Methods for Conceptual Flight Control System Design

Christopher S. Beaverstock∗ , Alireza Maheri † , Thomas S. Richardson ‡ ,

Mark H. Lowenberg § and Askin T. Isikveren ¶

Department of Aerospace Engineering University of Bristol,

Queens Building, University Walk, Bristol, BS8 1TR, UK

The traditional approach in aircraft conceptual design sizing for stability and controlemploys the so called “Tail Volume” method, which basically establishes static stability ofthe design via empirical handbook methods. The methodology dispenses with any formaldefinition of the Flight Control System architecture and topology, and, does not affordvisibility of critical sizing scenarios to the designer. This situation creates a measure ofuncertainty when attempts are made to model the flight physics problem, thus thwartingopportunities in performing an advanced assessment of flight handling qualities. This paperreviews the work-in-progress status of an innovative software package aimed at the con-ceptual design phase called Flight Control System Designer Toolkit (FCSDT) that permitsFlight Control Systems architecture definition for primary and failure modes, facilitatesgeneration of control laws, assists the designer in apportioning control allocation sched-ules, and finally, analyse the stability and control of aircraft models. Results regardingflight control system architecture design are based on a control surface layout obtainedfrom the Boeing 747 technical manual. Stability and control assessments were based onaerodynamic data generated by the aerodynamic model builder interface to Digital DAT-COM provided by the European funded Framework 6 Program based on the Boeing 747geometry.

Nomenclature

Acronyms:

CG Centre of GravityDoF Degree of FreedomEASA and European Aviation Safety AgencyESDU Engineering Science Data UnitsEU European UnionFAA Federal Aviation AuthorityFBW Fly-By-WireFCS Flight Control SystemFCSD Flight Control System DesignFCSDT Flight Control System Designer ToolkitFCSA Flight Control System ArchitectureFDD Fault Dependence DiagramFP6 Framework 6 ProgrammeICAO International Civil Aviation OrganizationLTIS+ Linear Time Invariant System Control SoftwareMCBF Mean Cycles Between Failure

∗Postgraduate Student†Research Associate‡Lecturer of Aerospace Engineering§Senior Lecturer of Aerospace Engineering & Head of Department¶Senior Lecturer of Aerospace Engineering & Director of Engineering Design

1 of 19

American Institute of Aeronautics and Astronautics

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-1620

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

MDO Multi-disciplinary Design OptimisationMoD Ministry of DefenceMTBF Mean Time Between FailureSCAA Stability & Control Analyser AssessorSimSAC Simulating aircraft Stability And ControlSMJ Small-Medium range regional Jet

Symbols:

c̄ Wing Mean Aerodynamic ChordCZα Non-dimensional Transverse Force Derivative due to Angle of IncidenceCZ ¯̇α Non-dimensional Transverse Force Derivative due to Angle of Incidence Temporal DerivativeCZq̄ Non-dimensional Transverse Force Derivative due to Pitch RateCMα Non-dimensional Pitch Moment Derivative due to Angle of IncidenceCM ¯̇α Non-dimensional Pitch Moment Derivative due to Angle of Incidence Temporal DerivativeCMq̄ Non-dimensional Pitch Moment Derivative due to Pitch RateIxx Rolling Moment of InertiaIyy Pitching Moment of InertiaIzz Yawing Moment of Inertiam MassQ Dynamic Pressure (= 1

2ρV2)

S Reference AreaU0 Cruise speedωsp Short period frequency (rads/s)ζsp Short period damping ratio

I. Introduction

The design of aircraft is an extremely inter-disciplinary activity produced by simultaneous considerationof complex, tightly coupled systems and functions. The design task is to achieve an optimal integration of allcomponents into an efficient, robust and reliable aircraft with high performance that can be manufacturedwith low technical and financial risks at an affordable cost over the whole lifetime of the aircraft.

Aircraft design is a part of a multiphase lifecycle process, which can be summarised by the followinglifecycle model presented by Moir & Seabridge1 :

• Conceptual Phase

• Definition Phase

• Design Phase

• Build Phase

• Test Phase

• Operational Phase

• Refurbish or Disposal Phase

The model closely resembles the Downey Cycle used by the UK Ministry Of Defence (MoD), althoughmany other models exist in both research institutes and industry. The conceptual design phase is responsiblefor understanding the emerging needs of the customer1 , as well as developing a technical solution to therequirements specification. The success of a project can largely be attributed by the quality of work conductedat the conceptual design phase, which should consume up to 10% of the resource budget, and up to 80%of the project total budget relies on the work conducted at this stage in the design process2 . During thisphase, preliminary studies are performed to establish a ‘paper’ design aircraft that meets both regulatoryconstraints and the required technical specifications.

2 of 19

American Institute of Aeronautics and Astronautics

Currently, designs are developed using semi-empirical or empirical ‘handbook’ methods, which are typ-ically parametric relationships or a series of multi-layered data-sheets. Databases used to generate these‘handbook’ methods are typically based on the conventional tail-plane aft type aircraft. This limits theconceptual designer to evolving tail-plane aft configuration aircraft, because of the restricted applicabilityof the methods available. Concurrently, no regulation or certification framework exists for atypical designconcepts, which can account for part of the reason why no resource is invested into developing novel concepts.

According to Chudoba3 , for the current design environment, it is becoming ever more difficult to certifyaircraft, with an ever increasing emphasis on environmental factors presents a huge challenge for aircraftdesigners. Chudoba comments that a large level of resource investment and time is required to evolve thealready well established tail aft aircraft, for insignificant gains in performance. This implies that it maybe necessary to investigated novel concepts for there enhanced level of performance and the potential tofurther develop the concept for future generations in a new evolutionary cycle. Before this can be a realisticsolution, a framework suitable to develop such designs is required. This would begin with a major assessmentof current design philosophies and methodology.

The contemporary philosophy is to begin investing significant effort on Flight Control System (FCS)design towards the end of the conceptual design phase, or early in the preliminary design phase when theconfiguration has been tentatively frozen. This circumstance arises due to a reliance on empirical/ handbookdata, or, if available, experimental data for predicted aerodynamic characteristics. Mistakes at this point inthe design process must be avoided, however, they are invariably made. All aircraft integrators have beensubjected to examples of pre-flight-test aerodynamic prediction errors and unidentified problems related tostability and control, which lead to an unacceptable increase in programme cost and extensive developmentaldelay, or, even catastrophic failure. Examples of actual cases include:

• 50 Passenger Regional: Wheel force characteristics caused delay in certification leading to a costlyredesign of the control system

• Narrow Body: Unexpected sensitivity to wing rigging resulted in unacceptable number of aircraft notpassing acceptance flights

• Long-Range Wide Body:

– Stalls more rapidly than expected with raked tips, vortilon pattern had to be developed

– Handling and flight control characteristics do not give appropriate cues to flight crew in avoidinglimit loads, e.g. loss of Flight AA587

• Ultra Long Haul Wide Body:

– Under-predicted horizontal tail effectiveness led to larger than needed horizontal tail

– Sudden loss of lateral control during test-flight stimulated engine failure in takeoff initial climb,resulting in the loss of aircraft and crew

Regulatory constraints are key factors in certifying an aircraft; and along with the aircraft technicalspecification provide the designer with a framework to develop a concept. These constraints are typicallyrelate to performance, noise, emissions, and safety factors, the final point of which is related to systems designand architecture, and the stability and control characteristics of the aircraft. Because of the ‘handbook’methods used at the conceptual design phase, confidence in the development of a flight mechanics model ofwhich a prototype flight control system can be designed is low. Due to the limited consideration of the FCSdesign, leads to a sub-optimal solution with respect to performance as the aircraft system is not modeled inits entirety.

This paper demonstrates the advantages of introducing advanced methods into the conceptual designphase. A sophisticated flight mechanics model is developed using data generated by more advanced tech-niques, not typically applied at the conceptual design phase. A holistic approach to the FCS design ispresented for the Boeing 747 aircraft, which is a medium-long haul civil transport airliner. Detailed stabilityand control analysis an aircraft model using the digital DATCOM interface produced by an aerodynamicmodel builder developed in the Framework 6 programme SimSAC (Simulation aircraft Stability And Con-trol).

3 of 19

American Institute of Aeronautics and Astronautics

II. Flight Control System Designer Toolkit

Recognising that higher fidelity methods and introducing FCS design from a conceptual design phase isdemonstrated by the European Union (EU) funding a Framework 6 programme (FP6), Simulating aircraftStability And Control (SimSAC). The vision of the programme is to introduce multi-disciplinary designoptimisation (MDO) into the conceptual design phase. It is envisaged that the effect of this will reduce thelife-cycle time and cost, in addition to an increase in knowledge, performance and safety of the design, all ofwhich is outlined in the programmes Technical Annex4 .

Figure 1 summarises the overall goal of EU FP6 SimSAC which is a (software) framework from whichcontrollability and manoeuvrability requirements can be analysed and assessed from the conceptual designphase. This relies on utilising more advanced techniques to model the aerodynamics, structural and weightand balance subspaces to construct a flight mechanics model, from which stability, control and manoeuvra-bility can be assessed with a reasonable level of confidence. Due to the higher fidelity methods employed,results in improved quality of data, and therefore information and knowledge of a design concept, owing tothe more accurate modelling of the flight physics.

Figure 1. Considerations when considering controllability and manoeuvrability

The methodology involves utilising tools within the software framework to generate the flight mechanicsmodel for analysis and assessment. A mixed or interlaced fidelity approach is employed, where both low andhigh fidelity methods are used to generate the model, depending on there respective regions of applicability.

The flight control systems (FCS) architecture and design primary intent depends on flight handlingquality criteria coupled to a given cost function. To fully integrate FCS considerations onto a conceptualaircraft design, which would facilitate designing a variety of FCS types including manual, boosted and fly-by-wire (FBW) systems, a software framework is required. This would require the development of appropriatedesign, analysis and assessment tools, allowing the designer to evaluate the physical FCS architecture, designa suitable prototype controller, perform open and closed loop analysis of the aircraft system, analyse criticalfailure scenarios and assessment of the aircraft stability and control characteristics. Figure 2 provides adetailed vision to develop a comprehensive Flight Control System Designer Toolkit (FCSDT), encapsulatingthe required elements in the FCSDT framework.

III. Flight Control System Analysis and Assessment

The safety of an aircraft largely depends on the reliability of the flight control system in the eventof failure, the inherent stability and control characteristics and the aircraft structure. The main concernregarding the aircraft structure is primarily associated with the fatigue life of the aircraft, which depending

4 of 19

American Institute of Aeronautics and Astronautics

Figure 2. Flight Control System Designer Toolkit comprehensive overview

on the structural design philosophy, determines the method in which to certify the aircraft. Structuralcontributions to safety are not the focal point of this paper and so will not be discussed any further.

A. Flight Control System Design

The flight control system includes all elements which are used to control the aircraft dynamics. Controlsurfaces and engines are two examples of effectors which are used to control the aircraft’ in-flight dynamics.Typically the reliability of the flight control system is analysed by a fault dependence diagram (FDD), whichassesses the probability of a failure condition to given fault, identifying the critical failure modes. FDD aregenerated by using the FCS architecture to generate a fault tree diagram, from which probability of failurecan be computed and critical faults identified. For more information on generation of fault tree analysis datasee Moir and Seabridge1 .

Assessment of these failure cases are not only for regulatory and certification purposes but also formaintenance scheduling, computing parameters such as the mean time between failure (MTBF) or meancycles between failure (MCBF). These are examples of system reliability assessment parameters5 . Toachieve certification there is a minimum requirement value for various types of failure which are summarisedin Table 1.

Failure Condition Classification Probability of Failure Failure Description

Catastrophic P ≤ 10−9 Extremely Improbable

Hazardous/Severe 10−9 ≤ P ≤ 10−7 Extremely Remote

Major 10−7 ≤ P ≤ 10−5 Remote

Minor 10−5 ≤ P ≤ 10−3 Reasonably Probable

No Safety Effect P ≥ 10−3 Frequent

Table 1. Failure Condition Failure Descriptions

A software tool has been developed at Bristol University to perform flight control system architecturedesign, along with the associated fault tree analysis. The software interface allows the user to load a pre-existing FCS topology from another project, edited accordingly to the current aircraft project, or to begina clean sheet flight control architecture.

Figure 3(a) presents the interface from which the user can edit the FCS architecture, which includesadding or removing control elements and editing components systems architecture to a control element.Once a systems architecture is developed and component links established, a failure mode analysis can be

5 of 19

American Institute of Aeronautics and Astronautics

performed to investigate the failure of various control element combinations. This can indicate the failurerate of a variety flight setups for the control system, for example take-off cruise and landing configurations,which may employ the use of a different combinations of control effectors. The event failure rate for a givenfailure condition can be compared with the appropriate failure condition probability, as is stated in table 1.

The example presented in figure 3(a) is a generic small-medium range regional jet (SMJ) aircraft, witha conventional arrangement of control effectors including spoilerons, ailerons, elevators and rudders. Thesystems architecture is based on a fly-by-wire (FBW) system with mechanical backup. This generic structurealong with the SMJ example provides the tool with sufficient enough capability to analyse most conventionaldesign concepts, other concepts can be programmed in a similar manner to generate a flight control systemarchitecture.

Figure 3(b) provides the interface to allocate the systems architecture for a given component. Thisinvolves connecting the various system components required to actuate a control effector, i.e. flight controlcolumn, computers and sensors to power sources and actuator components. This is performed by the useof a Boolean expression as is highlighted in figure 3(b), using either a predefined architecture or a manualinput to generate the expression.

(a) FCSA architecture definition interface (b) FCSA Boolean expression editor

Figure 3. Flight Control System Architecture (FCSA) software screenshots

Additionally, a presentation of the FDD is given in figure 4, where each logic gate can be investigate forits associated failure rate displayed in a text box above the logic gate. This presents the failure rate for thecomponents leading up to that particular logic gate, along with the boolean expression used to obtain it.This functionality can be used by a the flight control system designer to investigate the local failure rates,so that alterations can be made to the system to decrease the failure rate or to decrease cost by reducingfor example redundancy, typically leading to increased failure rate. A number of default component failurerate values are used, which can be altered to more appropriate values were available.

Figure 4. Fault Dependence Diagram Generated by FCSA

6 of 19

American Institute of Aeronautics and Astronautics

B. Stability & Control

Stability and control characteristics are generated by analysing and assessing both the open and closed loopproperties of an aircraft. Open loop assessment includes analysing linearised data of the aircraft over criticallocations in the flight envelope. For the aircraft to be certified, it must satisfy the requirements of the codewhich the aircraft has been designed. Regulatory bodies such as the Federal Aviation Authority (FAA) andEuropean Aviation Safety Agency (EASA) use MIL-SPEC6 , Engineering Science Data Units7 (ESDU) andInternational Civil Aviation Organization8 (ICAO) handling quality assessment criteria as a guide to formthe FAR and CS regulations respectively. A more comprehensive overview is provided by Chudoba.

Before an aircraft is certified, the design must be rigorously tested against airworthiness requirementsfor flight operations defined by the relevant regulatory body or code. According to Stinton9 , airworthinessrequirements can be summarised into the following categories:

• Flight crew workload

• Flight handling characteristics

• Performance within the flight envelope

• Safety Margins

• Welfare of occupant

• Dispatch Reliability

• Economics

Stability and control assessment is mainly concerned with flight handling qualities and safety margins,performance requirements are more closely associated with the aerodynamic and propulsion subspaces, andcrew workloads with the flight control system and aerodynamic loads, some of which for civil aircraft aresummarised in Table 2. Methods for assessment include figure of merit (FoM) charts, which assess standardmodal characteristics including the short period, phugoid, dutch roll, roll subsidence and spiral modes.

Scenario CG Location Requirement

Trim at take-off FWD minimum manoeuvrability

Trim at landing FWD manoeuvrability

VS1g demonstration FWD alpha max

Minimum rotation rate FWD pitch acceleration

Push-over FWD minimum man. full stick forward - no control loss

Steady turn at take-off FWD φ > 30◦

Steady turn at landing FWD φ > 40◦

Trim at take-off AFT minimum manoeuvrability

Trim at landing AFT manoeuvrability

CEV Manoeuvre AFT balance the pitch moment of the engines

Stability AFT margin w.r.t. manoeuvre point

Dutch Roll LATERAL damping

VMC LATERAL not greater than specified speed (sideslip constrained)

Steady sideslip LATERAL demonstrate specified minimum cross wind speed

Roll man. take-off LATERAL +30◦ to −30◦ in less than 11 s, OEI

Roll man. landing LATERAL +5◦ to +25◦ in less than 7 s, VMCL

Table 2. Generic rules for commertial transports - used for SMJ Technical Specification Summary

The short period is typically characterised by a well damped, high frequency oscillations of angle of attackand pitch rate. An example of a figure of merit is the ESDU 9200610 chart, to asses the short period damping

7 of 19

American Institute of Aeronautics and Astronautics

and frequency. Other standards of assessment exist for various aircraft specifications, such as the phugoidICAO8 assessment criteria or MIL-F-8785C11 for the dutch roll. These provide a framework from whichaircraft design and flight handling quality assessments can take place. However, the applicability of theseassessment codes are only suitable for current designs, or configurations which display similar characteristics.Therefore a new assessment criteria is required, established by developing a knowledge database about thestability characteristics on a spectrum of design configurations. Chudoba reiterates two definitions that aremandates for all aircraft, which in essence state that the appropriate authority should declare if an aircraftdesign is ‘fit to fly’.

Closed loop control typically augments dynamic derivatives in order to achieve the desired flying/ handlingqualities, to meet the fundamental stability and control requirement of ‘fit to fly’. A number of methods existto compute a suitable controller such as eigen structure assignment or H-Infinity (H∞) synthesis. Classically,these methods compute suitable gains for a linear controller composed of proportional, differential andintegral components using the pre-defined control laws, derived from the control philosophy as is illustratedin figure 5. The final component to complete the flight controller is the control allocation, which allocatesthe required control effector perturbations to meet a desired reference signal.

Figure 5. Control law philosophy

Bristol has developed an interface tool, Stability and Control Analyser Assessor (SCAA), which allowsrapid generation of trim and linear analysis data of an aircraft model across the flight envelope. These resultscan be analysed and assessed using classical analysis techniques or pre-existing figures of merit to assess theaircraft stability characteristics. Figure 6(a) is an example of an ESDU 92006 short period FoM, figure 6(b)is an example of the ICAO phugoid assessment criteria and figure 6(b) the MIL-SPEC dutch roll assessmentcriteria.

10−1

100

1

2

3

4

5

6

Poor

PoorUnacceptable

Acceptable

Satisfactory

ESDU Short Period Opinion Contours, ESDU 92006

Damping Ratio (−)

Und

ampe

d N

atur

al F

requ

ency

(ra

d/s)

Excessiveovershootdifficult tomanoeuvre

Response toosluggish

Excessive compensationrequired − difficult to trim

Too rapid an initial response −over sensitive tendency to PIO

(a) ESDU 92006 Short Period Figure ofMerit

−0.04 −0.02 0 0.02 0.04 0.06 0.080

20

40

60

80

100

120

UN

AC

CE

PT

AB

LE

ACCEPTABLEfor emergencyconditions

SATISFACTORY fornormal operation

ICAO Recommended Phugoid Characteristics

2 x zeta x omega (rad/s)

Phu

goid

Per

iod

(s)

(b) ICAO Phugoid Figure of Merit

0 0.5 1 1.5 2 2.5 3

−0.1

−0.05

0

0.05

0.1

0.15

Min

. Fre

quen

cy

Min. Damping

T/O, Appr and Landzeta x omega = 0.10

Clb, Crz and Deszeta x omega = 0.15

Minimum Dutch Roll MIL−F−8785C Level 1 − Cat. B and C

Undamped Natural Frequency (rad/s)

Dam

ping

Rat

io (

−)

(c) MIL-F-8785C Dutch Roll Figure ofMerit

Figure 6. Stability and Control Analiser Assessor (SCAA) Figure of Merit Screenshot

8 of 19

American Institute of Aeronautics and Astronautics

IV. Conceptual FCS Design Methodology

Traditionally, FCS design considerations are only concerned with flight control system architecture andbasic stability and control assessments using techniques such as volume coefficient, with little considerationof developing a prototype controller. The prototype controller requires computation of the control laws andallocation i.e. the governing software algorythms that control the aircraft response characteristics, which isnot typically considered from the conceptual design phase.

Figure 7 summarises the classical conceptual design approach. To provide an overview of the process,the initial stage involves concept inception, combining the emerging customer needs generated from marketresearch, in addition to the current design environment regulation and certification requirements. Therequirements specification captures these design constraints, providing a framework from which initial sizingcan be performed. The baseline design is progressively modified to meet the requirements specified, whilstoptimising performance parameters.

Figure 7. Summary of classic conceptual design approach

This paper aims to integrate FCS design into the aircraft conceptual phase. This includes a holisticapproach of not only the systems architecture, but also the control law formulation and allocation. Figure 8describes the integration of FCS into the conceptual design cycle; the modified cycle integrates control design,improving the aircraft flying qualities to acceptable levels over the flight envelope. During this process ifa feasible controller can not be synthesised, a designer decision is made to assess the design feasibility. Ifthe design is considered feasible, design modifications are performed, if the design is considered unfeasiblere-evaluation of the design concept is required.

This framework provides an environment to integrate FCS design into the optimisation of the geome-try. Flight Control System Designer Toolkit (FCSDT) is a EU FP6 SimSAC software development whichrepresents the software implementation required to demonstrate the advantages of integrated FCS design.The tool includes of the afore mentioned FCSA and SCAA software tools, also protocols that generate thecontroller gains and control allocation algorithms required to produce a flight controller are included.

V. Results

Results generated by the software interfaces FCSA and SCAA are presented, these are based on a Boeing747-100 aircraft model generated from the software framework developed by SimSAC. The model is a rigidbody representation of the Boeing 747 flight mechanics, combined with the relevant rigid body, flat earthequations of motion which includes the governing 6DoF rigid body equations. Euler angles are used todescribe the orientation, and Cartesian co-ordinates to describe the aircraft position of the aircraft.

The flat earth assumption is used due to the relatively short time span that the aircraft is to be analysed12 .Euler angles are used as the aircraft is not expected to be analysed or operate in conditions deemed necessaryto use the quaternion orientation representation.

9 of 19

American Institute of Aeronautics and Astronautics

Figure 8. Integrated FCS into conceptual design

A. Flight Control System Architecture

The Boeing 747 technical report15 contains the necessary information to estimate the control effector layout.However, lack of any information regarding the systems architecture to each effector prevents a comprehensiveinvestigation of the complete control systems architecture. As a demonstration, the control effector layoutshall be combined with the default generic SMJ control system architecture available within the software.Effectively, the additional components to augment the flight dynamics are 1 pair of additional spoilers, 2pairs of elevators and a split rudder. A demonstration of the algorithmic protocol developed to handle theflight control system architecture failure rate shall be presented.

The control effector layout can be seen in image presented in figure 9(a), which includes split rudder,ailerons, elevator, all moving tail, flaps, slats etc. Only control effectors associated to roll, pitch or yawcontrol shall be considered, thus slats and flaps will be omitted from the current investigation. Figure 9(b)shows the reduced control system architecture representation in the FCSA software interface.

(a) Reduced Flight Control System Architecture of Boeing747

(b) Software Representation of Boeing 747 Flight ControlSystem Architecture

Figure 9. Boeing 747 Flight Control System Architecture

10 of 19

American Institute of Aeronautics and Astronautics

Table 3 summarises the results obtained from the investigation using FCSA. The systems architecture isa modified version of the generic SMJ aircraft design. Component probabilities used are default values builtinto the software, which can be readily changed to values in where the component failure rate is available.

Failure Condition Probability of Failure Control Effectors

Pitch Option 1 4.0001 × 10−12 Inner and Outer Elevators

Pitch Option 2 1.2212 × 10−17 Inner and Outer Elevators, All Moving Tail

Roll Option 1 3.0000 × 10−08 Ailerons

Roll Option 2 3.0012 × 10−16 Ailerons, 4 Outer Spoilers

Yaw Option 1 1.0006 × 10−08 Upper or Lower Rudder

Yaw Option 2 1.0004 × 10−08 Upper and Lower Rudder

Table 3. Failure Rates Generated by FCSA

According to the results generated by this architecture and comparing with table 1, the pitch and rollcontrol options 2 are both fail catastrophic, however using only the primary control surfaces (options 1),reduces the redundancy leading to a significantly reduced failure rate with the roll control reduced to failsevere. The yaw control option 2 is only improves on option 1 by 2 × 10−12, suggesting that to improvethe failure rate the systems architecture of the upper or lower rudder is required to change. Both lower andupper rudders use the same computer architecture, altering this may significantly reduce the failure rate.

B. Stability & Control Assessments

Aircraft models generated by CEASIOM produce force and moment coefficient tables, based on the rigidbody equations of motion states. These are typically defined in the wind axes frame, which uses the statevector [α, MACH NO, β, P, Q, R] to generate the aerodynamic tables. Additional tables associated tocontrol surface deflections for example elevators, ailerons and rudders are also generated. Currently onlytrailing edge devices are modelled, as such does not encompass the entire flight control system available tothe aircraft, which may also includes flaps, spoilers and split ailerons for example.

These components are omitted as methods used to generate the data would not sufficiently model therelatively non-linear behavior of these components, for example, boundary layer separation is a phenomenonthat lower fidelity inviscid aerodynamic solvers such as vortex lattice are unable to predict. As a conse-quence only cruise flight conditions shall be considered for this investigation. However, issues regarding amethodology to size flight control effectors is highlighted, that to effectively design the flight control system,methods developed must attempt to encompass sizing of control elements which are normally excluded dueto the difficulties in modelling.

The model structure as seen in figure 10 represents the upper most level of the model hierarchy of theSimulink representation of the aircraft model. Each model is integral to a more complete investigation ofthe aircraft flight dynamics over the flight envelope for a fully augmented, closed loop aircraft model. Themodel can be reduced to an open loop model by considering the Aircraft Model, Equations of Motion andActuator Model. The open loop model can be used to assess the unaugmented dynamics, and apply theappropriate control gains to correct the dynamics, according to a predefined control design philosophy.

Figure 10. Upper Level Aircraft Model Structure

The model includes a rigid body aircraft model and simple thrust model. The rigid body aircraft modelinput is the previously stated state vector, along with a control vector of the aircraft control surface deflec-

11 of 19

American Institute of Aeronautics and Astronautics

tions. These are used to interpolate 2 and 3 dimensional tables, relating the states and control inputs to theforce and moment coefficients. The model is summarised by equation 1.

CΦ = CΦ0(α,Mach) + CΦβ(α,Mach, β) + CΦQ

(α,Mach,Q) + CΦP(α,Mach, P ) + CΦR

(α,Mach,R)

+CΦδelv(α,Mach, δelv) + CΦδrudd

(α,Mach, δrudd) + CΦδail(α,Mach, δail) − 7CΦ0(α,Mach) (1)

Φ = X,Y,Z, L,M,N (2)

To demonstrate the software interface, model inputs shall include perturbations over a CG, mass andinertia range. Results shall be compared with the cruise trim point of the Boeing 747-100 presented inEtkin.13 Table 4 summarises the modes about the cruise point of 40,000ft altitude and a Mach number of0.8.

Scenario Eigen Value Period (s) thalf(s) Nhalf(cycles)

Short Period -0.3719 ± 0.8875i 7.08 1.86 0.26

Phugoid -0.003289 ± 0.06723i 93.4 211 22.5

Dutch Roll -0.033011 ± 0.94655i 6.64 21 3.16

Roll Subsidence -0.56248 - 1.23 -

Spiral -0.072973 - 95 -

Table 4. Generic rules for commertial transports - used for SMJ Technical Specification Summary

By using the model generated by CEASIOM, and varying both the vertical and horizontal CG position,the behavior of the various poles can be observed in figure 11(a) and 11(b). Using the undamped naturalfrequency and short period damping, the ESDU 92006 plot can be generated yielding the results observedin figure 12(a). Comparing the results with equation 3 and 4, the relationship between frequency and CGposition is augmented through the pitch damping term CMq̄ and pitch stiffness term CMα(assuming CZq̄ isnegligible). The effect of CG is dependent on the relative effect between these two terms. As CG movesforward towards the nose of the aircraft, CMα decreases and CMq̄ increases. If the overall effect is to increasethe numerator of equation 3 then the frequency increases.

−0.4 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Real

Imag

DecreasingZ position

IncreasingStatic Margin

(a) Variation of longitudinal pole position due to CG per-turbations

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Real

Imag

(b) Variation of lateral pole position due to CG perturba-tions

Figure 11. Variations in aircraft modal pole positions due to CG perturbations

The case where CMq̄ is the dominant term, decreasing the static margin or de-stabalising the system bymoving the CG aft will increase this term and increase the undamped natural frequency. The damping isalso observed to increase due to the proportional relationship in equation 3 and 4.

12 of 19

American Institute of Aeronautics and Astronautics

10−1

100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Poor

Poor

Unacceptable

Acceptable

Satisfactory

Damping Ratio (−)

Und

ampe

d N

atur

al F

requ

ency

(ra

d/s)

Excessiveovershootdifficult tomanoeuvre

Response toosluggish

Excessive compensationrequired − difficult to trim

Too rapid an initial response −over sensitive tendency to PIO

(a) Variation in ESDU short period assessment due to vari-ations in CG position

−0.04 −0.02 0 0.02 0.04 0.06 0.080

20

40

60

80

100

120

UN

AC

CE

PT

AB

LE

ACCEPTABLEfor emergencyconditions

SATISFACTORY fornormal operation

2 x zeta x omega (rad/s)

Phu

goid

Per

iod

(s)

(b) Variation in ICAO phugoid assessment due to varia-tions in CG position

Figure 12. Aircraft assessment criteria variations with CG perturbations

ω2

sp =CZαCMq̄ − CMα((

2U2

0

QSc̄)m + CZq̄)

(Iyy

QSc̄)((

2U2

0

QSc̄)m + CZ ¯̇α)

(3)

2ζspωsp =QSc̄

Iyy

c̄

2U0

CMq̄((2U2

0

QSc̄)m − CZα) +

2U0Iyy

QSc̄2

2U0

c̄CZα + ((

2U2

0

QSc̄)m + CZq̄)CM ¯̇α

((2U2

0

QSc̄)m + CZ ¯̇α)

(4)

However, figure 12(b) indicates that the phugoid damping decreases with decreasing static margin, al-though the period (and frequency) remains relatively insensitive to variations in CG position. There is someamount of dependence as is indicated by equation 5, being primarily dependent on the Mα, Mq and Mu

derivatives which appear in both the numerator and denominator. Therefore the effect on the frequency isdependent on the relative weighting of each term.

The phugoid damping becomes remarkably more difficult to analyse due mainly to the lack of a simpleand reliable approximation to the phugoid characteristics. Lanchester’s equation16 is one of the earliest ap-proximations to the phugoid characteristics, which provides reasonable accuracy for predicting the frequency,but is very poor with respect to computing the damping. Pradeep & Kamesh17 present a more accuratemethod for predicting the phugoid damping, which is derived from the equations of motion, making fewassumptions to arrive at a 4th order longitudinal characteristic equation, substituting an appropriate shortperiod approximation, the phugoid can be approximated.

ωph =

√

g(MuZα − MαZu)

U1Mα − ZαMq

(5)

Comparing the modal results generated by the CEASIOM generated aerodynamic data, the short periodpositions suggests a CG aft configuration but a large difference in the damping is observed. The CGaft configuration is also supported when comparing the dutch roll pole positions with those presented intable 4. The results obtained for the roll subsidence, spiral and the phugoid are sensitive to both verticaland horizontal CG position and can be fixed to fit in the positions provided by Etkin. Reviewing theapproximate equations along with the aerodynamic data obtained from both Etkin and the model generatedby CEASIOM, large errors were observed with respect to control coefficients, leading to errors in the trimpoint obtained or no solution existing. The elevator control coefficient predicted by digital DATCOM isapproximately 5 times greater in the aerodynamic data presented in Etkin.

To obtain a solution at this trim point, artificially increasing the CMδelvderivative was required. Errors

were also observed in the zero angle of attack lift coefficient and lift-curve slope, the former compounding the

13 of 19

American Institute of Aeronautics and Astronautics

error in elevator angle, to predict an incorrect trim point. According to the equations presented equations 3and 4, this would not affect the prediction of the short period, as the results obtained for the derivativesinvolved in prediction of the short period are within the linear region and are unlikely to change with trimangle of attack, but will however be affected by the error in the lift coefficient, and relative error in CGposition, CMα and CMq̄ as a result of poor aerodynamic force prediction.

Although the error in trim point may not affect derivatives involved in the short period, all approximationsindicate that the phugoid is highly dependent on the calculated trim point. This is because derivatives suchas CXα are typically non-linear, due to the parabolic relationship between drag and angle of attack throughthe lift coefficient (CD = CD0 + kC2

L). Therefore deviations away from the trim point will certainly lead toerrors in phugoid prediction, as the linear derivative is only valid for a small perturbation in the trim pointparameters.

Figure 13- 17 investigates the effects of mass and inertia on the aircraft modes of motion. Mass is a scalerquantity, unlike the inertial properties which are vector quantities, and as such affects all modal properties.Variations in mass are shown in figure 13 to 14, which displays the effect in varying mass ±20% on theaircraft modes of motion. The short period damping is observed to decrease, or where as the frequencyappears to be relatively insensitive to variations in mass.

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Real

Imag

Roll Subsidence

Short Period

Dutch Roll

(a) Mass effects on short period, dutch roll and roll subsi-dence modes

−0.014 −0.012 −0.01 −0.008 −0.006 −0.004 −0.002 0−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Real

Imag

Phugoid

Spiral

(b) Mass effects on phugoid and spiral modes

Figure 13. Effect of mass on the aircraft modes of motion

Figure 13(b) and figure 14(b) indicates that a growth in mass increases the phugoid damping whilst thefrequency increases. The effect on the dutch roll characteristics however decreases the dutch roll damping,whilst increasing the frequency, which can be derived from figure 13(a) and figure 14(c). Unfortunatelydutch roll approximations rely on underlying assumptions for there accuracy, which in the approximationpresented by Etkin assumes that sideslip and yaw rate are the dominant modes where roll rate is assumednegligible. As can be observed by investigation of the associated Eigenvector, this is certainly not the caseacross the flight envelope. Closed form approximations may seem attractive for design purposes, but canbecome misleading if the assumptions are not treated carefully, implying that there use in design across theenvelope may be quite limited, thus supporting the notion of increased fidelity methods to optimise the FCSdesign according to flight dynamic requirements.

The inertial properties affect the mode which is most closely associated to the plane in which the modeacts as will be demonstrated. The results in figure 15 indicate that by increasing the pitching momentof inertia, both the frequency and damping decrease. The result of the decreasing frequency comply withthe analytical result obtained from equation 3. Equation 4 indicates that the variation of the short perioddamping is dependent on the proportion of the

2U0Iyy

QSc̄2

2U0

c̄CZα term. The results would indicate that the

contribution of this term on the numerator with variations in Iyy is minimal, and that the damping isdominated by the inverse relationship with the Iyy term, with little contribution from the short periodfrequency.

The phugoid frequency is insensitive to variations in Iyy, but decreases with aft migration of the CG,which is also suggested by the phugoid frequency approximation by Pradeep & Kamesh17 or equation 5.Unfortunately as highlighted previously the analytical solution leads to a complex interrelationship between

14 of 19

American Institute of Aeronautics and Astronautics

10−1

100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Poor

Poor

Unacceptable

Acceptable

Satisfactory

Damping Ratio (−)

Und

ampe

d N

atur

al F

requ

ency

(ra

d/s)

Excessiveovershootdifficult tomanoeuvre

Response toosluggish

Excessive compensationrequired − difficult to trim

Too rapid an initial response −over sensitive tendency to PIO

(a) Effect of mass on the ESDU short period assessmentcriteria

−0.04 −0.02 0 0.02 0.04 0.06 0.080

20

40

60

80

100

120

UN

AC

CE

PT

AB

LE

ACCEPTABLEfor emergencyconditions

SATISFACTORY fornormal operation

2 x zeta x omega (rad/s)

Phu

goid

Per

iod

(s)

(b) Effect of mass on the ICAO phugoid assessment criteria

0 0.5 1 1.5 2 2.5 3

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Min

. Fre

quen

cy

Min. Damping

T/O, Appr and Landzeta x omega = 0.10

Clb, Crz and Deszeta x omega = 0.15

Undamped Natural Frequency (rad/s)

Dam

ping

Rat

io (

−)

(c) Effect of mass on the MIL-F-8785C Dutch Roll assess-ment criteria

Figure 14. Effect of mass on the aircraft modes assessment criteria

15 of 19

American Institute of Aeronautics and Astronautics

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Real

Imag

Short Period

(a) Effect of Iyy on the aircraft pole positions

10−1

100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Poor

Poor

Unacceptable

Acceptable

Satisfactory

Damping Ratio (−)

Und

ampe

d N

atur

al F

requ

ency

(ra

d/s)

Excessiveovershootdifficult tomanoeuvre

Response toosluggish

Excessive compensationrequired − difficult to trim

Too rapid an initial response −over sensitive tendency to PIO

(b) Effect of Iyy on the ESDU assessment criteria

−2.21 −2.2 −2.19 −2.18 −2.17 −2.16 −2.15 −2.14 −2.13

x 10−3

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Real

Imag

Phugoid

(c) Effect of Iyy on the phugoid pole positions

Figure 15. Effect of Iyy on the aircraft modes of motion

16 of 19

American Institute of Aeronautics and Astronautics

the damping and Iyy, but the reader can refer to Pardeep & Kamesh for further information.Variations in the lateral mode frequency and damping properties are typically associated to changes in

Ixx and Izz, which is demonstrated by figures 16 and 17. The results regarding the dutch roll indicate thatfor this particular mode, the modal characteristics are more sensitive to variations in Ixx relative to Izz. Thissuggests that the mode may be predominantly a rolling motion, which is further supported by investigatingthe eigenvector magnitude, where the ratio is 5:1 when comparing roll and yaw rate normalised eigenvectorsrespectively. This is further supported by the results presented in Etkin, although the error of the roll rateseems to be far greater than the other normalised states relative to one another. This may suggest that themethod prediction has large deficiencies in the modelling of roll damping and stiffness terms. This wouldalso invalidate the assumption of negligible rolling motion in the dutch roll approximation.

−0.01 −0.005 0 0.005 0.01 0.015 0.02 0.025 0.03−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Real

Imag

Increasing Ixx

Increasing Izz

(a) Effect of Ixx and Izz on the aircraft Dutch Roll polepositions

0 0.5 1 1.5 2 2.5 3

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Min

. Fre

quen

cy

Min. Damping

T/O, Appr and Landzeta x omega = 0.10

Clb, Crz and Deszeta x omega = 0.15

Undamped Natural Frequency (rad/s)

Dam

ping

Rat

io (

−)

(b) Effect of Ixx and Izz on the aircraft MIL-F-8785CDutch Roll assessment

Figure 16. Effect of Ixx and Izz on the aircraft Dutch Roll mode

The assessment criteria presented in figure 16(a) is based on assessment criteria for landing configuration,and so is inappropriate to draw a conclusion for this particular flight condition. However the results demon-strate the effect of varying mass properties which can be altered in the materials used to produce the aircraft,or simply due to shifting fuel loads in the wing and tail. Figure 17 shows the effect of varying Ixx and Izz

on the remaining lateral modes of motion. The results suggest that the roll subsidence mode characteristicsare more sensitive to variations in Ixx, or the rolling moment of inertia. Also, the figure 17(a) implies thatincreasing both rolling and yawing moment of inertia increases the roll subsidence time constant.

The effect of rolling and yawing moment of inertia on spiral mode characteristics can be seen in fig-ure 17(b), which indicates the mode is more sensitive to variations in yawing moment of inertia. Again, theeffect of yawing moment of inertia is observed to increase the modes time constant, however increasing therolling moment of inertia decreases the modes time constant.

17 of 19

American Institute of Aeronautics and Astronautics

−0.56 −0.54 −0.52 −0.5 −0.48 −0.46 −0.44 −0.42−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Real

Imag

Increasing I

xx

Increasing Izz

(a) Effect of Ixx and Izz on the roll subsidence mode

−0.012 −0.0118 −0.0116 −0.0114 −0.0112 −0.011 −0.0108−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Real

Imag

Increasing I

xx

Increasing Izz

(b) Effect of Ixx and Izz on the spiral mode

Figure 17. Effect of Ixx and Izz on aperiodic lateral aircraft modes

VI. Conclusion

Presented was a methodology to address the inclusion of flight control system design, along with a softwareframework capable of analising the flight control system design. Models and systems design were based on aBoeing 747, due to the availability of stability and control data to compare to the aircraft model generatedby the CEASIOM software. Investigation of the flight control architecture was based on the control effectorlayout found in the Boeing 747 technical manual, although the results are derived from a arbitrary controlsystem architecture.

The FCSA software interface demonstrated that the flight control system architecture problem could besolved by adopting a novel algorithmic protocol approach to represent the flight control system. This can beused to combine the control effector topology, with the systems architecture of each effector to compute thefailure rates, and generate the fault dependence diagram of all control effector combinations. This providesthe required framework to develop and analyse all control system configuration setups across the flightenvelope, such as take-off, landing and cruise configurations.

Results for stability and control analysis to demonstrate the SCAA software interface were based on thetrim point of a Boeing 747-100 from Etkin. The software results using the model presented in Etkin producesthe same results, suggesting that any variation in the stability and control results are due to the methodsused to produce the model. Results for the model generated by CEASIOM appeared produce ‘ball park’results with respect to eigenvalues when compared to the results presented by Etkin, although some amountof latitude was required to obtain the results.

It is clear that the CG position can be used to fix the eigenvalue position to that of the results displayedin Etkin, although these may be at different CG positions for other modes. However, the variation is far moresignificant in the eigenvectors, which defines the mode shape, leading to errors in simulation time historieswith respect to relative amplitude and phase of the states. Digital DATCOM was the method used to producethe aerodynamic data, and is proven to yield reasonable results, although closer investigation of the datashows gross underestimated lift coefficients and control derivatives. This may lead to the discrepancies shownin the aircraft modal characteristics. Digital DATCOM is based on HTP aircraft and therefore this is not afeasible option to integrate into a conceptual aircraft design for unconventional aircraft morphologies. Theintegration of a vortex lattice code to generate the aircraft model has also been considered due to the quicktime to a solution, and more analytical approach, increasing the applicability of the model to other designconcepts. This has been part integrated into CEASIOM, allowing for generation of the inviscid aerodynamicdata, although Mach corrections have not been applied.

The SCAA interface provides the means to analyse trim points within the limits of applicability of themodel. Linear results are generated at each trim point, which can be used to analyse and assess the designaccording to a set of assessment criteria. This data can then be used to generate controllers across the flightenvelope, to augment the aircraft dynamics and improve the flight handling qualities. Furthermore, eachtrim point can then be used to simulate a set of inputs to generate time histories, for investigation of the

18 of 19

American Institute of Aeronautics and Astronautics

performance of the open and closed loop responses.The software framework presented is a work in progress representation of the methodology to integrate

development of a prototype FCS into the conceptual design phase. Further work is required to fully integratecontrol design into the software framework, although work on a methodology and tools are required for sizingof the control effectors.

References

1Moir I. & Seabridge A., “Aircraft Systems: Mechanical, Electrical & Avionics subsystems integration”, John Wiley &Sons Ltd., England, Third Edition, 2008.

2Fabrycky W.J. & Blachard B.S. , “Life-Cycle Cost and Economic Analysis”, Prentice Hall, 1991.3Chudoba B., “Stability & Control of Conventional & Unconventional Aircraft Configurations: A Generic Approach”,

Collage of Aeronautics, Cranfield University, England, April 2001.4Rizzi A. et al, “Annex 1: Description of Work”, July 2006.5Jackson S., “Systems Engineering for Commertial Aircraft”, Ashgate Publishing Limited, Hants, England, 1997.6US Air Force, “Military Standard, Flying Qualities of Piloted Aircraft”, MIL-STD-1797, 1987.7Engineering Science Data Units, “A Background to the Handling Qualities of Aircraft”, ESDU 92006, July 2006.8International Civil Aviation Organization, “ICAO Airworthiness Technical Manual”, 1974.9Stinton D., “Flying Qualities & Flight Testing of the Aeroplane”, Blackwell Science Ltd., England, 1996.

10Thomas H.H.B.M. et al, “A background to the handling qualities of aircraft”, ESDU International Plc., Royal AeronauticalSocioty, Issue with Amendment A, May 2006.

11US Air Force, “Military Specification, Flying Qualities of Piloted Aircraft”, MIL-F-8785C, 1980.12Tewari A., “Atmospheric & Space Flight Dynamics”, Birkhauser, Boston, 2007.13Etkin B., Reid L., “Dynamics of Flight: Stability & Control”, 3nd Edition, John Wiley and Sons Inc., New Jersey, 1996.14Stevens, B., Lewis, F., “Aircraft Control and Simulation”, 2nd Edition, John Wiley and Sons Inc., New Jersey, 2003.15Boeing Commertial Airplane Company, “747 Aiplane Characteristics Airport Planning”16Lanchester F.W., “Aerodonetics”, A. Constable & Co. Ltd., London, 1908.17Kamesh, S., Pradeep S., “Refined Phugoid Approximations for Conventional Aircraft”, AIAA-98-4269, 1998.

19 of 19

American Institute of Aeronautics and Astronautics