. Consider the ailer- Institute of Flight System Dynamics, RWTH Aachen University, ons as an example: During hover flight, at a tilt angle of Aachen, Germany 90, the ailerons primarily induce a yawing moment, Corresponding author: since they are positioned in the slip stream of the F Binz, Ru¨tscher Str. 94, 52072 Aachen, Germany. main engines. However, during forward flight, at a Email: [email protected] Creative Commons Non Commercial CC BY-NC: This article is distributed under the terms of the Creative Commons Attribution- NonCommercial 4.0 License (http://www.creativecommons.org/licenses/by-nc/4.0/) which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us. sagepub.com/en-us/nam/open-access-at-sage). 2 International Journal of Micro Air Vehicles 11(0) Figure 2. Side view of the aircraft. Figure 2 shows the wing-fixed coordinate system. Figure 1. Example tiltwing aircraft in hover configuration. Conceptually, the origin of the wing-fixed coordinate system lies in the tilt axis of the wing. Since the centre of gravity and the tilting axis are close to each other, we Table 1. Actuator effectivity in hover and tilt configuration. don’t consider the distance between the origins of the body-fixed and wing-fixed coordinate systems in the Hover flight Forward flight following treatment. Asym. throttle dasym Roll Yaw To transform a vector given in the body-fixed coor- Aux. throttle daux Pitch (–) dinate system (Index b) to the wing-fixed coordinate Ailerons n Yaw Roll system, we define the following transformation matrix Elevator g (–) Pitch " # Tilt angle r 90 0 cos r 0 Àsin r Twb ¼ 01 0 (1) sinr 0 cosr coordinate system. In the wing-fixed coordinate system the direction of the induced moments is con- stant. Of course, this simple – and in hindsight obvi- The tilt angle r assumes a value of ca. 90 resp. 0 in ous – observation by itself does not lead to more hover resp. forward flight configuration. robust controllers, but should be understood as a tool for understanding tiltwing aircraft dynamics Transformation of moment of inertia and exploring the design space of attitude For the scope of this work, we assume that the aircrafts controllers. moment of inertia is constant w.r.t. the tilt angle r. • Inspired by the body of work concerning robust con- Nevertheless, we need to transform the moment of iner- trol schemes in recent years (e.g. Incremental tia given in the body-fixed coordinate system into the 1 Nonlinear Dynamic Inversion (INDI) or wing-fixed coordinate system. The moments acting on Incremental Backstepping2), we propose the combi- the aircraft expressed in the body-fixed coordinate nation of a wing-fixed coordinate system with an system Mb are linked to the body-fixed accelerations _ attitude acceleration controller based on the princi- Xb by the body-fixed moment of inertia Jb ple of INDI to yield a robust attitude controller. In _ the spirit of INDI, which is a sensor-based control Mb ¼ Jb Á Xb (2) concept, we derive the needed actuator effectivity not on the basis of characteristic maps at certain The body-fixed moments Mb can be expressed in the trimmed flight states, but instead use the available wing-fixed coordinate system using the transformation measurements and simple empirical and analytical matrix Twb models to estimate the actuator effectivity in the cur- rent operating conditions. Mw ¼ Twb Á Mb (3) À1 _ The wing-fixed coordinate system ¼ Twb Á Jb Á Twb Á Xw (4) In this paper, we are exclusively considering tiltwing ) ¼ Á Á À1 aircraft with a single tiltable wing as depicted in Jw Twb Jb Twb (5) Figure 1 and described in Hartmann et al.3 Our approach should however be also applicable to other Using equation (5), we calculate the wing-fixed iner- tiltwing aircraft with only slight modifications (i.e. tia based on the current tilt angle and the body- quad-tiltwing designs4). fixed inertia. Binz et al. 3 Actuator effectivity wing-fixed coordinate system We introduced the wing-fixed coordinate system with " # " # uAw VA the main goal of simplifying the description of the actu- ! ¼ ¼ Á ator effectivity. For attitude control, we are interested V Aw 0 Twb 0 (7) in the actuator effectivity concerning the roll, pitch and wAw 0 yaw moments (L, M and N). In this section, we will ! discuss the models we employ for the different actua- Only the x-component uAw of V Aw is used as an tors available. When modelling the actuator effectivity, input to the thrust model. we try to find simple models which still result in satis- Using the lever arms of the main motors, we obtain factory controller performance. We are thus neglecting the following effectivity of the main motors various effects, the most important of which are: @N @FmotorðV; dÞ ¼ Á Á • 2 ymotor (8) No cross-coupling between actuators. Every actua- @dasym @dasym V¼uAw;d¼dsym;0 tor only induces a moment along one axis in the wing-fixed coordinate system. where dsym;0 denotes symmetric throttle signal in the • Every actuator is exposed to the same free stream current controller timestep and ymotor denotes the velocity, disregarding effects like downwash from lever arm between the motor and the aircrafts centre the main wing onto the elevator. of mass. The factor 2 accounts for the two motors, one on each side of the aircraft. Motor model. We assume that the thrust produced by a Similarly, for the auxiliary motor we obtain fixed-pitch propeller is primarily influenced by two fac- @M @FauxðV; dÞ tors: the angular velocity of the propeller and the ¼ xaux Á (9) @ @ ¼ ; ¼ inflow speed. Based on this assumption, we first intro- daux daux V 0 d daux;0 duce a thrust model Fmotor ¼ fðV; dÞ (6) Control surfaces. We distinguish between two different kinds of control surfaces: those which are assumed to where d is the throttle signal corresponding to the be completely in the free stream and those which are in motor currently considered. Based on prior measure- the slip stream of a propeller. Both kinds of ments of electric motors performance, we assume control surfaces are modelled as thin plates of that the angular velocity of an electric motor is finite length, where the lift Flift changes with the approximately linear to the throttle signal applied control surface deflection d according to the follow- to the electronic speed controller. This means, that – ing equation lacking a direct measurement of the propeller angular @Flift K velocity – the throttle signal can be used as an equiva- ¼ q 2 Á Á @ V S 2p K þ (10) lent signal.

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