An Integrated Approach to Aircraft Modelling and Flight Control Law Design

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(1)An Integrated Approach to Aircraft Modelling and Flight Control Law Design Gertjan H.N. Looye.

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(3) An Integrated Approach to Aircraft Modelling and Flight Control Law Design.

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(5) An Integrated Approach to Aircraft Modelling and Flight Control Law Design. PROEFSCHRIFT. ter verkrijging van de graad van doctor aan de T ech nisch e U niversiteit D elft, op gezag van de R ector M agnifi cu s p rof. dr. ir. J .T . F okkem a, voorzitter van h et C ollege voor P rom oties, in h et op enb aar te verdedigen op w oensdag 1 6 janu ari 2 0 0 8 om 1 0 .0 0 u u r. door. Gertjan Hendrik Nicolaas LOOYE. ingenieu r lu ch tvaart en ru im tevaart geb oren te M aasland.

(6) Dit proefschrift is goedgekeurd door de promotor: P rof.dr.ir. J .A . M ulder Toegev oegd promotor: Dr. Q .P . C hu Samenstelling promotiecommissie: R ector M a gn ifi cus P rof.dr.ir. J .A . M ulder Dr. Q .P . C hu P rof.dr. C .W . S cherer P rof. Dr.-In g. P . V örsma n n P rof. Dr.-In g. R . L uckn er P rof.dr.ir. M . V erha egen Dr.-In g. J . B a ls P rof.dr. Z . G u ¨ rda l. v oorz itter Techn ische U n iv ersiteit Delft, promotor Techn ische U n iv ersiteit Delft, toegev oegd promotor Techn ische U n iv ersiteit Delft Techn ische U n iv ersitä t C a rolo-W ilhelmin a , B ra un schw eig, Duitsla n d Techn ische U n iv ersitä t B erlin , Duitsla n d Techn ische U n iv ersiteit Delft Deutsches Z en trum für L uft- un d R a umfa hrt, O b erpfa ff en hofen , Duitsla n d Techn ische U n iv ersiteit Delft, reserv elid. C ov er: The highly ma n oeuv ra b le a n d post-sta ll ca pa b le X -3 1 A ex perimen ta l a ircra ft: con cepts from this thesis w ere a pplied to this a ircra ft in the V EC TO R progra m. A cry lic on ca n v a s pa in tin g b y R ob ert J a n L ooy e ( Private collection Dr. Steinhauser). c 2 0 0 7 b y G .H .N . L ooy e C opy right A ll rights reserv ed. N o pa rt of the ma teria l protected b y this copy right n otice ma y b e reproduced or utilised in a n y form or b y a n y mea n s, electron ic or mecha n ica l, in cludin g photocopy in g, recordin g or b y a n y in forma tion stora ge a n d retriev a l sy stem, w ithout the prior permission of the a uthor. IS B N / EA N : 9 7 8 -9 0 -5 3 3 5 -1 4 8 -2 Ty peset b y the a uthor usin g the LATEX Documen ta tion S y stem. P rin ted b y R idderprin t O ff setdrukkerij B V , R idderkerk, The N etherla n ds..

(7) To Claudia.

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(9) Summary LIGHT Control Laws (FCLs) make the difference between the dynamic behaviour of an aircraft of its own, and what it actually fl ies and feels like to the pilot and passenger. To this end, FCLs consist of dynamic feedback and feedforward transformations of sensor and command signals into suitable control defl ections, providing desired manual or automatic fl ying behaviour and passenger comfort, under clear as well as turbulent atmospheric conditions. Flight control laws have to meet a large amount of performance and safety req uirements in order to ensure they perform reliably in all fl ight conditions, under adverse operating conditions, in the event of hardware failures, etc. Feedback of sensor measurements hereby not only infl uences, but also brings about strong interaction between aircraft fl ight – , airframe structural – , control system hardware – , sensor – , engine – , and landing gear dynamics, thus involving several engineering disciplines simultaneously. As a conseq uence, the design of fl ight control laws is a challenging, multi-disciplinary design task. The multi-disciplinary aspect in FCL design is becoming more and more important. In order to improve over-all effi ciency, aircraft designs are continuously pushed to physical limits. This results in for example more fl exibility of the airframe structure and “ just-right” sized actuators and control surfaces. Also, the availability of control laws is more and more exploited, e.g. to actively reduce loads on the airframe, to provide active stabilisation, and to reduce structural vibrations. The current design process for fl ight control laws is not well configured for an inherently multi-disciplinary approach. The main reason is that multi-disciplinary aspects are addressed only after the principal design loop, in analyses performed by specialist departments. This usually gives rise to req uests for fixes, resulting in additional design loops. The objective of this thesis is to develop concepts and methods for a new process that allows for easy incorporation of multi-disciplinary aspects in fl ight control design from the beginning. The prereq uisite for doing this is the availability of integrated multi-disciplinary aircraft models that not only include fl ight dynamics, but also accurately describe structural dynamics, airframe loading, systems dynamics, etc. As an example, an integrated model allows control bandwidth to be adjusted, while keeping a close watch on airframe loading. This will save time consuming design iterations with the loads department afterwards. Multi-disciplinary aircraft modelling req uires a generic model structure that al-. F.

(10) viii. Summary. lows for straight-forward integration of components from various disciplines, as well as methods for appropriate incorporation of data sources behind these components, especially in case overlaps exist. In this thesis, such a model structure is defined exploiting object-oriented modelling techniques. The difference between object-oriented modelling and contemporary approaches is that implementation is based on “native” physical rather than “simulation-ready” differential equations. This allows model components on the one hand to be implemented using engineering discipline-specific physical equations, and on the other hand to interconnect these components in integrated models based on a common modelling language. The first contribution of this thesis is the development of a new generalised structure for multi-disciplinary aircraft models and its implementation in the object-oriented modelling language M odelica. Even in case of a multi-disciplinary design, the flight control laws still have to go through discipline-specific analyses, especially flutter, loads, and systems. It is therefore very important to directly incorporate data sources from these departments, so that design iterations due to model incompatibilities are avoided. Particularly in the case of aeroelasticity, this is a challenging problem, since aeroelastic and rigid aircraft flight dynamics models have several overlaps. The second contribution of this thesis is a procedure for merging equations of motion and aerodynamics behind both types of models in an appropriate way. Simulation requires the model to be available in the form of Ordinary Differential Equations (ODEs) or Differential Algebraic Equations (DAEs). A characteristic aspect of object-oriented modelling is that these equations are automatically generated from the implemented physical model equations. To this end, reliable symbolic algorithms are readily available. Besides suitable models for control design analysis, this offers the interesting possibility of automatic model inversion. Various nonlinear synthesis techniques, like Nonlinear Dynamic Inversion, are based on inversion of nonlinear model equations, resulting in control laws for a part of or the full flight envelope in one shot. The th ird contribution of this thesis is the idea of combining automatic model inversion and inversion-based controller synthesis for rapid-prototyping. This allows the control designer to experiment with control command variables, control allocation, requirements for control sizing sizing, etc. in very short design cycles, supporting key decisions that heavily impact the eventual control structure, or even the over-all control concept. It also allows the control department to release preliminary, but representative control laws to other engineering departments early on in the aircraft design process, e.g. allowing for early closed loop assessment of flight loads. In this thesis rapid-prototyping control law design from an object-oriented aircraft model is demonstrated on manual control laws for an aircraft manoeuvring on the ground. In case the rapid prototyping design is promising, detailed design follows. In this thesis this is discussed for nonlinear dynamic inversion-based control laws for inner loops of an automatic landing system for a small aircraft. Hereby especially feedback signal synthesis and robustness issues due to differences between the actual aircraft dynamics and the inverted model equations are addressed. In case of NDI the traditional approach is to achieve robustness in design of the outer-loop.

(11) Summary. ix. control law. As a fourth contribution, this thesis proposes a different way. Uncertain model parameters, which also appear in the inverse model equations, are used as additional degrees of freedom in parameter synthesis. The combined NDI and outer loop control laws are then tuned simultaneously to meet performance and robustness specifications using multi-objective optimisation. Robustness is hereby addressed by directly incorporating robustness measures as optimisation criteria, and by simultaneously addressing nominal and selected worst-case parameter combinations in the optimisation. In the current design process, tuning of control laws is mostly performed manually. However, multi-disciplinary design requires a considerably larger set of criteria set to be addressed simultaneously. For this reason the use of multiobjective optimisation for tuning of free control law parameters is recommended. The underlying min-max approach allows the large amounts of (usually conflicting) multi-disciplinary design criteria and constraints to be addressed efficiently, aiming to achieve best-compromise solutions. Relative importance of criteria is expressed using scaling functions that have a clear physical interpretation. The optimisation problem is not necessarily convex: the main objective however is to automatically search for satisfactory design solutions. Obviously, suitable aircraft dynamics models needed for evaluation of numerical criteria are automatically generated from the object-oriented model structure described above. As a fifth contribution this thesis extends the approach of multi-objective optimisation to large controller structures that consist of multiple interacting functions. A sequential tuning strategy is proposed in which new controller functions are sequentially added to the synthesis, eventually resulting in optimisation of the over-all control system. This strategy allows inner loop functions to be tuned in combination with various outer loop functions. This may considerably reduce control law complexity, since duplication of functionality is avoided. The contributions described above have been combined into a simplified flight control law design process. This process has been applied for the design of an automatic landing system for a small passenger aircraft. The proposed tuning strategy allowed the same set of inner loops to be used with all outer loop controller functions, like glide slope and localiser tracking, and flare and runway alignment in case of cross wind. Before flight testing, autoland control laws are extensively tested using Monte Carlo (MC) analysis, often giving rise to new design iterations in a second design loop as described above. In the autoland design MC analysis has been directly incorporated in the tuning process, demonstrating that this additional loop can be avoided using the proposed design process. The autoland system was successfully tested in six automatic landings, without the need for any re-tuning of control law parameters..

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(13) Contents Summary 1. 2. In tro d uc tio n 1.1 Flight control laws . . . . . . . . . . 1.2 The flight control law design process 1.3 Future developments in flight control 1.4 Objective of the thesis . . . . . . . . 1.5 General approach . . . . . . . . . . . 1.6 Overview and contributions . . . . .. vii. . . . . . . . . . . . . . . law design . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 1 5 7 10 12 13 15. M ulti-d isc ip lin ary airc raft mo d e l d e ve lo p me n t usin g o b je c t-o rie n te d mo d e llin g te ch n iq ue s 19 2.1 Current practice in multi-disciplinary modelling . . . . . . . . . . . 21 2.1.1 Model implementation . . . . . . . . . . . . . . . . . . . . . 23 2.1.2 Model integration . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.3 Aircraft modelling for flight control law design . . . . . . . 27 2.2 The aircraft model structure . . . . . . . . . . . . . . . . . . . . . . 28 2.2.1 The world model . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.2 The atmosphere model . . . . . . . . . . . . . . . . . . . . . 30 2.2.3 The terrain model . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.4 The airport infrastructure model . . . . . . . . . . . . . . . 31 2.2.5 Rigid and flexible aircraft models . . . . . . . . . . . . . . . 31 2.3 The Modelica Flight Dynamics Library . . . . . . . . . . . . . . . . 37 2.4 Automatic code generation . . . . . . . . . . . . . . . . . . . . . . 39 2.5 Application example: ATTAS . . . . . . . . . . . . . . . . . . . . . 40 2.5.1 Starting the model project . . . . . . . . . . . . . . . . . . 41 2.5.2 Aircraft-specific model components . . . . . . . . . . . . . . 43 2.5.3 Specification of inputs, outputs, and parameters . . . . . . 43 2.5.4 Model translation . . . . . . . . . . . . . . . . . . . . . . . 45 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47.

(14) xii. Contents. 3 Integration of rigid and aeroelastic aircraft models using the residualised model method 3.1 Review of aircraft flight dynamics models . . . . . . . . . . . . . . 3.1.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . 3.1.2 External forces and moments . . . . . . . . . . . . . . . . . 3.2 Review of aeroelastic aircraft models . . . . . . . . . . . . . . . . . 3.2.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . 3.2.2 External forces . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Integration of flight dynamics and aeroelastic models . . . . . . . . 3.3.1 Equations of motion . . . . . . . . . . . . . . . . . . . . . . 3.3.2 External forces and moments: the residualised model method 3.4 Application example . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Coupling using aeroelastic state space models . . . . . . . . . . . . 3.5.1 Aeroelastic state space model . . . . . . . . . . . . . . . . . 3.5.2 The RM method in state space form . . . . . . . . . . . . . 3.5.3 Correction of aeroelastic state space models . . . . . . . . . 3.6 Application example (Continued) . . . . . . . . . . . . . . . . . . . 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53 57 57 58 59 59 61 62 62 64 65 67 70 71 72 73 76. 4. R apid prototyping using inversion-based control and object-oriented modelling 81 4.1 Object-oriented modelling of aircraft flight dynamics . . . . . . . . 84 4.1.1 Object-oriented modelling . . . . . . . . . . . . . . . . . . . 84 4.1.2 Object-oriented modelling of the aircraft-on-ground . . . . 87 4.2 Translation of object-oriented models . . . . . . . . . . . . . . . . . 90 4.3 Inverse model generation . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 A rapid prototyping design process . . . . . . . . . . . . . . . . . . 97 4.5 Aircraft-on-ground control design application . . . . . . . . . . . . 101 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. 5. D esign of robust autopilot control law s w ith N onlinear D ynamic Inversion 113 5.1 Nonlinear Dynamic Inversion . . . . . . . . . . . . . . . . . . . . . 116 5.2 The Aircraft Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2.1 Nonlinear model equations . . . . . . . . . . . . . . . . . . 119 5.2.2 Linearised model equations . . . . . . . . . . . . . . . . . . 120 5.3 Dynamic inversion attitude control laws . . . . . . . . . . . . . . . 122 5.3.1 Automatic control law generation . . . . . . . . . . . . . . . 124 5.3.2 Implementation aspects . . . . . . . . . . . . . . . . . . . . 125 5.4 Robust parameter synthesis . . . . . . . . . . . . . . . . . . . . . . 128 5.4.1 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.4.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.4.3 Design criteria . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.4.4 Scaling of criteria . . . . . . . . . . . . . . . . . . . . . . . . 132 5.4.5 Parameter synthesis . . . . . . . . . . . . . . . . . . . . . . 133.

(15) Contents. 5.5. 5.6 5.7. Assessment . . . . . . . . . . . . . . . . 5.5.1 Analysis w.r.t. synthesis criteria 5.5.2 Robust stability analysis with µ Flight test results . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . .. xiii. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 6 Design of autoland controller functions with multi-objective timisation 6.1 The aircraft model . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 The applied design process . . . . . . . . . . . . . . . . . . . . 6.3 The controller architecture . . . . . . . . . . . . . . . . . . . . . 6.4 Optimisation problem set-ups . . . . . . . . . . . . . . . . . . . 6.5 Controller optimisation strategy . . . . . . . . . . . . . . . . . . 6.6 Formulation of the basic optimisation problem . . . . . . . . . 6.7 Controller optimisation results . . . . . . . . . . . . . . . . . . 6.8 Flight test results . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. C onclusions 7.1 An integrated flight control law design process 7.2 Recent application examples . . . . . . . . . . . 7.3 Lessons learnt . . . . . . . . . . . . . . . . . . . 7.4 Recommendations for future research . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . . .. . . . . .. op155 . . 160 . . 161 . . 162 . . 168 . . 174 . . 176 . . 177 . . 182 . . 185 . . . .. . . . .. A ppendices A. B. 134 134 137 150 150. 189 191 196 198 200 20 3. Model building for control law design A.1 Simulation models for design analysis . . . . . . . A.2 Interactive desktop simulation . . . . . . . . . . . A.3 Computation of initial conditions . . . . . . . . . A.3.1 Trim computation using the model ODE . A.3.2 Trim computation by model inversion . . A.4 Linearisation of the aircraft model . . . . . . . . A.5 Parametric models for robustness analysis . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. 20 5 207 210 210 211 217 218 219. E quations of motion of a fl ex ible aircraft B.1 Review of structural dynamics . . . . . . . . . B.1.1 Structural eigenvalue problem . . . . . . B.1.2 The half-generalised equations of motion B.1.3 The generalised equations of motion . . B.1.4 Recovery of physical degrees of freedom B.1.5 Orthogonality of modes . . . . . . . . . B.2 The equations of motion of a flexible aircraft . B.2.1 Approach for derivation . . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. 221 223 223 224 225 226 227 229 230. . . . . . . . ..

(16) xiv. Contents. B.2.2 Kinetic energy . . . . . . . . . . . . . . B.2.3 Floating reference frames . . . . . . . . B.2.4 Potential energy . . . . . . . . . . . . . B.2.5 Application of Lagrange’s equations . . B.2.6 Kinematic equations . . . . . . . . . . . B.2.7 Application of local forces and moments B.2.8 Summary of result . . . . . . . . . . . . B.3 Concluding remarks . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. 233 235 238 238 239 241 242 243. Bibliography. 245. Nomenclature. 259. Index. 271. Samenvatting. 275. Ack nowledgements. 279. Curriculum vitae. 281.

(17) Chapter 1. Introduction.

(18) 2. Introduction. Abstract Control laws as present in the flight control computers of modern aircraft provide the functionality for safe manual and automatic control in flight. The design of flight control laws (F CL s) consists of the actual design phase, followed by a validation phase that involves ex tensive simulations, rig tests and, eventually , flight tests. Multi-disciplinary aspects play an important role, since F CL s not only improve aircraft flight dy namics, but also aff ect structural dy namics, airframe loading, sy stem dy namics, etc. Currently these aspects are not addressed until the validation phase, freq uently resulting in late design iterations. In future aircraft design projects interactions between flight control and other engineering disciplines will become considerably stronger, req uiring multi-disciplinary aspects to be addressed from the beginning. This is where this thesis aims to contribute. Three aspects will be addressed in detail: development of integrated multidisciplinary aircraft models to allow a wide range of design criteria to be evaluated and addressed in sy nthesis of the control laws, development of approaches for handling various ty pes of uncertainty and model variation in tuning of design parameters, and the integration of these methodologies into a design process structure that allows complex control law structures to be handled effi ciently and transparently ..

(19) 3. N the early days of aviation, the pilot used to control the aircraft with the help of cockpit controls that were directly linked with aerodynamic control surfaces via mechanical elements such as rods, cables and trolleys. Stabilisation, compensation of coupled responses to steering inputs (e.g. turn co-ordination), rejection of atmospheric disturbances, manoeuvring of the aircraft, and navigation were performed by the pilot alone, supported by early cockpit instruments only. The current situation in military and civil aircraft is quite different. Although mechanical linkage between cockpit control devices and control surfaces and engines has remained in designs well into the seventies and eighties of the previous century, the tasks of the pilot in military and civil aircraft have been increasingly automated. Starting with active dampers – basic autopilot modes, stability and command augmentation systems and automatic landing systems have evolved over decades, leading to full-authority digital control systems as present in today’s aircraft. A detailed historical overview and interesting references can be found in Ref. [84]. Modern civil transport aircraft are flown using the so-called flight guidance and control (FG& C) systems [38, 15], comprising the flight control system (FCS), the flight management system (FMS), the automatic flight control system (AFCS), and mostly also some form of structural control (SC) or active loads control (ALC). In Figure 1.1 the functions of these systems have been ordered according to their hierarchical level in the form of a block diagram. Several components of the system, to be discussed subsequently, are operated via control devices, displays, and panels in the cockpit (top left). Eventually, actuation systems are commanded that drive control surfaces (painted black in the aircraft depicted top right) and engines to make sure the aircraft responds in the desired way.. I. 1. flight control (FC). This task is performed by the FCS. This system allows the pilot to manually steer the aircraft with the help of the side stick or control column, and pedals. With the help of feedback and feedforward control algorithms the FCS allows the (auto-) pilot to directly command aircraft motion variables, such as body angular rates, accelerations, or combinations thereof, and makes sure these commands are tracked accurately and independently (de-coupling), especially under atmospheric disturbances. Extensive protection features prevent the pilot from bringing the aircraft into dangerous flight situations, outside its envelope of safe operation. Velocity and flight path are controlled with the help of throttles and speed brakes. In case of system failures, the cockpit controls are electronically directly linked to control surfaces (“direct law”), bypassing all levels of automation. The pilot uses the FCS to perform manual, short-term steering tasks, mainly during take-off, landing, and ground operation. 2. flight guidance (FG ). This task is performed by the AFCS, consisting of the autopilot and autothrottle. The pilot selects modes of operation and enters target values for speed, altitude, vertical speed, and heading via the glare shield control unit (see Figure). The autopilot and autothrottle compute appropriate command signals that are executed by the FCS. Stability and.

(20) 4. Introduction. command augmentation is provided by the FCS, or by the AFCS itself. The pilot uses the AFCS to perform longer term tasks automatically. 3. flight management (FM). The FMS has extensive capability to predict and optimise aircraft performance as a function of flight plan parameters and to automatically execute complete flight plans using autopilot and autothrottle modes. The pilot may enter and optimise the flight plan or load a stored one via the multi-purpose control and display unit (MCDU, see Figure). The pilot uses the FMS to manage long term tasks that may span nearly the entire flight. In modern aircraft, the control surface and engine actuators are commanded with the help of electronic signals. For this reason, electronic flight control systems are more commonly known as fly-by-wire (FBW) systems. The FC functionality is implemented in the flight control computer (FCC). Besides probable weight reduction due to partial replacement of mechanical equipment and considerable reduction in maintenance costs, the greatest virtue of fly-by-wire lies in the FCC. The possibility of tailoring the dynamic aircraft responses to command inputs considerably reduces pilot work load and has allowed for the development of highly agile combat aircraft with otherwise unflyable aerodynamically unstable and aerodynamically nonlinear airframe configurations. In the civil sector, FBW has allowed the airliner manufacturer Airbus to develop a complete aircraft family with a high level of handling commonality, allowing transition of flight crews from one type to the other with minimum training effort. Flight control, flight guidance, and flight management are so-called primary aircraft control functions, intended for stabilising and manoeuvring of the over-all aircraft. Since the early seventies aircraft are more and more equipped with socalled secondary control functions, addressing the loading and dynamic behaviour of the airframe structure. The airframe is a lightweight construction that has to withstand peak and fatigue loads caused by gusts, manoeuvring, engine and system failures, etc. Active Loads Control (ALC) functions allow for reduction of these loads at critical locations in the airframe, for example by active damping of structural modes, or by distributing loads in a more favourable way (e.g. using ailerons to move the lift distribution over the wing in-board, in order to reduce bending moments at the root). To this end, ALC functions use strategically distributed accelerometers and available control surfaces. In this way, fatigue life of the structure is increased and peak loads are reduced, allowing for reduction of structural weight. As an example, the introduction of active loads control avoided the need for structural reinforcement of the outer wing of the longer range (500 series) derivative of the Lockheed 1011 Tristar [13]. Structural control functions may be implemented to dampen resonant airframe structural modes that cause passenger and pilot discomfort. An example is the comfort in turbulence function (CIT) in the Airbus A340 [119]. Besides primary and secondary flight control functions, actuators are equipped with local control systems as well, allowing for accurate positioning of the control surface, and with the possibility to detect internal failures. Most engines are.

(21) 1.1 Flight control laws. 5. equipped with a full authority digital engine control (FADEC) system, which augments the otherwise highly nonlinear throttle responses and allows for direct commanding of for example the engine pressure ratio (EPR) or fan shaft speed (N1 ).. F. g. l a c. d. i s. p. l a. y. r e. o. n. s. t r o. h. i e. l. u. n. M G F. C. =. F. F. =. S. L. C. A. L. C. S. C. =. A. P A. T. i t. S. C. R. u S. t o. p. t o. t h. t a. b. i l o. e. l. a a. e. c. n. t. e. l. n. d. d. l. m. n. t r o. o r a. g a. n. r a L. t u. a. i d. o. e c. n. u. C t u. t i v. u. A =. c. a G. t. t r u. A. =. A. c. M. t. h. t r u. A S. = H. t h. l i g. S. =. h. l i g. F. =. l d. l i g. F. =. L. C. C. o. o. o. n. a. d. n. t r o. t r o. l. C. o. n. t r o. l. l. t. r o. t t l e. i l i t y. a. n. d. C. o. m. m. a. n. d. A. u. g. m. e. n. t a. t i o. n. s p. r i m s. M. C. D. e. a. n. r y. s. o. c. o. n. t r o. l. s. u. r f a. c. e. s. r s. U. c. o. n. e. t r o. v. i c. l. e. s. t h. r o. t t l e. s. d. b. a. " d. 3. 2. c. k. - u. i r e. p. c. t. l a. A F M A. P. G. ,. A. T. H. F R. C. S. F. j e. l i g. h. c. t o. t. f l i g. r y. g. u. s. i d. a. n. h. p. t. c. e. e. e. p. a. t h. C. a ,. S. t t i t u r a. a. a. n. d. c. o. n. t r o. c. l. A. e. s. d t e. c. y. e. L. L C. t e. a. m. E. g. y o. r f a n. t i o. d c c i n. n n. e e. a t r o. s. n l. A. i r c d. y. n. r a a. f t m. i c. s. S. e. n. s. o. r s. s. C. A ,. l .. s. C , S. e s. *. u. a. r o i c. s. A. &. d. t u. m. A. t r a. ". c *. F. w. 1. t t i t u. d. c. l e. c. e. e. r a r a. t i o. t e n. s. ,. s. s. Figure 1.1: The relation between displays, controls, and control laws in a modern transport aircraft. 1.1. Flight control laws. Subject of this thesis are the algorithms in the various systems that contain the intelligence to perform the various control and guidance tasks discussed in the previous section: the flight control laws (FCLs). The dynamic behaviour of the flight control system, and therefore the dynamic behaviour of the complete aircraft, is governed by these control laws. Consequently, the FCS and its FCLs are flight-critical and obviously must be available at all times during flight. The probability of failure resulting in loss of the aircraft has to be extremely remote, i.e. less than 1 in 1 billion flight hours (< 10−9 ) (paragraph 25.1309 in [49]). The design of the flight control laws is a very challenging task for a variety of reasons:.

(22) 6. Introduction. • Even the most basic control tasks are subject to a large number of design requirements. For example, handling qualities criteria have to be met, stability must be guaranteed (which may be challenging in case the pilot is in the loop), and control activity must be limited (especially in turbulent conditions). Control law behaviour must further be accepted by pilots, often giving rise to additional qualitative and subjective criteria to be met; • Control laws have to work over the full operating envelope of the aircraft1 . Aircraft flight dynamics may be highly nonlinear as a function of the flight condition and flight attitude, requiring control law scheduling as a function of these parameters; • Sensor signals can usually not be used directly, but need processing through complementary filters to reduce the effect of atmospheric disturbances, through notch filters to reduce structural dynamics content of signals, through estimation algorithms to compute signals not directly measurable (e.g. side slip angle often requires this), etc.; • Implementation aspects must be kept in mind, like capacity of the FCC and certification of software; • Most control law development work is performed well before the first aircraft has flown. This means that the design team has to rely on data from theoretical methods, wind tunnel experiments, and extrapolation from previous programs. Consequently, robustness to tolerances in the data is an important issue in design and clearance of the FCLs; • Control laws rely on sensors and use actuators to perform their tasks. These devices may fail. The design team has to make sure that the control laws under no circumstance make things worse than they are (uncontrollability, instability!). Failures must be handled properly, even if this means that functionality is reduced or completely deactivated (so-called “direct law”, see Figure 1.1); • As already discussed in the previous section, FCLs consist of many many functions. Each function requires the above issues to be considered individually, but ...; • ... at the same time, have to be safely integrated in the over-all system; • Beyond handling of complex aircraft flight dynamics, flight control law design integrates many engineering areas. The reason is illustrated in the form of a block diagram in Figure 1.2. The collection of interconnected blocks constitutes the over-all dynamics of the aircraft, involving: – flight dynamics (aerodynamics, propulsion, environment, loading, etc.); 1 Actually, even beyond, since the aircraft must be recoverable from the most awkward flight attitudes.

(23) 1.2 The flight control law design process. 7. – airframe structural dynamics; – sensor system dynamics; – actuation system dynamics; – engine dynamics; – flight control laws. By closing the feedback interconnection, FCLs bring about strong interaction between dynamics of all sub-systems. As already noted, in case of manual control the integrated dynamics in turn are influenced by the human pilot closing an additional loop. These interactions need to be addressed carefully in the design process and involve close co-operation with other engineering departments.. co n tro l co m m an d s. e le ctro n ic actu ato r / e n gin e s ign als. co n tro l s u rface d e fle ctio n s thru s t. aircraft m o tio n / d e fo rm atio n , airflo w , e tc.. Au to p ilo t s e ttin gs F light C o n tro l L aw s. EFC S d e lay s & filte rin g. Actu atio n s y s te m & e n gin e d y n am ics. Aircraft flight & s tru ctu ral d y n am ics. S e n so r s y s te m d y n am ics. P ilot steering atmospheric disturbances s e n s o r s ign als (b u s ). D isplay s, motions, ... Integrated aircraft dynamics. Figure 1.2: Feedback interaction of flight control laws, aircraft dynamics, and system dynamics. 1.2. The flight control law design process. In order to handle the challenges described in the p rev iou s sections, flight control laws req u ire a thorou gh and well organised design p rocess. A lthou gh the details of this p rocess look diff erently at each aircraft manu factu rer, a general stru ctu re can mostly be recognised. In the frame of the G A R T E U R Flight M echanics A ction G rou p 0 8 on R obu st Flight C ontrol [7 7 ], Irv ing dev elop ed a model of su ch an indu strial flight control law design p rocess for military aircraft flight control laws [5 3 ]. T his model describes the interactions between the flight control and other inv olv ed engineering discip lines in detail. Figu re 1 .3 dep icts a more simp lifi ed form, based on a scheme p resented by Fielding and L u ckner in R ef. [3 8 ]. S tarting p oint are C u stomer and A irworthiness R eq u irements, the fi nal resu lt is the control laws integrated within the fu lly q u alifi ed and certifi ed aircraft..

(24) 8. Introduction. C u s to m e r & A ir w o r th in e s s R e q u ir e m e n ts. D esig n P h ilo so p h y. A irc ra ft / S ystem s D a ta & M o d els. D eta iled d esig n req u irem en ts B a selin e F C L S tru c tu re B a s e lin e F C L C o m p . / G ra p h . D esig n C riteria. Off-line Design. D eta iled F C L D esig n / A n a lysis. Ok? yes. no. 1. F C L In teg ra tio n / C o d in g. C o m p . / G ra p h . A ssessm en t C riteria , T est S p ec ific a tio n s. A ssessm en t (C lea ra n c e). Ok?. no. A S E (* ) A n a lysis. 2 D e s ig n s ta n d a r d F C L. yes H /W & S /W P ro d u c tio n /In teg ra tio n. F C S S ystem T est S p ec ific a tio n. R ig T estin g (Iro n B ird ). Ok?. no. 3. yes. F lig h t s ta n d a r d F C L. A irc ra ft In teg ra tio n. F lig h t T est S p ec ific a tio n. F lig h t T estin g. Ok?. no. yes. F u lly C e r tifie d a n d Q u a lifie d F lig h t C o n tr o l L a w s. 4. P r o d u c tio n s ta n d a r d F C L (fin a l u p d a te ). (* ) A S E = A ero serv o ela stic , c o n d u c ted b y a ero ela stic ity d ep a rtm en t (* * ) C o n d u c ted b y lo a d s d ep a rtm en t. Figure 1.3: Flight control laws design process (based on [38]). L o a d s (* * ) A n a lysis.

(25) 1.2 The fl ight control law design process. 9. The depicted process has four main iteration loops: • Loop 1: Off-line design. In this phase actual design of control laws takes place. B ased on their required functionality, a baseline structure is developed. The choice of control devices, command variables, functional breakdown into loops and components, etc. will largely depend on the philosophy of the design team. The nex t step is detailed design of control law functions, based on the baseline structure and aircraft and system models/ data that are available at the time. D etailed design requirements are based on customer and airworthiness requirements, as well as in-house criteria. These in turn may be formulated in the form of computational and graphical criteria that relate to design methods that are used within the design group. For ex ample, specific minimum stability margins may be required, or bounds on time and frequency responses may be imposed. W ithin the controller structure, parameters, complementary filters, estimators, nonlinear functions, etc. are defined and tuned to best meet the specifications, after which the control laws are ex tensively tested using linear and nonlinear simulations. N owadays, for control law synthesis and analysis a wide range of methodologies is available, see for ex ample [77]. • Loop 2 : A ssessm ent a nd c lea ra nce. After integration of designed control law functions, ex tensive assessment is carried out. This assessment may involve real time simulation in the flight simulator, ex tensive robustness analysis against tolerances in model data (especially in the case of military aircraft), performance of analyses as required for certification (e.g. Monte Carlo analysis in the case of automatic landing), etc. In this phase not only control law performance and robustness is addressed, but also interaction with airframe structural dynamics and loads. To this end, the control law specification is released to the disciplinary departments involved. The aeroelastic department will perform ex tensive aeroservoelastic analysis in order to make sure flutter margins of the closed-loop system (Figure 1.2 ) are preserved over the aircraft flight envelope, for all weight and balance conditions and configurations. Loads analysis is performed to make sure that a.o. manoeuvre and gust loads design envelopes are not ex ceeded due to flight control system action. Any design deficiency that shows up in this phase gives rise to the second design cycle. According to Irving, control laws that passed this phase have reached the maturity of D esign S ta nda rd. • Loop 3: R ig testing. B efore installation in the first aircraft, all on-board systems are integrated in a test rig, the so-called iron bird. As part of the over-all FCS, the flight control laws are ex tensively tested in this iron bird in order to validate proper functioning in interaction with the systems hardware. Especially failure cases are investigated that are risky and costly.

(26) 10. Introduction. to test in flight. The iron bird may be operated in combination with the flight simulator, allowing realistic test scenarios to be performed. Design deficiencies may arise from over-looked aspects (e.g. unanticipated failure scenarios), or deficiencies in system models. Especially nonlinearities may adversely affect control law performance. In this case, the model needs to be updated before adapting the control laws (Figure 1.3, top right). The flight control laws status after satisfying the hardware test specifications is designated Flight Standard by Irving. • Loop 4 : Flight testing. This loop involves extensive validation of the control laws in the aircraft in flight. O bviously, the number of tests will be limited because of time, cost, safety, and environmental constraints. Therefore, flight test results are partly intended to validate results from the second design phase. In case of design deficiencies, control law updates may be required. The final version (p ro du ctio n standard) will be certified with the aircraft. The design cycles may involve various stages in the off-line design process. Design modifications may be initiated in Detailed FC L Design / Analy sis, in the B aseline FC L Stru ctu re, as well as in the Detailed Design Req u irements. Even a change in design philosophy may appear to be necessary, but hopefully at an early stage. Especially in the case of military aircraft, the Assessment and C learance phase may proceed on parts of the flight envelope or specific functions, as FCLs for other parts, or other FCL functions, enter rig and flight testing. In case of a new aircraft type or derivative, the development of the aircraft models (top right in Figure 1.3) is a process by itself, which runs in parallel with the FCL design. Major updates usually result from new wind tunnel experiments (e.g. after configuration changes) and, in a later stage, from flight tests. Model improvements require most analyses to be performed over again and frequently force the control laws to be updated as well. Clearance results as presented to the authorities for certification must eventually be produced using the most up-todate model data, since consistency with flight test results has to be demonstrated [37].. 1.3. Future developments in fl ight control law design. The design and certification of flight control laws is hardly ever a routine job. In the first place, automation in the cockpit progresses continuously from aircraft program to aircraft program, and existing functions are expected to deliver more performance with each new design (e.g. higher cross-wind limits for automatic landing). In the near future, new modes such as automatic take-off and drive-bywire control laws during taxiing will be introduced, further reducing pilot work load and eventually allowing for full automation of the flight from push-back at the departure airport until parking at the terminal of the destination airport [28]..

(27) 1.3 Future developments in fl ight control law design. 11. Besides the extension of FCS functionality, also aircraft design is progressing rapidly, pushing more and more towards physical limits. Currently, the relative amount of composites in the structure is about to increase dramatically. For example, both the Boeing 787 and the Airbus A350 X WB will feature fuselages made out of Carbon Fibre Reinforced P lastic (CFRP ). Composites allow for optimisation of fibre directions and density, resulting in dramatic weight reduction of the over-all airframe, but simultaneously increasing its flexibility (see Figure 1.4). Also system hardware is more and more subject to weight reduction, resulting in. Figure 1.4: H ighly flexible wing design of the Boeing 787 Dreamliner (Image source: The Boeing Company, photo nr. K 6 39 6 5-03) “ just-right” selection of actuators [112]. Increased airframe flexibility and “ just-right” siz ing of actuators heavily impact control law performance. The other way around, the flight control system will also more and more impact (transport aircraft) airframe design, since it for example allows for relaxation of natural stability of the aircraft, resulting in lower fuel consumption2 . From the above it will be clear that flight control laws will become more complex and that their interaction with other engineering areas in aircraft design will become more important than ever. The current industrial design process is not well configured to accommodate this. The most important reasons are: 1. Even nowadays, too many design deficiencies are sorted out via iteration loops beyond the off-line design phase [38, 76 ]. This causes high costs, since 2 Relaxed stability allows the tailplane to be smaller and lighter, and the centre of gravity of the aircraft may be moved aft, so that the tailplane will contribu te to over-all lift in eq u ilibriu m cru ise fl ight [1 5 ]..

(28) 12. Introduction. from loop 2 onwards (Figure 1.3), more and more people, departments, and test equipment get involved. Depending on the required modification, intermediate steps may have to be performed over again, costing progressively more engineering time and resources. As can be seen from the figure, loads and aeroelasticity aspects are not addressed in detail until specialist departments perform flight loads analyses with the FCLs included. The impact of late design iterations along the third loop will increase significantly as actuators are sized more tightly. Finding trade-offs between control law performance and, for example, airframe loading via loop 2 will be impractical and expensive; 2. Models used for FCL design allow for evaluation of criteria primarily related to flight dynamics and handling characteristics. Usually, only static aeroelastic effects (flight shape deformation of the airframe) are taken into account. Analysis of flight loads, detailed analysis of actuation system dynamics, and assessment of structural dynamics influences require special models, only available within the respective engineering departments; 3. Controller synthesis parameters are mainly tuned by hand. Design requirements for control laws usually do not translate directly into specifications for the applied controller synthesis method. This requires manual iteration between controller synthesis and validation against the requirements. Multidisciplinary design means that additional criteria and constraints must be taken into consideration. Finding trade-offs then quickly becomes a very tedious task; 4. There is a lack of design methodologies that allow for fast adaptation of flight control laws to changes in the aircraft configuration. Such a methodology allows the flight control design team to contribute and rapidly adapt representative flight control laws to the emerging (preliminary) aircraft configuration from the earliest design stages. This will be very valuable as FCLs are to become a more and more integral part of the over-all aircraft design and design optimisation. Furthermore, this allows the FCL design team to more accurately (less conservatively) formulate specifications for sizing and positioning of aerodynamic control surfaces and for sizing of control system hardware.. 1.4. Objective of the thesis. The general objective of this thesis is formulated as follows: Propose a design process (focusing on the off-line phase) and methodologies that inherently facilitate multi-disciplinary design of fl ight control laws. In response to the shortcomings listed in the previous section, the following detailed objectives are set:.

(29) 1.5 General approach. 13. • Develop a model structure for aircraft flight dynamics that allows for easy and intuitive integration of model components and data from other engineering disciplines, allowing for multi-disciplinary design analysis; • Develop a model integration methodology that specifically allows aeroelastic effects to be included in flight dynamics models, based on agreed-on model data from loads and aeroelasticity disciplines; • Develop a rapid-prototyping methodology that allows for quick generation of representative control laws for aircraft design analysis in the preliminary design phase; • Extend methodologies that allow for automatic robust tuning of flight control laws, eventually allowing for automatic multi-disciplinary compromise tuning of FCL parameters. As a principal constraint, the methodologies must be able to fully incorporate existing know-how, experience and lessons learnt in the flight control department.. 1.5. General approach. At the DLR Institute of Robotics and Mechatronics the (off-line) design process for flight control laws has been a central research area since the mid-nineties. In 1997 a process structure as depicted in Figure 1.5 was proposed, developed in the frame of a German national project called First-Shot Approach in flight control law design (FSA). The process consists of the following steps: • Modelling. This involves development of the aircraft model, including all relevant dynamic effects (flight dynamics, actuator and sensor dynamics, etc.), and modelling of the FCS with the selected controller structure. The model depends on varying or uncertain parameters p and tuning parameters T . The formulation of numerical design criteria from the functional design requirements is another important modelling activity. Modelling work that was performed in the frame of the FSA project is described in [91]. • Analysis and Selection. Before tuning of design parameters (T ), open loop dynamics are analysed and a selection of parameter configurations (e.g. flight cases) as well as design criteria is made, based on which the design parameters are to be tuned. • Tuning and Compromising. This step is mostly performed automatically with the help of multi-objective optimisation. To this end, the software environment MOPS is used [52]. An important means of achieving a robust design is to simultaneously address nominal and worst-case parameter configurations (selected in the previous step) in the optimisation..

(30) 14. Introduction. Modelling * F u nc tiona l des ign req u irem ents * P h y s ic s * Model da ta. * * * * *. c om p onents (p ,T ) a irc ra ft m odel (p ,T ) c ontroller / filters (T ) F C S (p ,T ) c riteria (p ,T ). Ana ly s is & S elec tion * E v a lu a tion & s y nth es is m odels * S u b ta s k s & c riteria. T u ning & C om p rom is ing (T -V a ria tion) no. Ok?. A. y es. As s es s m ent (p -V a ria tion). Ok?. no. B. 1. y es. Figure 1.5: FSA Flight control laws off-line design process • Assessment. Finally, before release for hardware implementation, the control laws are tested extensively as a function of model parameters p in worstcase analyses. The process consists of two main loops. The first loop (A) is based on optimisation results where the designer decides upon shifting trade-offs (via criteria scaling), or in some cases, structural changes to the controller. Loop (B) is based on assessment results and may involve replacement or selection of additional parameter cases to be taken into account in the optimisation in order to improve robustness. The design work based on the process described above is discussed in detail in [50]. The FSA process has two key elements that make it highly suitable for multidisciplinary flight control law design. Firstly, the adopted object-oriented modelling technology is well suited for multi-disciplinary model integration, as will be explained in the following section. Secondly, multi-objective optimisation is able to handle large amounts of criteria simultaneously (up to O(102 ) or more). This provides enough room to address multi-disciplinary aspects..

(31) 1.6 Overview and contributions. 15. The structure of the FSA process puts less emphasis on control law architecture design (in Figure 1.5 referred to as a modelling activity) and on the way how complex control laws are handled. These aspects are to be improved upon in the frame of this thesis.. 1.6. Overview and contributions. The structure of this thesis is depicted in Figure 1.6. Each of the five core chapters addresses a different aspect of flight control law design and aircraft modelling, and therefore can be read independently. As indicated by the fat flare trajectory, the chapters sequentially add key elements that result in a new design process structure proposed in Chapter 7. A pp.B 3 . F le x . a ircra ft m ode l inte g r.. 7 . C onclus ions. 1. Introduction. 2 . M ulti-dis cip lin. A /C m ode lling A pp.A 4 . R a p id F C L p rototy p ing. 5 . N D I-b a s e d F C L de s ig n. 6 . A utola nd s y s te m de s ig n. Figure 1.6: Structure of the thesis. Chapter 2: Multi-disciplinary aircraft model development using object-oriented modelling techniques This chapter proposes the use of object-oriented modelling techniques to develop integrated aircraft models that allow flight dynamics as well as inter-disciplinary effects to be addressed from the beginning in the design process. Object-oriented.

(32) 16. Introduction. modelling allows model components from various engineering areas to be combined in a single model, but still to be represented in their discipline-specific form. The contribution of the chapter is a new physically-oriented generic aircraft model structure, suitable for implementation of rigid as well as flexible aircraft, in slow low up to fast high flight regimes. In addition, the underlying methodology allows for easy implementation of model uncertainty and for automatic generation of run-time code for various types of control design analysis.. Chapter 3: Integration of rigid and aeroelastic aircraft models using the residualised model method One aspect that is absent in contemporary aircraft models for control design is airframe flexibility. The influence of control laws on flutter margins and airframe loading is currently left to the loads and aeroelasticity department, giving rise to design iterations along loop 2 (Figure 1.3) in case problems show up. Taking aeroelastic aspects into account in the flight control design model allows these design iterations to be eliminated. This however requires the integration of rigid and aeroelastic aircraft models, which is not an obvious task due to overlaps between both model types. In Chapter 3 these overlaps are identified and solved mathematically in the form of the so-called residualised model method. In addition, a procedure is developed that also allows the aeroelasticity department to improve its models regarding flight mechanical aspects.. Chapter 4: Rapid prototyping using inversion-based control and object-oriented modelling As depicted in Figure 1.3, two key aspects in the off-line design phase are the adopted control design philosophy, and the baseline controller structure. In case of standard flight control functions the design choices are strongly influenced or even imposed by previous aircraft programs. However, in the near future new functions will be introduced, like drive-by-wire for taxiing on the ground. Key decisions like selection of control variables, control allocation and sizing, etc. are still open. A possibility for rapid prototyping would be an excellent means to study the implications of such choices and to support fundamental decisions, both in flight control as well as over-all aircraft design. Even for conventional control functions, rapid prototyped control laws may be passed on as a preliminary design to other departments for aircraft-level design analysis (e.g. control sizing). Such a rapid-prototyping process is enabled by object-oriented modelling. This methodology namely allows for automatic generation of nonlinear control laws based on inversion of model equations, like Nonlinear Dynamic Inversion (NDI). This will be demonstrated in, and is main contribution of, Chapter 4..

(33) 1.6 Overview and contributions. 17. Chapter 5: Design of robust autopilot control laws with nonlinear dynamic inversion As has been demonstrated in Chapter 4, Nonlinear Dynamic Inversion (NDI) is a nonlinear multi-variable design technique providing decoupled and uniform command responses over the aircraft flight envelope in one shot. In combination with automatic generation of the control laws from an object-oriented model implementation, NDI is a highly attractive methodology from a design effi ciency point of view. However, the method may result in design solutions that, if not appropriately taken care of, are highly sensitive to modelling errors. Chapter 5 addresses this issue in two ways. In the first place, it is shown how with the help of multiobjective optimisation a robust design can be achieved by combining robustness measures (like gain and phase margins) as design criteria, and by simultaneous tuning of control law parameters for different uncertain parameter combinations. It is further shown that uncertain model parameters that also show up in the inverse model equations in the controller, may be effectively used as additional degrees of freedom to achieve a robust design. The chapter covers a complete FCL design from modelling to flight test, demonstrating the capabilities of NDI and the proposed method for robust control law synthesis.. Chapter 6: Design of autoland controller functions with multiobjective optimisation This chapter combines and extends Chapters 3 to 5 into an integrated off-line design process, applied to the design of an autoland control system. The proposed process allows for structured design of complex control laws that consist of multiple interacting functions. This allows controller complexity to be reduced, since a single control function can be tuned for use with various outer loop functions. It is shown that multi-objective optimisation allows for direct incorporation of a variety of criteria and assessment methods (including Monte Carlo analysis) into the tuning process of control law parameters, avoiding design iterations in loop 2 (Figure 1.3) afterwards.. Chapter 7: Conclusions In this chapter the design process proposed in Chapter 6 is generalised and it is shown how the other contributions of this thesis fit in. Current developments and some recent applications are discussed. In addition, some lessons learnt will be shared and recommendations for future work are made..

(34) 18. Introduction.

(35) Chapter 2. Multi-disciplinary aircraft model development using object-oriented modelling techniques.

(36) 20. Multi-disciplinary aircraft model development. Abstract In this chapter a physically-oriented model structure for complex multidisciplinary aircraft dynamics models is presented. For implementation the object-oriented modelling language M odelica is used. Object-oriented modelling (OOM ) is based on implementation of “ nativ e” physical, rather than simulation-ready differential and algebraic equations, allowing v arious engineering discipline-specific modelling methods to be combined in a single model implementation. The proposed aircraft flight dynamics model structure comes with the Flight Dynamics Library, a M odelica library containing re-usable components, as well es base classes for aircraft-specific components. The model structure allows for implementation of flexible as well as rigid aircraft, in slow low up to fast-high flight regimes. Another important adv antage of OOM is that v arious types of runtime models may be automatically generated from a single implementation. From a control point of v iew, this allows for automatic generation of models for nonlinear simulation analysis, inv erse models for trimming and inv ersion-based synthesis techniques, linear symbolic models for robustness analysis, etc. In this chapter the main principles of OOM , the new aircraft model structure, and an example aircraft model implementation will be described.. C o n tributio n s • A new, physically-oriented generic structure for air v ehicles and env ironment models, v alid for: – rigid as well as flexible airframe structures ... – ... of v ehicles in slow or fast flight, at low or high altitudes, or anywhere in between. • The presented modelling methodology is the basis for contributions in subsequent chapters.. P ublicatio n G ertjan Looye, Simon H eck er, Thiemo K ier, Christian Reschk e, J ohann Bals: Multi-disciplinary aircraft model development using object-oriented modelling techniques, International Forum on Aeroelasticity and Structural Dynamics (IFASD), M unich, G ermany, J une 2 0 0 5 ..

(37) 2.1 Current practice in multi-disciplinary modelling. 21. IMULATION plays an important role in aircraft design and certification. Well known is the role of simulation in the development of flight control laws and in the analysis of flight loads. Also in specification, testing and integration of on-board systems, simulation is more and more used to reduce development time and hardware cost. In the continuous drive to improve efficiency, the aircraft design is more and more pushed to its physical limits. An obvious result is that interactions between engineering disciplines become stronger and stronger. A classical example is increasing airframe flexibility as a result of light weight design, interfering with aircraft flight dynamics, and affecting passenger comfort. For this reason, there is a growing need to address these interactions in simulation (or other model-based) analyses. This in turn requires the involved engineering aspects to be present in the underlying models, requiring the availability of multi-disciplinary aircraft dynamics models. A major problem hereby is that engineering departments responsible for the various aspects of aircraft design develop models for their specific types of analysis, based on modelling methods and tools that are common place in the specific engineering area. Consequently, bringing model implementations and data together into a multi-disciplinary simulation model is a very challenging task. In the following section various approaches to achieve this will be reviewed and compared.. S. 2.1. Current practice in multi-disciplinary modelling. In order to put current practice in model integration of physical systems in general, and aircraft dynamics in particular, in perspective, it is helpful to have a look at steps a model typically goes through from conception to simulation1 . These steps are depicted in Figure 2.1. The first step is to clearly define what is to be modelled. This involves the system, its behaviour of interest, and the role of and the bounds with respect to its environment. Of course, this is mostly determined by the intended application of the model. For example, for flight loads analysis the dynamic distribution of air loads over the aircraft is of prime interest, whereas the influence of the environment is limited to gravity and the (ideal) atmosphere. For piloted flight simulation, only the total aerodynamic forces and moments acting on the airframe are of interest, whereas the detailed modelling of for example the terrain and Earth’s rotation and curvature are relevant. This first step in the modelling process will be referred to as specification level. The second step, which takes place at level referred to a as system level, is the break down of the system into components and the specification of their interconnections. This in most cases is obvious. An important decision to be made is which data sources will be used. For example, the aerodynamic model may be obtained from an aerodynamics department, computed in-house using some 1 As will be discussed later on, the steps also apply to model applications other than simulation..

(38) 22. Multi-disciplinary aircraft model development .. 1 Sp ec ific a tio n level. 2 System level. Physical system and mod elling scope. Physical component b reak -d ow n. 3 Physical component / connecP h ysic a l level. tion eq u ations, alg orithms. 4 M a th ema tic a l level. .. O rd inary D ifferential / D ifferential A lg eb raic E q n.’s. 5 S imu lation mod el. R u n time level. .. Figure 2.1: Levels in development of a physical system CFD method, or obtained from model identification during a planned flight test campaign. The third step is to actually formulate the equations and algorithms that underlie the model components and to make sure the required data is available. The equations are based on laws of physics, application rules that come with data sources (e.g. aerodynamics), international model standards (e.g. International Standard Atmosphere), algorithms as implemented in a system’s control unit, etc. Interconnections between model components may for example be constraints, energy flows, or signal flows. The third step in the modelling process will be referred to as physical level. The fourth step is to collect all equations and to derive mathematical standard forms, like ordinary differential (ODEs) or differential algebraic equations (DAEs), suitable for time simulation of the model. For this reason, the level this step is performed at will be referred to as mathematical level. For derivation of ODEs or DAEs it is necessary to specify which variables are to be considered as inputs2 , as outputs, or as states. This means that from this moment on, the causality of the model is fixed. Finally, the model is connected with a simulation algorithm, allowing the actual model simulation to be performed. This algorithm strongly depends on the nature of the model. For example, whether the model has been brought into the form of ordinary differential or differential algebraic equations (ODEs or DAEs), the extent of stiffness of these equations, whether the simulation model contains 2 If any, since systems do not necessarily have inputs. However, physical systems considered in this thesis (aircraft) in general do..

(39) 2.1 Current practice in multi-disciplinary modelling. 23. continuous states, discrete states or both, or whether state events should be handled or not. T he im p lem entation m ay involve inline (local) integ ration of m odel states, a state vector m ay be p assed to an ex ternal integ ration alg orithm , or various com p onents m ay be integ rated seq uentially using diff erent alg orithm s in a seq uence of m ini sim ulation runs. T his fi fth step in the m odelling p rocess is at the so-called simulation level.. 2.1.1. Model implementation. F rom F ig ure 2 .1 an interesting observation can be m ade. A ctual im p lem entation of m odel com p onents, storing into and retrieving from reusable libraries, and integ ration into a full m odel usually tak es p lace at a m athem atical level (step 4 ). A fter sorting and solving the m odel eq uations and alg orithm s based on the unk nown variables, a function or collection of functions is coded. F or a continuous sy stem such a function ty p ically im p lem ents: x˙ y. = =. f (x, u, p) h(x, u, p). (2 .1 ). where x ∈ IR nx is a vector containing m odel states with dim ension nx , the vector u ∈ IR nu contains m odel inp uts, y ∈ IR ny contains m odel outp uts, and p ∈ IR np contains constant p aram eters that m ay be set by the user p rior to sim ulation. In the p ast, coding of this function was p erform ed using a p rog ram m ing lang uag e lik e C or F O R T R A N . N owaday s, block diag ram s have becom e very p op ular, allowing subsy stem s in the above form to be g rap hically interconnected via their inp uts and outp uts. S ince the variables in u and y have been ex p licitly identifi ed as inp uts and outp uts resp ectively , m odel im p lem entation at this level is also referred to as “ causal” m odelling . In a num ber of eng ineering dom ains im p lem entation at the p hy sical level (step 3 ) has becom e com m on p ractice. F or ex am p le, for construction of m ulti-body sy stem m odels software is available that off ers com p onent libraries (bodies, joints, hing es, ex ternal forces, etc.) from which a m odel m ay be constructed g rap hically . T he sam e holds for electronic circuits, for which a rang e of p rog ram s and com p onent libraries is readily available. T he diff erential (alg ebraic) eq uations are g enerated autom atically , ex p loiting the discip line-sp ecifi c m odel structures. A well k nown m odelling p aradig m that has found ap p lication in various eng ineering discip lines are bond g rap hs, based on energ y and energ y ex chang e between com p onents [1 6 ]. In 1 9 9 1 W illem s laid the foundation for what has becom e k nown as the B ehavioural A p p roach to the descrip tion of dy nam ical sy stem s [1 0 2 ], strong ly advocating m odel descrip tion at the p hy sical level and p roviding a m athem atical fram ework for describing sy stem behaviour and (control-relevant) sy stem p rop erties. In the B ehavioural A p p roach p hy sical com p onent break -down is referred to as “ tearing ” and describing the com p onent behaviour as “ z oom ing ” [1 3 9 ]. Im p lem entation at the p hy sical level has a num ber of advantag es over doing this at a m athem atical level:.

(40) 24. -. R 1= 10. R 2 = 10 0. C = 0 .0 1. L = 0 .1. R 2. 1/L +. 1 S. + +. A C =220. +. Multi-disciplinary aircraft model development. +. 1/R 1. 1/C. 1 S. -. G. Figure 2.2: Block diagram implementation (right) of an electronic circuit (left). From [8 8 ].. 1. In level 3, causality of the model is not fixed yet, whereas at level 4 causality is inherent to the implemented differential equations. As a result, from an implementation at level three, different runtime models with different sets of (reversed) inputs and outputs may be generated from one and the same model. 2. D ifferential equations for simulation are just one form of executable model code. Other forms are static equations, symbolic linear state space models, L inear Fractional Transformations (L FTs), etc. From level 3, the form of the runtime model is still open. 3. In level 3 model component interconnections may be specified via physical equations. From step 4 onwards, model components can only be interconnected via their inputs u and outputs y. This makes adding new components more complicated and easily results in a non-physical model structure. The latter becomes even worse, since within the components all unknowns have to be brought to the left-hand side, obscuring the original physical equations. This can be illustrated via a (by now) classical example in Figure 2.2. To the left a simple electronic circuit is shown. To the right the same model is depicted as a block diagram. It will be clear that, when only provided with the block diagram, quite some reverse engineering effort is required to find the underlying physical equations and to picture the original circuit structure. In practice, the above restrictions do not pose severe problems, since within most engineering areas application-specific work-arounds and program libraries have been developed that considerably reduce the coding effort. For example, for the block diagram-based modelling tool Simulink [8 1] libraries for various engineering domains are readily available..

(41) 2.1 Current practice in multi-disciplinary modelling. 2.1.2. 25. Model integration. Multi-disciplinary modelling involves the integration of model components and data from various engineering disciplines into a single model. In Figure 2.3 it is shown that this may be done at the three candidate levels of implementation. The first problem that nearly always arises is that different engineering disciplines use different modelling methods and simulation tools. Looking at Figure 2.3, a pragmatic approach would be to couple models at the very lowest level, namely by means of distributed or co-simulation. This avoids the need of translating or importing any model from the one simulation tool into the other, and allows for geographically distributed simulation. Standards for hierarchical organisation and interfaces for data exchange are available, like for example the H igh-Level Architecture (H LA) [26]. The latter is for example used by the U S Department of Defence (DoD) to perform battle field simulations with multiple players. The modelling scope of this chapter however is initially limited to a single aircraft. In this respect, co-simulation (also referred to as “loosely coupled” simulation) is for example used in coupling multi-body packages with engineering-specific environments, like FE M software, CFD solvers, etc. [62]. Aircraft models used for fl ight control and loads analysis must be fast in order to allow ten thousands of simulations to be performed in a reasonable amount of time (so-called “loop-capability”). An important disadvantage of co-simulation is that it involves multiple simulations-processes only communicating via computed trajectories. This does not allow for optimisation of the integrated model and causes problems as soon as algebraic loops between model components arise. Several control analysis methods require the model to be available in a specific form, like a Linear Fractional Transformation (LFT). Being at the lowest modelling level, co-simulation provides the runtime model in one form only. Finally, as soon as more than two or three disciplines are involved, mastering the model and simulation becomes a complicated task for a single engineer and may become costly because of software licenses of involved programs. Therefore, a more usual approach is to integrate models at level 4. This requires a common implementation platform, if only at the point of linking compiled model component software. This approach is greatly facilitated by the fact that many modelling platforms nowadays allow for model export in the form of runtime simulation code. A main program may then be written that sequentially calls the involved model component codes and provides data exchange in between. Another possibility is to import an external model code into the (designated) main model by means of a function call. Disadvantages of this approach is that the model code from the one engineering department remains a black box to engineers in the other. In some cases, model platforms used by different disciplines are identical. For example, the block diagram modelling tool Simulink provides dedicated libraries for various engineering areas and finds ever wider acceptance. For fl ight dynamics modelling for example, several libraries are readily available [104, 126, 29]. Integration of model components based on a common implementation platform is.

(42) 26. Multi-disciplinary aircraft model development Disc ip line A 1. Sp ec ific a tio n level. 2. System level. 4. O rd inary D ifferential / D ifferential A lg eb raic E q n.’s. 5. R u n time level. 2. Physical component b reak -d ow n. Physical component / connection eq u ations, alg orithms. M a th ema tic a l level. 1. Physical system and mod elling scope. 3. P h ysic a l level. Disc ip line B. S imu lation mod el. P h y sic al interc onnec tion. I/O interc onnec tion. T rajec tory interc onnec tion. Physical system and mod elling scope. Physical component b reak -d ow n. 3 Physical component / connection eq u ations, alg orithms. 4. O rd inary D ifferential / D ifferential A lg eb raic E q n.’s. 5 S imu lation mod el. Distributed / Co-simulation H /W in th e loop simulation. Figure 2.3: Various levels of interconnection between physical system models relatively easy. Unfortunately, Figure 2.2 clearly shows that this still does not solve the “black box” problem. Another important problem remains. Model components may only communicate via data flows and model components must be executed in a given sequence. This causes problems as soon as components algebraically depend on each others data. Such algebraic loops require expensive iterative solving or very short simulation time steps in case loops are broken artificially. Apparently, level 4 is not necessarily a suitable level to (1) implement models and (2) to integrate models. The problems sketched above disappear when taking the model implementation one level up, namely to level 3. Since at this level interconnection equations are still physical, connection of model components can be performed in the form of physical equations as well. Of course, this implementation approach has an important prerequisite. It must be possible to combine models from various disciplines and based on various modelling paradigms into a single implementation. As it is diffi cult and unnatural to, for example, implement a block diagram in a multi-body package. This problem was recognised by Elmqvist, who in 197 8 proposed a dedicated modelling language, called Dymola (Dynamic Modelling Language) [30]. The basic philosophy behind this language is: 1. implementation takes place at the level 3: physical objects and phenomena and their interactions may be implemented as model objects and model interactions respectively in a one-to-one fashion; 2. the language serves as a common base for development of discipline-specific component libraries. The result of the second point is that model components may be composed from discipline-specific libraries. The common language base allows these components.