Large transport aircraft: Solving control challenges of the future

Annual Reviews in Control 38 (2014) 220–232

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Large transport aircraft: Solving control challenges of the future q Thomas Jones ⇑ Department of Electrical and Electronic Engineering, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa

a r t i c l e

i n f o

Article history: Received 13 June 2014 Accepted 10 September 2014 Available online 12 October 2014

a b s t r a c t The evolution of large transport aircraft is driven by safety, cost, passenger comfort and environmental impact, all within a highly competitive and regulated environment. As a result, creating the aircraft of the future presents various interesting control challenges. For the past 7 years, Stellenbosch University has partnered with Airbus and the National Aerospace Centre to investigate and solve some of these challenges. This paper focusses on key projects within this partnership, serving Airbus centres of competence in France, Germany and the UK. Goals range from improving efficiency (e.g. automated formation flight) to improvements in safety (e.g. automatic return to flight envelope) and general automation (e.g. automatic in-flight refuelling). Where appropriate, it is illustrated how detailed analysis and the application of advanced techniques may often lead to relatively simple answers and quite general conclusions. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The three primary drivers behind control technology development for large transport aircraft are the improvement of efficiency, safety and general functional automation (Jones, 2014; Traverse, Lacaze, & Souyris, 2004; Wise, Tilden, Abbott, Dyck, & Guide, 1994). In addition, safety and efficiency are key aspects that form part of the manifests and responsibilities of aircraft manufacturers and aviation authorities alike. Stellenbosch University, Airbus and the South African National Aerospace Centre (NAC) teamed up in 2008 to solve a number of future control and automation challenges that align directly with these drivers. In part, the success of this pilot five year collaboration programme lead to the extension thereof for another term and the inclusion of all South African (SA) universities, based on a project merit evaluation process. The latest collaboration projects focus on fields ranging from maintenance, structures and aerodynamics to control and automation at five SA universities. The author was invited to write this paper based on his plenary lecture with the same title delivered at the 2014 IFAC World Congress in Cape Town (Jones, 2014). The purpose of this document is to provide a review of the control system challenges for future operation of large commercial transport aircraft being solved at Stellenbosch University with the support of Airbus and the NAC. As is the case with most review papers of this nature, the paper q This article is an extended version of a plenary lecture delivered at the 19th IFAC World Congress, Cape Town, 25–29 August 2014. ⇑ Tel.: +27 21 8084319. E-mail address: [email protected] URL: http://www.ee.sun.ac.za

http://dx.doi.org/10.1016/j.arcontrol.2014.09.005 1367-5788/Ó 2014 Elsevier Ltd. All rights reserved.

itself does not represent a sufficient body of knowledge to repeat all of the experiments or to fully prove all conclusions made. When read together with the referenced material, complete repetition and detailed analysis of results are indeed possible. The research described here is aimed towards practical implementation on certified aircraft. As such, the goal is to find the simplest, most general, practical and robust solutions to the challenges that present themselves. Complex analysis and design techniques are often employed specifically to create and validate these solutions, but this should not be mistaken for creating complex solutions. Non-deterministic algorithms and adaptive control techniques are specifically avoided, wherever possible, in an attempt to avoid flight certification issues. Following this short introduction, the paper focusses on the key challenges, methods of solution and interesting results associated with three selected multi-year and multi-researcher projects categorised within each of the stated technology drivers.

2. General functional automation: automated in-flight refuelling 2.1. Introduction In recent years, there has been a resurgence of interest in airborne refuelling of large transport aircraft. Advantages of this process include flight range extension without the requirement for landing and the assignment of a larger component of take-off mass to real payload rather than fuel. Refuelling operation is difficult and strenuous, especially for the pilot of the large and relatively sluggish receiver aircraft. Refuelling would therefore typically be

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Fig. 1. Side and rear views of the boom envelope, defining the boom angles connect and outer disconnect envelopes are illustrated.

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r and v and the boom extension k (added to the 12 m fixed-length portion of the boom). Inner

accomplished via a solid boom in order to manage the large amount of fuel transfer within a minimum time frame. Fig. 1 illustrates the relatively small connect and disconnect envelopes (roughly a 4 m cube describing the latter) within which the Receiver Receptacle (RR) must be maintained at all times. The problem is further exacerbated by the long distance between the Centre of Gravity (CG) and the receptacle on a typical large transport aircraft, as opposed to the short distances on smaller (e.g. jet fighter) aircraft. Even small pitch angle variations on the former will result in large receptacle position displacements, as shown in Fig. 2. These challenges serve as motivation for developing flight control laws for Autonomous In-Flight Refuelling (AIFR) for large transport aircraft. Claase (2013) and Kriel, Engelbrecht, and Jones (2013) cite and classify more than 20 relevant papers, but very few of these are directly applicable to large transport aircraft. The objective of the research is specifically to design flight control laws able to regulate the receptacle position of the receiver aircraft within the boom envelopes of Fig. 1 under conditions of light and medium turbulence. Flight control should be robust to model uncertainties and must obey actuator deflection and slew rate limits. Where possible, flight control should be accomplished via an aircraft’s certified Fly-By-Wire (FBW) system, since various mode and flight protection systems are embedded therein. Airbus supplied a high fidelity flight simulation, FBW and conventional autopilot simulation model of a representative aircraft as basis for modelling and simulation of both the tanker and the receiver aircraft. The relatively sluggish engine response for this size aircraft was quickly identified as a limiting factor when performing accurate longitudinal control. Therefore, as a first step, the model was slightly expanded to further increase the fidelity of the engine simulation in order to provide the most accurate throttle to thrust response. AIFR is normally accomplished somewhere within a relatively large flight envelope (e.g. altitudes of between 10,000 ft and 33,000 ft) and under various flight conditions, such as straight and level flight, toboggan manoeuvres and race-track patterns

(including banked turns). During 20 min of refuelling the receiver’s mass can vary by 80 tons (relative to a representative 230 ton maximum all-up weight), resulting in varying trim and dynamic responses associated with total loading and CG shift. As part of the initial investigation, the aerodynamic coupling between the tanker and receiver aircraft was split into two modelled effects, namely a trim change and a change of angle of attack of the incoming air stream towards the receiver, similarly to the standard approaches suggested and followed by Dogan, Venkataramanan, and Blake (2005) and Ryan (1998). The extent of these two effects was modelled according to separation principles in the references and can therefore be considered to result in representative (but by no means perfectly accurate) interaction when applied to a suitable simulation model sourced form Airbus. The effect on the tanker of the bow wave of the receiver in such close proximity should not be underestimated. Airbus operational tests show that this is significant, but can mainly be handled by slowly approaching the boom envelope, thereby allowing the tanker to adapt to a new trim setting (i.e. enforcing time-scale separation on the coupling). 2.2. Advancing a conventional design process The first approach investigated towards realising AIFR was to make use of relatively conventional or classical methods to adapt models and synthesise control systems based on a fundamental understanding of the problem dynamics. This research is detailed in Kriel et al. (2013). Dynamic models are traditionally created relative to the CG or Centre of Pressure (CP) of aircraft and therefore describe the motion of the CG or CP (Blakelock, 1991). The refuelling receptacle on large transport aircraft is however far forward of the CG. A relatively standard aircraft dynamics model, based on a NASA Dryden aerodynamic model was therefore adapted to describe the motion of the Receiver Receptacle (RR). Fig. 3 illustrates the variation in the longitudinal poles and zeros of the receiver as a function of

Fig. 2. Pitch and displacement coupling of the RR vs. CG position, for variously sized aircraft.

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Fig. 3. Elevator input to normal acceleration output: (a) poles and zeros for varying RR vs. CG positions. (b) Open loop step response for varying RR vs. CG positions Kriel et al. (2013).

engine thrust settings and a new trimmed angle of attack, chosen mainly to compensate for the static effects of the trim spoiler deflection. A variety of different control system architectures were designed by mathematical calculation, approximation and LQR methods and evaluated during tens of thousands of semi-automated simulation runs, first at Stellenbosch University and later at an even higher fidelity simulator at Airbus, in order to determine the best classical control strategies at various flight conditions and under the influence of stochastic wind disturbance models constituting light and medium turbulence. The results of this part of the study prove to be very promising, as can be seen from a typical 20 min straight and level flight AIRF simulation in Fig. 4 under medium turbulence conditions, where the RR never exits the disconnect envelope and seldom exits the more constrained connect envelope. Important findings in Kriel et al. (2013) are summarised in the following paragraphs. Focussing control on the RR automatically results in added CG acceleration (and therefore increased load factors towards the rear of the aircraft), since it is a combination of motion of the CG and attitude changes that result in RR motion. Various simulations show that the RR can be kept neatly within the disconnect envelope, while the CG shows significant position variation in order to accomplish this feat. As usual, the right-half-plane (RHP) zeros limit the bandwidth of control that can be achieved. Under relevant flight conditions these zeros resulting from the Airbus simulation model do not overly restrict the achievable control bandwidth. Given that the receiver and tanker aircraft models are quite similar, the best along-track (axial) control performance is

sin

deg

lx , the forward distance between the RR and the CG. It is clear that the pole positions are independent of lx , but that additional zeros are introduced and that these vary greatly. It is this variation that captures the primary control challenge associated with accurate vertical control of the RR within the boom envelope. It can easily be shown that the existence of these zeros may be ignored when lx is quite short, but not when lx is long (as is typically the case for large transport aircraft). A similar situation results when analysing the lateral dynamics. The most obvious way to deal with the dominant left-half-plane (LHP) zeros remains pole-zero cancellation. Such cancellation can never be perfect. The effect of residuals resulting from imperfect placement or imperfect models was verified to be negligible for typical variations as part of a robustness test performed by Kriel et al. (2013). The following paragraphs mainly focus on the challenge of accurate longitudinal control, in order to illustrate the design process and associated results. The coupling between pitch angle and airspeed is typically used to control the airspeed of an aircraft. It is however not possible to exploit this coupling alone when attempting to keep the RR within the allowed vertical boom envelope. Dynamic thrust control is in fact identified as a more useful mechanism for along-track longitudinal control and the approach remains successful while assuming a conservative thrust response. The most reliable high bandwidth controller is however created by also making use of existing hydraulically actuated wing spoilers. Spoilers (sometimes known as air brakes) are usually employed to reduce lift, increase drag and therefore allow controlled flight along steeper glide paths. For AIFR the spoilers can be slightly deflected at a non-zero trim angle and then operated up and down relative to this set point. This results in a careful trade-off in terms of operating airspeed,

cos ( )

deg

Fig. 4. Classically synthesised control: RR 2D displacement plot for nominal straight and level tanker @30,000 ft, @300 kts, with connect and disconnect envelopes indicated.

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achieved when the tanker is placed under conventional heading hold, altitude hold and bank angle hold control at a constant throttle setting. Active airspeed control results in additional relative position variation under the influence of turbulence. It is more effective to match the gust responses of the aircraft in the axial sense. Generally, simulations with heavier (more sluggish) tanker configurations result in the smallest control errors. Longitudinal control is accomplished by making use of an LQR to optimise throttle, spoiler and elevator inputs in order to control vertical and axial displacement of the RR. Off-diagonal terms added to the LQR weighting matrix proves to be an effective means to accomplish coordinate transformation during LQR design, since the boom envelope is more accurately described by a pitched cube rather than being parallel to the horizon. Care is taken to ensure that the weighting matrix remains positive definite. Good control performance is accomplished via the standard FBW system serving as inner loop controllers, with flight protection systems in place. AIFR control can be improved somewhat (see the next subsection) when the filters on protection systems are slightly relaxed or when alternative inner loop control strategies are followed, e.g. Peddle and Jones (2011). A cost, safety and accuracy trade-off will need to be made in order to choose the optimal design. 2.3. Optimal robust design With a good understanding of the problem, various linear control solutions tested and a high fidelity model in place, the next step is to make use of modern formal methods to create an optimal robust controller. A literature survey on previous research attempts towards AIFR reveals that most attempts rely on LQR/LQG control (Campa et al., 2004; Dogan, Sato, & Blake, 2005; Tandale, Bowers, & Valasek, 2006), with limited application of techniques such as l-synthesis (Chen, Dong, Xu, & Lin, 2007), neural adaptive controllers (Wang, Patel, Cao, & Hovakimyan, 2006) and Quantitative Feedback Theory (QFT) (Pachter, Houpis, & Trosen, 1997). Actuation limits and control accuracy requirements are not explicitly included as part of the optimisation process in prior work on AIFR control. Researchers at Stellenbosch University proposed designing AIFR flight control laws using Linear Matrix Inequality (LMI) optimisation. With LMIs, optimised regulation of stochastic systems subject to time-varying uncertainties and coloured noise disturbance can be achieved. At the same time transient behaviour and multiple outputs and actuators can be constrained to operate within limits, as illustrated by Boyd and Hindi (1998). Such constraints are formulated as inequalities. In this study, H2 norms are employed to capture these inequalities. A complete description of the work can be found in Claase (2013). In summary, LMI control design can in this instance be approached as follows:

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dynamics between the boom on the tanker and the RR on the receiver. An improved turbulence model is then developed according to the Dryden model (Dryden, 1961) in order to accurately represent the similarities in turbulence experienced by both aircraft. Several well-posed controller architectures are created (guaranteeing zero-mean steady state tracking) for the receiver aircraft, with the tanker placed under conventional autopilot control as described in the previous sub-section. Nine low order controller variants are then optimised and validated within the available high-fidelity non-linear simulation environment for the most common AIFR flight conditions. Controller structures are again based on Linear Time Invariant (LTI) output feedback, in keeping with an attempt to create simple solutions. It is important to note that optimal control is attempted without making use of the FBW system, in order to explore the limits performance. This structure is absorbed into the LMIs and step 3 above is applied. The linear formulation of the synthesis problem relies on the separation principle, where feedback controllers and estimators are designed separately via LMI optimisation and then combined, as is usual. The controller-estimator structure is therefore chosen to correspond to the representation in Fig. 5, where G; L; K; y; x; p; q; w; z and u represent the dynamics matrix, estimator gain matrix, feedback gain matrix, output vector, states vector, uncertainty input vector, uncertainty output vector, turbulence driving process noise vector, performance output vector and control input vector respectively. D is a structured norm-bounded uncertainty matrix representing the non-linear time variant components. Once the problem has been correctly formulated (including the objective function and feasibility constraints posed in Claase (2013)), various LMI solvers may be applied to find optimal controller parameters subject to the LMIs. SDPT 3 is applied as part of Matlab and found to be one of very few solvers that are efficient, robust and reliable in this instance, where approximately 3300 scalar variables associated with this AIFR problem and true 64-bit

1. Formulate a set of closed-loop system stability conditions and performance measures using LMIs such as Lyapunov stability, H2 , and H1 . 2. Absorb the control variables into LMI structures. 3. Perform substitutions and transformations, apply theorems and Lyapunov’s shaping paradigm, etc. to remove non-linearities resulting from controller variables. 4. Define a linear, scalar objective function in terms of LMI variables, with the minimum value of the objective corresponding to the best desired closed-loop performance. 5. Solve the controller variables corresponding to the minimum objective with a suitable algorithm. A 60th order norm-bounded state-space model is developed in order to represent the AIFR dynamics, including the relative

Fig. 5. Predictor estimator-based state-feedback structure block diagram Claase (2013).

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double precision calculations are employed. The specific linear feedback controller and estimator internal structures and resulting optimised parameters are described in detail in Claase (2013) for 9 different controller variants. It is essential to note that the guarantees on robust performance inherent in the LMI technique become invalid when the norm-bounded model uncertainty is reduced (as is required to compensate for the conservatism typically involved in the technique). Non-linear simulation is therefore used to validate the closed loop behaviour, as opposed to simply choosing parameters and assuming that appropriate robust performance is guaranteed. Figs. 6 and 7 illustrate the typical performance achieved for a 5 min high fidelity non-linear simulation of straight and level AIFR operation in medium turbulence under the same flight conditions as for the classical controller in the preceding subsection. It is most interesting to note that the performance of the best LMI synthesised controller is improved relative to that of a classically synthesised and optimised controller as presented in Fig. 4. The LMI synthesised version is after all in some sense optimised and does not operate the aircraft via a protected FBW system. A more detailed study would need to be made to compare the general robustness and sensitivity of the two methods of synthesis. By design, both approaches result in LTI controllers, resulting in similar implementation and testing processes. The classically synthesised controller is however simpler to design under a variety of flight conditions. The LMI-based design does in some sense provide an indication of the ‘‘limits of performance’’ to be expected of LTI control.

Fig. 7. LMI synthesised control: RR time history plot for nominal straight and level tanker flight at 10,000 ft in medium turbulence, with connect envelope indicated Claase (2013).

3. Improving safety: an automatic return to envelope function 3.1. Introduction By design, instances where aircraft severely exit their normal operating flight envelopes rarely occur, but can have severe consequences (North, 2000). Aircraft manufacturers are interested in exploring the concept of an automatic Return to Envelope Function (AREF) to safely recover aircraft to their nominal flight envelopes. Such a system should recover the aircraft with pilot approval, but without the need for pilot action during the recovery process,

since an upset could induce partial or complete pilot disorientation. Typical loss of control or upset events are associated with high angular rates, high aerodynamic incidence angles, unusual bank and pitch angles, too high or too low airspeeds and high load factors (Traverse et al., 2004; Wilborn & Foster, 2004). Fig. 8 illustrates a large component of this definition. A review of modern recovery strategies was performed by Crespo, Kenny, Murri, and Cox (2012). Various AREF strategies may be proposed, including highly non-linear and optimal

Fig. 6. LMI synthesised control: RR 2D displacement plot for nominal straight and level tanker @30,000 ft, @300 kts AIS, with connect and disconnect envelopes indicated Claase (2013).

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Fig. 8. Attitude, aerodynamic flow angles and airspeed bounds defining a normal operational flight envelope Wilborn and Foster (2004).

approaches for specific scenarios (Dongmo, 2012; Raghavendra, Sahai, Kumar, Chauhan, & Ananthkrishnan, 2005; Sinha & Rao, 2010 and others). The aim of this study is however to analyse common practice mainly applied to smaller aircraft and to attempt to generally validate such simple, common-sense, practical and robust strategies for automatic recovery of large transport aircraft. Unfortunately very few accurate and high fidelity aerodynamic models of large transport aircraft operating significantly outside their normal flight envelopes are freely available, since these aircraft are not normally characterised in this manner. The focus of this work relates mainly to dynamics and control, but it is also important to constrain load factors to prevent structural failure and injury. Post-stall spin recovery is used as an illustrative example for an AREF.

3.2. Proposed AREF strategy The following relatively straight-forward and practical AREF strategy is therefore proposed and analysed, as described in more detail in Engelbrecht, Pauck, and Peddle (2012) and Engelbrecht

and Pauck (2013) and built on the recommended training practice in FAA (2008): 1. Attempt to recover angular rates and the aerodynamic envelope of an aircraft in order to regain linear control. Once the aerodynamic envelope is recovered, the control surfaces again will produce predictable forces and moments. 2. Recover the attitude of the aircraft, typically to wings-level and level flight (i.e. nominal pitch and roll angles). 3. Recover over-speed and altitude deviation. Fig. 9 presents this strategy in the form of a logical flow chart. Each subcomponent of the strategy requires its own component solution. In the following discussion, these basic components are developed based on very intuitive motivations before the over-all strategy is tested. The initial focus on angular rate reduction is of paramount importance and deals with bringing the fastest dynamic components of the aircraft under control. A logical approach would be to assume that the aircraft does exhibit natural rate damping and that this can be augmented though angular rate feedback to

Fig. 9. Flow chart of the proposed AREF strategy Engelbrecht and Pauck (2013).

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control surfaces. Unfortunately the control surfaces do not provide predictable control forces and moments when the aircraft is operating outside its nominal flight envelope. Recovery of the aerodynamic envelope requires sufficient airspeed to be able to maintain nominal angles of attack and side-slip and to recover these angles to their nominal values. Gravity may be used to recover airspeed, as is routinely done by pilots, and flow angles may be recovered by relying on the natural directional stability of a well-designed aircraft combined with active control (if required). Again the control surfaces may not produce predictable effects prior to recovery and flow angles may not be within the ability of standard sensors to measure. In addition, there may not be sufficient altitude available to trade for the necessary airspeed. The most troubling aspect from a dynamical point of view is however that the aircraft may be attracted to and enter one or many stable non-linear dynamical behaviours outside the flight envelope. This may complicate recovery. It is therefore important to attempt to reveal the stable modes of the aircraft outside its flight envelope and to be able to determine which initial conditions will stabilise to desirable or undesirable envelopes. Bifurcation analysis is clearly a suitable option for the former (Goman, Zagainov, & Khramtsovsky, 1997; Richardson, Lowenberg, DiBernardo, & Charles, 2006), especially when combined with techniques such as Lyapunov Analysis to determine the latter. Once linear control has been recovered, the bank angle and flight path angle (or pitch) may be recovered using the available FBW control system of the aircraft. FBW systems typically implement the necessary and certified protection systems in order to avoid unsafe load factors, but over-speed may still occur if the aircraft exhibits a significant initial nose-down attitude. Airspeed may be recovered together with altitude. A positive flight path angle can be used to allow gravity to reduce airspeed and once airspeed is recovered the flight path angle can be set to recover lost altitude. These actions are again taken through the protected and certified FBW control system, thereby limiting risks of further excursion from the nominal flight envelope. Under severe conditions it is conceivable that catastrophic over-speed may not be avoided when keeping the normal load factor within limits. Little may be done to solve such a scenario with uncomplicated recovery approaches. NASA’s Generic Transport Model (GTM) is used as part of a generic large transport aircraft simulation in order to evaluate and test the above strategy. The GTM was created through a combination of wind tunnel testing, CFD and flight testing of a twin-turbine scale model in order to represent an accurate model under extensive ranges of flow angles, control surface deflections and attitude rates. It was specifically created for research use (Murch & Foster, 2007) and was made available by NASA for this project. Even though the GTM does model the effects of control surface deflection over a very large flight envelope, it would be safe to assume that this information would not be available for most large transport aircraft. As such, the first (and most robust) attempt at solution would be to rely solely on the natural dynamics of these aircraft to damp high angular rates and perform aerodynamic recovery, while at most setting the control surfaces to fixed positions during various stages of recovery.

the Matlab Dynamical Systems Toolbox (Coetzee, Krauskopf, & Lowenberg, 2010) after the GTM simulation model was conditioned to be compatible with the software, as described in Engelbrecht et al. (2012). It is initially assumed that all control surfaces are held at constant zero deflection angles and that the elevator is then varied as an independent parameter around a typical trim setting for the horizontal stabiliser. The throttle is set to zero in order to decouple the aerodynamic effects from thrust effects for this study. Typical bifurcation diagram outputs, in this case the equilibria of angle of attack and roll rate, are presented in Figs. 10 and 11 respectively. These are two of many such diagrams used to analyse the branches of equilibria as a function of various static elevator deflections. Further recovery is then accomplished via the FBW system. For elevator deflections near zero, analysis of the various diagrams and associated transient response simulations show that only one stable equilibrium branch exists within the normal flight envelope. No stable equilibria are found outside the envelope. The desirable equilibrium corresponds to an aircraft gliding under the influence of gravity with aerodynamic flow angles within the normal envelope. This clearly shows that, if loads and other extraneous factors allow, the aircraft will return to a safe glide slope through natural damping when the throttle and all control surfaces are set to zero. This constitutes a recovery of the aerodynamic and rate envelopes and results in the restoration of largely linear flight and actuator dynamics. At large elevator deflections the desired stable equilibrium branch splits into two stable branches and one unstable branch, where the two stable branches correspond to stable spins in opposite directions. In short, if the elevator is severely deflected, the aircraft stalls, then rolls to a high bank angle (to either side) and enters a stable spin with high angular rates in a steep downward spiral. During this spiral, the aircraft remains outside the normal flight envelope by exhibiting an unusually high angle of attack, but maintains a small side slip angle. Retaining a large (nose-up) elevator deflection therefore prevents natural recovery. This is intuitive behaviour, proven by sophisticated analysis techniques. 3.4. Non-linear simulation analysis Bifurcation analysis reveals steady-state equilibria, but does not clearly reveal transient behaviour. Non-linear simulations are therefore employed to confirm the equilibria and analyse transient

3.3. AREF bifurcation analysis Aircraft may exhibit multiple stable equilibria outside of their near-linear designed-for flight envelopes and may be attracted or repelled from these equilibria depending mainly on initial conditions and actuator inputs. Bifurcation analysis is used as a tool to reveal all equilibria of the full non-linear aircraft model, both inside and outside the normal flight envelope. The stability of equilibria is also analysed in this way. Bifurcation is performed using

Fig. 10. Bifurcation diagram of angle of attack as a function of elevator deflection. Solid lines and dashed lines represent stable and unstable branches respectively.

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This simple multi-mode recovery strategy clearly shows promise when tested on the GTM. Research towards generalising this strategy for large transport aircraft and determining the level of robustness there-of is on-going. Results from further bifurcation analysis and analysis of regions of attraction towards safe stable equilibria are positive. 4. Improving efficiency: automated formation flight 4.1. Introduction

Fig. 11. Bifurcation diagram of body roll rate as a function of elevator deflection. Solid lines and dashed lines represent stable and unstable branches respectively.

behaviour. The simulation is set up to include the complete recovery process, where the aerodynamic and rate recovery is accomplished using natural dynamics at near-zero elevator set points and the FBW controllers are used to first recover attitude then over-speed and finally altitude, while keeping load factors within acceptable limits. The maximum load factor is typically applied to quickly result in a positive flight path angle as a measure to avoid unnecessary increases in airspeed. Using the GTM simulation and a matched generic FBW controller based on Airbus control laws Engelbrecht and Pauck (2013), the simulated aircraft is artificially placed in a steady state spin by first inducing stall with a sustained severe elevator deflection (as described in the previous subsection). The process and results are summarised in the aerodynamic flow angle plots of Fig. 12 and the displacement plot of Fig. 13. The simulated scenario clearly shows safe aerodynamic rate recovery and subsequent attitude, speed and altitude recovery. Throughout the simulation the load factor and airspeed never exceed safe limits. In this instance, the aircraft lost about 2200 ft of altitude between initial stall and final recovery, of which the most part is attributed to the pre-recovery stage.

The FAA estimates a 66% increase in commercial airliner traffic between 2013 and 2033, while data shows that airlines find it increasingly difficult to maintain profitability with rising fuel costs, as per Federal Aviation Administration (2013). Formation flight has been proposed and analysed by Brachet, Cleaz, Denis, Diedrich, and King (2004), Ning et al. (2011), Bangash, Sanchez, Ahmed, and Khan (2006) and others as a possible strategy for reducing drag and thereby reducing fuel consumption by as much as 40% on the trailing aircraft. Researchers at Stellenbosch University, the University of Cape Town and Airbus have teamed up to analyse the possibilities of performing formation flight with large transport aircraft in order to realise fuel savings. Traditionally the demonstration of formation flight has been limited to military usage and air shows, largely because of the dangers associated with increased pilot workload and aircraft proximity. Extended formation flight for commercial purposes, however, aims to exploit the advantages of persistent cruise wakes thereby extending the longitudinal separation between aircraft to at least ten wingspans while utilising automatic flight control to maintain formation. In this way, risks can be mitigated and potential fuel savings can be realised. Studies such as Zou, Pagilla, and Ratliff (2009) show an increased interest in formation flight for fuel savings, though suitable detailed formation flight aerodynamics were not yet adequately modelled or employed at the time. 4.2. Modelling A study performed at the University of Cape Town (UCT) by Bizinos and Redelinghuys (2012) investigated the aerodynamic

Fig. 12. Angle of attack (alpha) and sideslip (beta) vs. time, illustrating the various AREF phases Engelbrecht and Pauck (2013).

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Fig. 13. Aircraft 2D vertical and horizontal displacement during the various AREF phases Engelbrecht and Pauck (2013).

interaction of two large transport aircraft in formation flight. Earlier studies include Bangash et al. (2006) and Ning, Flanzer, and Kroo (2011). The UCT study was based on physical and aerodynamic parameters of a Boeing 747 aircraft extracted from an paper by Heffley and Jewell (1972) and the wing model was simplified to remove dihedral and sweep. An aerodynamic model was derived for the forces and moments experienced by a trailing aircraft due to the trailing vortices of the lead aircraft, showing highly non-linear relationships as a function of aircraft separation. Gradients are particularly steep near the optimum separation. These variations result in non-linear dynamic behaviour of the trailing aircraft and lead to unconventional required trim settings, such as nonzero aileron trim in order to compensate for a constant rolling moment resulting from the wake vortex. Researchers at Stellenbosch University were consequently tasked to investigate the influence of these variations on the flight control system of the trailing aircraft. The following discussion describes the initial steps undertaken to address this study and provides a brief description of continuing work. The aerodynamic influence of the leading aircraft on the trailing aircraft can be modelled as severe changes in the aerodynamic stability and control derivatives of the trailing aircraft, described by

C D ¼ C Do0 þ C Df 0 hg; fi C L ¼ C Lo0 þ C Lf 0 hg; fi C Y ¼ C Yo0 þ C Yf 0 hg; fi C l ¼ C lo0 þ C lf 0 hg; fi

ð1Þ

C m ¼ C mo0 þ C mf 0 hg; fi C n ¼ C no0 þ C nf 0 hg; fi where the coefficients C are denoted as per the standard Dryden aerodynamic model (Blakelock, 1991), the subscript o0 denotes ori0 ginal coefficients calculated in free flight and the subscript f

denotes coefficients induced by aircraft proximity during formation 0 flight. The mathematical formulations of the f coefficients are clearly described in Buchner, Engelbrecht, Adams, and Redelinghuys (2014). For simplicity, the coefficients are expressed as functions of normalised multiples of wingspan, where lateral separation is denoted by g and vertical separation by f. The changing coefficients directly affect the simulation model and therefore result in necessary adaptations to the trim and control gains that were originally calculated for a free flight model. If trims and gains are not adapted, then reduced performance or even instability may result. One approach would be to schedule these adaptations as a function of separation, again normalised to wingspan. Formation flight reduces fuel consumption by exploiting the two trailing vortices behind a leader aircraft. The upward flow in a vortex creates an apparent increase in the angle of attack along a portion of the trailing aircraft’s wing, fuselage and empenage, dramatically improving the lift to drag ratio. The added lift is countered by reducing the pitch angle of the trailing aircraft in order to remain in formation (a key indicator of the drag savings) and the associated reduction in drag requires a reduced throttle setting. Unfortunately the vortices also result in non-symmetric roll forces and moments on the aircraft. Fig. 14 illustrates the dominant effects of lateral separation, i.e. changes in the induced drag and the rolling moment experienced by the trailing aircraft (at Mach 0.8, an altitude of 40,000 ft and 10 wingspans behind the leading aircraft). It is clear that the separation resulting in minimum drag (i.e. maximum benefit) also corresponds to the maximum roll moment. A static roll moment would need to be countered by altered trim settings and this can only be accomplished if the aircraft is able to safely trim to the necessary condition. Fig. 15 clearly shows that two regions of lateral separation exist where the aircraft still remains trim-able. The middle or ‘‘sandwich’’ region results in the maximum drag reduction, but it is challenging to

Fig. 14. Induced drag and rolling moment as functions of lateral separation (f ¼ 0) Buchner et al. (2014).

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(or differential thrust setting) and resulting offset roll angle to counter the vortex-induced roll moment. This is being explored in an attempt to bring the inner extent of the outer region closer to the optimum wake position without violating safe trim constraints. Most importantly, however, evidence suggests that there is at least one relatively safe separation area to attempt to exploit for formation flight. As pointed out, varying levels of lateral and vertical separation also result in changing dynamic behaviour. The changes in aerodynamic coefficients as a result of separation are absorbed into a standard aircraft dynamics model where the state vector is expanded to include g; f and Dw as follows:

Fig. 15. Aileron and throttle trim regions for f ¼ 0 Buchner et al. (2014).

safely approach and remain in this region, especially since this region is surrounded by non-trim-able zones. In addition, in the sandwich region, the core of a trailing vortex intersects with the wing, resulting in high angles of attack (which may invalidate simulation data) and turbulent excitation of the aircraft (resulting in much reduced ride comfort). The safer ‘‘outer’’ region delivers less apparent fuel savings, but is more accessible and less turbulent. Note that the inner extent of the outer region is bounded by the amount of allowable aileron trim. It should be noted that alternative combinations of trim may be employed to trim the aircraft with lower aileron angles. One example would be to trim the aircraft at a small non-zero side-slip angle with an offset rudder angle

Vt Vt f_ ¼ sinðh  aÞ  ðh  aÞ b b Vt Vt g_ ¼ sinðDwÞ  ðDwÞ b b w_ ¼ q sin / sec h þ r cos / sec h

ð2Þ

Dw is the difference in heading between the leading and trailing aircraft, V t denotes free-stream velocity at the trim condition, b denotes wingspan and p; q; r and /; h; w denote the conventional body rotation rates and Euler angles respectively. The model is then linearised to be able to track the flightmechanical eigenvalues of the trailing aircraft as the lateral deviation is perturbed from g ¼ 0:7 (in the sandwich region) and g ¼ 1:3 (in the outer region). The results of this process are illustrated in Fig. 16. It is clear that the dynamics changes are most sensitive to vertical separation and that deviation from a trim position in the sandwich region results in more severe dynamics changes than in the outer region. This again reinforces the complexities associated with exploiting the benefits of the sandwich region.

Fig. 16. Eigenvalue loci around trim regions. Vertical separation variation: moving from dark to light indicates upward motion of the trailing aircraft. Lateral separation variation: moving from dark to light indicates inward motion of the trailing aircraft. Conventional free flight poles are marked with crosses Buchner et al. (2014).

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Fig. 17. Overall controller and aircraft simulation model for formation flight.

4.3. Control and automation The fidelity of the aerodynamic interaction model between the leading and trailing aircraft is undergoing further improvement, but in its current state it is already a very valuable tool during the initial phases of control system evaluation and design. This work is currently in progress. The general structure of a controller architecture is presented in Fig. 17. A conventional flight controller with altitude, airspeed and heading hold functions is employed on the leading aircraft and also on the trailing aircraft when the separation distance is large. A formation hold controller allows the trailing aircraft to approach the expected optimum separation and an extremum seeking controller finds the true ‘‘sweet spot’’. The controllers are deliberately structured to allow practical implementation, i.e. they are of low complexity, practically implementable and intuitively adjustable during test flights. It is important to note that the trim and dynamics modelling performed in the previous subsection is expected to yield representative results, but that the detail effects of unsteady aerodynamics, turbulence, differences in physical parameters, etc. make it virtually impossible to predict the exact location of an achievable sweet spot relative to the leading aircraft, as illustrated by Brodecki, Kamesh, and Chu (2013). The extremum seeking controller aims to converge to this sweet spot when close proximity (i.e. the expected optimal separation) is reached. This deterministic non-linear controller seeks to minimise the average pitch angle of the aircraft, as per the work of Binetti, Ariyur, Krstic, and Bernelli (2003), but needs to be constrained not to exit the allowable trim envelope of the aircraft, as per the results of the model analysis. Fig. 18 illustrates a typical extremum seeking controller employing the formation hold controller and a dither signal excitation. A correctly phased demodulation function identifies the optimal direction of motion in order move the trailing aircraft in the direction where the allowed extremum of the pitch angle is reached, subject to trim constraints. At this stage, conventional and robust formation hold controllers have been implemented for the outer region, based on the work of Binetti et al. (2003) and others. The initial results are still under evaluation, but appear promising, indicating that formation is well maintained for 1:2 < g < 1:3, with limited passenger comfort penalty under low turbulence conditions and an average engine throttle command reduction of approximately 14%. It is assumed that the leading aircraft’s state is transmitted to the trailing aircraft via a low bandwidth link, with a refresh rate of 5 Hz or less. The effect of link latency is under investigation.

Fig. 18. Typical dither signal-based extremum seeking controller.

It is important to keep in mind that the goal of this project is to prove that true fuel savings is possible, while operating safely and ensuring passenger comfort. As such, the National Aerospace Laboratory of the Netherlands (NLR) high order engine model known as the Gas turbine Simulation Program (GSP) is applied. It includes thrust and fuel dynamics, as described by Visser and Broomhead (2000), and is operated inside the simulated control loop for maximum simulation fidelity. Passenger comfort is currently investigated by analysing aircraft motion data. In future, added active control will be investigated specifically to improve comfort.

5. Conclusions Three example projects are reviewed in order to illustrate how research at Stellenbosch University aims to support and advance the key drivers of control and automation development for large transport aircraft, namely: improvement of efficiency, safety and general functional automation. Promising results are presented and, where possible, are distilled into uncomplicated solutions to these future challenges. Automated formation flight is presented and analysed as a method for conserving fuel over long distance flights, i.e. to improve efficiency. Previous research has been expanded by researchers at UCT and two trim-able regions (relative to the leading aircraft) have been identified that should result in fuel savings for the trailing aircraft. Initial results show that an ‘‘outer’’ region can be exploited under light turbulence conditions, with LTI controllers, but that an extremum seeking controller will be required

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to track the true location of the sweet spot behind the trailing aircraft. This research is on-going. An AREF for large commercial transport aircraft is presented and analysed using bifurcation techniques and non-linear simulation. The AREF strategy is based on simple principles, good practice and the use of certified FBW components and is shown to be a promising solution, resulting in safe flight envelope recovery without exceeding aircraft structural limits. This is a clear example of the improvement of safety. Various LTI AIFR controllers are created as candidates for the improvement of general functional automation of large transport aircraft. The controllers are designed by classical, state-space and LMI means and are shown to be effective under light and medium turbulence conditions. These controllers are also aimed at improving safety and pilot workload during AIFR. This research is evidence of a successful partnership between Airbus, the NAC, Stellenbosch University, UCT, and other universities in South Africa and beyond and illustrates the value of such partnerships. The invited session Bridging the Gap between Academia and Industry: Successful Aerospace Collaborations at the 2014 IFAC World Congress was established specifically to showcase the value of such collaborations to both industry and academia. Acknowledgements This research is carried out within the Electronic System Laboratory (ESL) in the Department of Electrical and Electronic Engineering at Stellenbosch University. The author wishes to acknowledge the support (organisational, financial, technical and otherwise) provided by Airbus and the NAC, and specifically the efforts of Daniel Cazy, Etienne Coetzee, Michel Goulain, David Hills, Dale King and their teams at Airbus and Philip Haupt at the NAC. Appreciation and thanks are expressed to Mark Lowenberg and his colleagues at the University of Bristol for collaboration on bifurcation analysis. This work constitutes the contributions of various graduate students and staff at Stellenbosch University under the leadership of Thomas Jones, Japie Engelbrecht and Corne van Daalen. The automated formation flight project is performed in close collaboration with a team at UCT under the leadership of Chris Redelinghuys. The GSP and GTM are used with kind permission of the NLR and NASA, respectively. References Bangash, Z. A., Sanchez, R. P., Ahmed, A., & Khan, M. J. (2006). Aerodynamics of formation flight. AIAA Journal of Aircraft, 43(4), 907–912. Binetti, P., Ariyur, K. B., Krstic, M., & Bernelli, F. (2003). Formation flight optimization using extremum seeking feedback. AIAA, Journal of Guidance, Control, and Dynamics, 26(1), 132–142. Bizinos, N., & Redelinghuys, C. (2012). Tentative study of passenger comfort during formation flight within atmospheric turbulence. AIAA, Journal of Aircraft, 50(3), 886–900. Blakelock, J. H. (1991). Automatic control of aircraft and missiles (2nd ed.). New York: John Wiley & Sons Inc. Boyd, S., & Hindi, H. (1998). Analysis of linear systems with saturation using convex optimization. Proceedings of the 37th IEEE conference on decision and control. IEEE. Brachet, J.-B., Cleaz, R., Denis, A., Diedrich, A., & King, D. (2004). Reference material for a proposed formation flight system. Technical report, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. Brodecki, M., Kamesh, S., & Chu, Q. P. (2013). Formation flight control system for inflight sweet spot estimation. In AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition. AIAA 2013-1037. Buchner, D., Engelbrecht, J. A. A., Adams, J., & Redelinghuys, C. (2014). Towards automatic flight control for commercial airliners in formation flight. In 19th IFAC world congress, Cape Town, August 2014. IFAC. Campa, G., Fravolini, M. L., Ficola, A., Napolitano, M. R., Seanor, B., & Perinschi, M. G. (2004). Autonomous aerial refuelling for UAVs using a combined GPS-machine vision guidance. In AIAA guidance, navigation and control conference and exhibit, August 2004. AIAA. Chen, B., Dong, X., Xu, Y., & Lin, Q. (2007). Disturbance analysis and flight control law design for aerial refuelling. In Proceedings of the 2007 IEEE international conference on mechanics and automation, August 2007. IEEE.

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L1 adaptive neural network controller for autonomous aerial refueling with guaranteed transient performance. In AIAA guidance, navigation and control conference and exhibit, August 2006. AIAA. Wilborn, J. E., & Foster, J. V. (2004). Defining commercial transport loss-of-control: A quantitative approach. In AIAA atmospheric flight mechanics conference and exhibit, August 2004. AIAA. Wise, J. A., Tilden, D. S., Abbott, D., Dyck, J., & Guide, P. (1994). Managing automation in the cockpit. In International federation of airworthiness, 24th international conference, October 1994. IFA. Zou, Y., Pagilla, P. R., & Ratliff, R. T. (2009). Distributed formation flight control using constraint forces. Journal of Guidance, Control and Dynamics, 32(1), 112–120. Thomas Jones received his PhD from the Department of Aeronautics and Astronautics at MIT in 2003. He currently serves as Professor and Head of the

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Department of Electrical and Electronic Engineering at Stellenbosch University in South Africa and leads a research group of approximately 30 graduate students and staff specialising in vehicle dynamics, automation and control within the Electronic Systems Laboratory (ESL). In 2008 he co-founded S-Plane Automation, an aircraft electronic sub-system design and manufacturing company, where he serves as Director. Prior to joining Stellenbosch University, Prof. Jones worked at

CSIR Aerotek as a missile guidance system analyst and as the project manager for the CS Draper/MIT Technology Development Partnership Programme. Prof. Jones is inter alia a member of IFACs Technical Committee on Aerospace, an Associate-Editor of Control Engineering Practice and a member of the Executive Committee of the South African Council for Automatic Control (an IFAC NMO).