Methods for Conceptual Flight Control System Design

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5 - 8 January 2009, Orlando, Florida

AIAA 2009-1620

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 control employs the so called “Tail Volume” method, which basically establishes static stability of the design via empirical handbook methods. The methodology dispenses with any formal definition of the Flight Control System architecture and topology, and, does not afford visibility of critical sizing scenarios to the designer. This situation creates a measure of uncertainty when attempts are made to model the flight physics problem, thus thwarting opportunities in performing an advanced assessment of flight handling qualities. This paper reviews the work-in-progress status of an innovative software package aimed at the conceptual design phase called Flight Control System Designer Toolkit (FCSDT) that permits Flight Control Systems architecture definition for primary and failure modes, facilitates generation of control laws, assists the designer in apportioning control allocation schedules, and finally, analyse the stability and control of aircraft models. Results regarding flight control system architecture design are based on a control surface layout obtained from the Boeing 747 technical manual. Stability and control assessments were based on aerodynamic data generated by the aerodynamic model builder interface to Digital DATCOM provided by the European funded Framework 6 Program based on the Boeing 747 geometry.

Nomenclature Acronyms: CG DoF EASA ESDU EU F AA F BW F CS F CSD F CSDT F CSA F DD FP6 ICAO LT IS+ M CBF

Centre of Gravity Degree of Freedom and European Aviation Safety Agency Engineering Science Data Units European Union Federal Aviation Authority Fly-By-Wire Flight Control System Flight Control System Design Flight Control System Designer Toolkit Flight Control System Architecture Fault Dependence Diagram Framework 6 Programme International Civil Aviation Organization Linear Time Invariant System Control Software Mean Cycles Between Failure

∗ Postgraduate

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

1 of 19 American Institute of Aeronautics and Astronautics

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

M DO M oD M T BF SCAA SimSAC SM J

Multi-disciplinary Design Optimisation Ministry of Defence Mean Time Between Failure Stability & Control Analyser Assessor Simulating aircraft Stability And Control Small-Medium range regional Jet

Symbols: c¯ CZα CZ α¯˙ CZ q¯ CM α CM α¯˙ CM q¯ Ixx Iyy Izz m Q S U0 ωsp ζsp

Wing Mean Aerodynamic Chord Non-dimensional Transverse Force Derivative due to Angle of Incidence Non-dimensional Transverse Force Derivative due to Angle of Incidence Temporal Derivative Non-dimensional Transverse Force Derivative due to Pitch Rate Non-dimensional Pitch Moment Derivative due to Angle of Incidence Non-dimensional Pitch Moment Derivative due to Angle of Incidence Temporal Derivative Non-dimensional Pitch Moment Derivative due to Pitch Rate Rolling Moment of Inertia Pitching Moment of Inertia Yawing Moment of Inertia Mass Dynamic Pressure (= 21 ρV2 ) Reference Area Cruise speed Short period frequency (rads/s) Short period damping ratio

I.

Introduction

The design of aircraft is an extremely inter-disciplinary activity produced by simultaneous consideration of complex, tightly coupled systems and functions. The design task is to achieve an optimal integration of all components into an efficient, robust and reliable aircraft with high performance that can be manufactured with 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 following lifecycle 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), although many other models exist in both research institutes and industry. The conceptual design phase is responsible for understanding the emerging needs of the customer1 , as well as developing a technical solution to the requirements specification. The success of a project can largely be attributed by the quality of work conducted at 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 this phase, preliminary studies are performed to establish a ‘paper’ design aircraft that meets both regulatory constraints and the required technical specifications.


Currently, designs are developed using semi-empirical or empirical ‘handbook’ methods, which are typically 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 the conceptual designer to evolving tail-plane aft configuration aircraft, because of the restricted applicability of the methods available. Concurrently, no regulation or certification framework exists for atypical design concepts, 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 certify aircraft, with an ever increasing emphasis on environmental factors presents a huge challenge for aircraft designers. Chudoba comments that a large level of resource investment and time is required to evolve the already well established tail aft aircraft, for insignificant gains in performance. This implies that it may be necessary to investigated novel concepts for there enhanced level of performance and the potential to further develop the concept for future generations in a new evolutionary cycle. Before this can be a realistic solution, a framework suitable to develop such designs is required. This would begin with a major assessment of 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 the configuration has been tentatively frozen. This circumstance arises due to a reliance on empirical/ handbook data, or, if available, experimental data for predicted aerodynamic characteristics. Mistakes at this point in the design process must be avoided, however, they are invariably made. All aircraft integrators have been subjected to examples of pre-flight-test aerodynamic prediction errors and unidentified problems related to stability and control, which lead to an unacceptable increase in programme cost and extensive developmental delay, or, even catastrophic failure. Examples of actual cases include: • 50 Passenger Regional: Wheel force characteristics caused delay in certification leading to a costly redesign of the control system • Narrow Body: Unexpected sensitivity to wing rigging resulted in unacceptable number of aircraft not passing 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 avoiding limit 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 technical specification provide the designer with a framework to develop a concept. These constraints are typically relate to performance, noise, emissions, and safety factors, the final point of which is related to systems design and 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 of which a prototype flight control system can be designed is low. Due to the limited consideration of the FCS design, leads to a sub-optimal solution with respect to performance as the aircraft system is not modeled in its entirety. This paper demonstrates the advantages of introducing advanced methods into the conceptual design phase. A sophisticated flight mechanics model is developed using data generated by more advanced techniques, not typically applied at the conceptual design phase. A holistic approach to the FCS design is presented for the Boeing 747 aircraft, which is a medium-long haul civil transport airliner. Detailed stability and control analysis an aircraft model using the digital DATCOM interface produced by an aerodynamic model builder developed in the Framework 6 programme SimSAC (Simulation aircraft Stability And Control).


II.

Flight Control System Designer Toolkit

Recognising that higher fidelity methods and introducing FCS design from a conceptual design phase is demonstrated by the European Union (EU) funding a Framework 6 programme (FP6), Simulating aircraft Stability And Control (SimSAC). The vision of the programme is to introduce multi-disciplinary design optimisation (MDO) into the conceptual design phase. It is envisaged that the effect of this will reduce the life-cycle time and cost, in addition to an increase in knowledge, performance and safety of the design, all of which is outlined in the programmes Technical Annex4 . Figure 1 summarises the overall goal of EU FP6 SimSAC which is a (software) framework from which controllability and manoeuvrability requirements can be analysed and assessed from the conceptual design phase. This relies on utilising more advanced techniques to model the aerodynamics, structural and weight and balance subspaces to construct a flight mechanics model, from which stability, control and manoeuvrability 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 to the 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 mechanics model for analysis and assessment. A mixed or interlaced fidelity approach is employed, where both low and high 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 handling quality criteria coupled to a given cost function. To fully integrate FCS considerations onto a conceptual aircraft design, which would facilitate designing a variety of FCS types including manual, boosted and fly-bywire (FBW) systems, a software framework is required. This would require the development of appropriate design, analysis and assessment tools, allowing the designer to evaluate the physical FCS architecture, design a suitable prototype controller, perform open and closed loop analysis of the aircraft system, analyse critical failure scenarios and assessment of the aircraft stability and control characteristics. Figure 2 provides a detailed vision to develop a comprehensive Flight Control System Designer Toolkit (FCSDT), encapsulating the 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 event of failure, the inherent stability and control characteristics and the aircraft structure. The main concern regarding the aircraft structure is primarily associated with the fatigue life of the aircraft, which depending


Figure 2. Flight Control System Designer Toolkit comprehensive overview

on the structural design philosophy, determines the method in which to certify the aircraft. Structural contributions 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. Control surfaces 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), which assesses the probability of a failure condition to given fault, identifying the critical failure modes. FDD are generated by using the FCS architecture to generate a fault tree diagram, from which probability of failure can be computed and critical faults identified. For more information on generation of fault tree analysis data see Moir and Seabridge1 . Assessment of these failure cases are not only for regulatory and certification purposes but also for maintenance scheduling, computing parameters such as the mean time between failure (MTBF) or mean cycles between failure (MCBF). These are examples of system reliability assessment parameters5 . To achieve certification there is a minimum requirement value for various types of failure which are summarised in Table 1. Failure Condition Classification Catastrophic Hazardous/Severe Major Minor No Safety Effect

Probability of Failure P ≤ 10−9 10−9 ≤ P ≤ 10−7 10−7 ≤ P ≤ 10−5 10−5 ≤ P ≤ 10−3 P ≥ 10−3

Failure Description Extremely Improbable Extremely Remote Remote Reasonably Probable Frequent

Table 1. Failure Condition Failure Descriptions

A software tool has been developed at Bristol University to perform flight control system architecture design, along with the associated fault tree analysis. The software interface allows the user to load a preexisting FCS topology from another project, edited accordingly to the current aircraft project, or to begin a clean sheet flight control architecture. Figure 3(a) presents the interface from which the user can edit the FCS architecture, which includes adding 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 failure rate 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 given failure 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, with a conventional arrangement of control effectors including spoilerons, ailerons, elevators and rudders. The systems architecture is based on a fly-by-wire (FBW) system with mechanical backup. This generic structure along with the SMJ example provides the tool with sufficient enough capability to analyse most conventional design concepts, other concepts can be programmed in a similar manner to generate a flight control system architecture. Figure 3(b) provides the interface to allocate the systems architecture for a given component. This involves connecting the various system components required to actuate a control effector, i.e. flight control column, computers and sensors to power sources and actuator components. This is performed by the use of a Boolean expression as is highlighted in figure 3(b), using either a predefined architecture or a manual input 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 for its associated failure rate displayed in a text box above the logic gate. This presents the failure rate for the components 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 reducing for example redundancy, typically leading to increased failure rate. A number of default component failure rate values are used, which can be altered to more appropriate values were available.

Figure 4. Fault Dependence Diagram Generated by FCSA


B.

Stability & Control

Stability and control characteristics are generated by analysing and assessing both the open and closed loop properties of an aircraft. Open loop assessment includes analysing linearised data of the aircraft over critical locations in the flight envelope. For the aircraft to be certified, it must satisfy the requirements of the code which the aircraft has been designed. Regulatory bodies such as the Federal Aviation Authority (FAA) and European Aviation Safety Agency (EASA) use MIL-SPEC6 , Engineering Science Data Units7 (ESDU) and International Civil Aviation Organization8 (ICAO) handling quality assessment criteria as a guide to form the 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 requirements for flight operations defined by the relevant regulatory body or code. According to Stinton9 , airworthiness requirements 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, and crew workloads with the flight control system and aerodynamic loads, some of which for civil aircraft are summarised in Table 2. Methods for assessment include figure of merit (FoM) charts, which assess standard modal characteristics including the short period, phugoid, dutch roll, roll subsidence and spiral modes. Scenario Trim at take-off Trim at landing VS1g demonstration Minimum rotation rate Push-over Steady turn at take-off Steady turn at landing Trim at take-off Trim at landing CEV Manoeuvre Stability Dutch Roll VM C Steady sideslip Roll man. take-off Roll man. landing

CG Location FWD FWD FWD FWD FWD FWD FWD AFT AFT AFT AFT LATERAL LATERAL LATERAL LATERAL LATERAL

Requirement minimum manoeuvrability manoeuvrability alpha max pitch acceleration minimum man. full stick forward - no control loss φ > 30◦ φ > 40◦ minimum manoeuvrability manoeuvrability balance the pitch moment of the engines margin w.r.t. manoeuvre point damping not greater than specified speed (sideslip constrained) demonstrate specified minimum cross wind speed +30◦ to −30◦ in less than 11 s, OEI +5◦ to +25◦ in less than 7 s, VM CL

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 attack and 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 phugoid ICAO8 assessment criteria or MIL-F-8785C11 for the dutch roll. These provide a framework from which aircraft design and flight handling quality assessments can take place. However, the applicability of these assessment 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 the stability characteristics on a spectrum of design configurations. Chudoba reiterates two definitions that are mandates for all aircraft, which in essence state that the appropriate authority should declare if an aircraft design is ‘fit to fly’. Closed loop control typically augments dynamic derivatives in order to achieve the desired flying/ handling qualities, to meet the fundamental stability and control requirement of ‘fit to fly’. A number of methods exist to 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 and integral components using the pre-defined control laws, derived from the control philosophy as is illustrated in figure 5. The final component to complete the flight controller is the control allocation, which allocates the required control effector perturbations to meet a desired reference signal.

Figure 5. Control law philosophy

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

ICAO Recommended Phugoid Characteristics 120

Too rapid an initial response − over sensitive tendency to PIO

0.15

Excessive overshoot difficult to manoeuvre

4 3 2

Acceptable Response too sluggish

Satisfactory

Poor Unacceptable Excessive compensation required − difficult to trim

1 −1

10

80 60 40

ACCEPTABLE for emergency conditions

Damping Ratio (−)

Poor

UNACCEPTABLE

100

5

Phugoid Period (s)

Undamped Natural Frequency (rad/s)

ESDU Short Period Opinion Contours, ESDU 92006 6

Min. Frequency

Bristol has developed an interface tool, Stability and Control Analyser Assessor (SCAA), which allows rapid generation of trim and linear analysis data of an aircraft model across the flight envelope. These results can be analysed and assessed using classical analysis techniques or pre-existing figures of merit to assess the aircraft 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 assessment criteria.

SATISFACTORY for normal operation

20 0 −0.04

0

10 Damping Ratio (−)

(a) ESDU 92006 Short Period Figure of Merit

0.1

T/O, Appr and Land zeta x omega = 0.10 Clb, Crz and Des zeta x omega = 0.15 Min. Damping

0.05 0 −0.05 −0.1

−0.02

0 0.02 0.04 2 x zeta x omega (rad/s)

0.06

0.08

(b) ICAO Phugoid Figure of Merit

0

0.5

1 1.5 2 Undamped Natural Frequency (rad/s)

2.5

3

(c) MIL-F-8785C Dutch Roll Figure of Merit

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


IV.

Conceptual FCS Design Methodology

Traditionally, FCS design considerations are only concerned with flight control system architecture and basic stability and control assessments using techniques such as volume coefficient, with little consideration of developing a prototype controller. The prototype controller requires computation of the control laws and allocation i.e. the governing software algorythms that control the aircraft response characteristics, which is not 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 market research, in addition to the current design environment regulation and certification requirements. The requirements specification captures these design constraints, providing a framework from which initial sizing can be performed. The baseline design is progressively modified to meet the requirements specified, whilst optimising 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 holistic approach of not only the systems architecture, but also the control law formulation and allocation. Figure 8 describes 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 if a feasible controller can not be synthesised, a designer decision is made to assess the design feasibility. If the design is considered feasible, design modifications are performed, if the design is considered unfeasible re-evaluation of the design concept is required. This framework provides an environment to integrate FCS design into the optimisation of the geometry. Flight Control System Designer Toolkit (FCSDT) is a EU FP6 SimSAC software development which represents 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 the controller 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 Boeing 747-100 aircraft model generated from the software framework developed by SimSAC. The model is a rigid body representation of the Boeing 747 flight mechanics, combined with the relevant rigid body, flat earth equations of motion which includes the governing 6DoF rigid body equations. Euler angles are used to describe 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 necessary to use the quaternion orientation representation.


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 comprehensive investigation of the complete control systems architecture. As a demonstration, the control effector layout shall 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, 2 pairs of elevators and a split rudder. A demonstration of the algorithmic protocol developed to handle the flight 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 yaw control 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 Boeing 747

(b) Software Representation of Boeing 747 Flight Control System Architecture

Figure 9. Boeing 747 Flight Control System Architecture


Table 3 summarises the results obtained from the investigation using FCSA. The systems architecture is a modified version of the generic SMJ aircraft design. Component probabilities used are default values built into the software, which can be readily changed to values in where the component failure rate is available. Failure Condition Pitch Option 1 Pitch Option 2 Roll Option 1 Roll Option 2 Yaw Option 1 Yaw Option 2

Probability of Failure 4.0001 × 10−12 1.2212 × 10−17 3.0000 × 10−08 3.0012 × 10−16 1.0006 × 10−08 1.0004 × 10−08

Control Effectors Inner and Outer Elevators Inner and Outer Elevators, All Moving Tail Ailerons Ailerons, 4 Outer Spoilers Upper or Lower Rudder 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 roll control 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 fail severe. The yaw control option 2 is only improves on option 1 by 2 × 10−12 , suggesting that to improve the failure rate the systems architecture of the upper or lower rudder is required to change. Both lower and upper 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 rigid body equations of motion states. These are typically defined in the wind axes frame, which uses the state vector [α, MACH NO, β, P, Q, R] to generate the aerodynamic tables. Additional tables associated to control surface deflections for example elevators, ailerons and rudders are also generated. Currently only trailing edge devices are modelled, as such does not encompass the entire flight control system available to the 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 the relatively non-linear behavior of these components, for example, boundary layer separation is a phenomenon that lower fidelity inviscid aerodynamic solvers such as vortex lattice are unable to predict. As a consequence only cruise flight conditions shall be considered for this investigation. However, issues regarding a methodology 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 due to the difficulties in modelling. The model structure as seen in figure 10 represents the upper most level of the model hierarchy of the Simulink representation of the aircraft model. Each model is integral to a more complete investigation of the aircraft flight dynamics over the flight envelope for a fully augmented, closed loop aircraft model. The model can be reduced to an open loop model by considering the Aircraft Model, Equations of Motion and Actuator Model. The open loop model can be used to assess the unaugmented dynamics, and apply the appropriate 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 model input is the previously stated state vector, along with a control vector of the aircraft control surface deflec-


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

= CΦ0 (α, M ach) + CΦβ (α, M ach, β) + CΦQ (α, M ach, Q) + CΦP (α, M ach, P ) + CΦR (α, M ach, R) +CΦδelv (α, M ach, δelv ) + CΦδrudd (α, M ach, δrudd ) + CΦδail (α, M ach, δail ) − 7CΦ0 (α, M ach) (1)

Φ =

(2)

X, Y, Z, L, M, N

To demonstrate the software interface, model inputs shall include perturbations over a CG, mass and inertia range. Results shall be compared with the cruise trim point of the Boeing 747-100 presented in Etkin.13 Table 4 summarises the modes about the cruise point of 40,000ft altitude and a Mach number of 0.8. Scenario Short Period Phugoid Dutch Roll Roll Subsidence Spiral

Eigen Value -0.3719 ± 0.8875i -0.003289 ± 0.06723i -0.033011 ± 0.94655i -0.56248 -0.072973

Period (s) 7.08 93.4 6.64 -

thalf (s) 1.86 211 21 1.23 95

Nhalf (cycles) 0.26 22.5 3.16 -

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 natural frequency and short period damping, the ESDU 92006 plot can be generated yielding the results observed in figure 12(a). Comparing the results with equation 3 and 4, the relationship between frequency and CG position is augmented through the pitch damping term CM q¯ and pitch stiffness term CM α (assuming CZ q¯ is negligible). The effect of CG is dependent on the relative effect between these two terms. As CG moves forward towards the nose of the aircraft, CM α decreases and CM q¯ increases. If the overall effect is to increase the numerator of equation 3 then the frequency increases. 2.5

1.5

0.8 0.6

1

0.4

0.5

0.2

Imag

Imag

1

Decreasing Z position Increasing Static Margin

2

0

0

−0.5

−0.2

−1

−0.4

−1.5

−0.6

−2

−0.8

−2.5 −0.4

−0.35

−0.3

−0.25

−0.2 −0.15 Real

−0.1

−0.05

0

−1 −1

0.05

(a) Variation of longitudinal pole position due to CG perturbations

−0.8

−0.6

−0.4

−0.2 0 Real

0.2

0.4

0.6

0.8

(b) Variation of lateral pole position due to CG perturbations

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

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


6

120 Too rapid an initial response − over sensitive tendency to PIO 100

5 Poor

4


3.5 3

Acceptable Response too sluggish Satisfactory

2.5 2

80

60

40

UNACCEPTABLE

4.5

Phugoid Period (s)


5.5

SATISFACTORY for normal operation ACCEPTABLE for emergency conditions

Poor

1.5

Unacceptable

1

20

Excessive compensation required − difficult to trim

0.5 −1

0 −0.04

0

10


(a) Variation in ESDU short period assessment due to variations in CG position

−0.02


0.06

0.08

(b) Variation in ICAO phugoid assessment due to variations in CG position

Figure 12. Aircraft assessment criteria variations with CG perturbations

2U 2

2 ωsp

=

2U 2

2ζsp ωsp

0 CZα CM q¯ − CM α (( QS¯ c )m + CZ q¯)

I

2U 2

yy 0 ( QS¯ ¯˙ ) c )(( QS¯ c )m + CZ α

2U 2

2U I

0 yy 2U0 0 0 QS¯ c c¯ CM q¯(( QS¯c )m − CZα ) + QS¯c2 c¯ CZα + (( QS¯c )m + CZ q¯)CM α¯˙ = 2 2U Iyy 2U0 (( 0 )m + C ¯ )

QS¯ c

(3)

(4)

Zα ˙

However, figure 12(b) indicates that the phugoid damping decreases with decreasing static margin, although the period (and frequency) remains relatively insensitive to variations in CG position. There is some amount 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 is dependent on the relative weighting of each term. The phugoid damping becomes remarkably more difficult to analyse due mainly to the lack of a simple and reliable approximation to the phugoid characteristics. Lanchester’s equation16 is one of the earliest approximations 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 accurate method for predicting the phugoid damping, which is derived from the equations of motion, making few assumptions to arrive at a 4th order longitudinal characteristic equation, substituting an appropriate short period approximation, the phugoid can be approximated. s g(Mu Zα − Mα Zu ) (5) ωph = U1 Mα − Zα Mq Comparing the modal results generated by the CEASIOM generated aerodynamic data, the short period positions suggests a CG aft configuration but a large difference in the damping is observed. The CG aft configuration is also supported when comparing the dutch roll pole positions with those presented in table 4. The results obtained for the roll subsidence, spiral and the phugoid are sensitive to both vertical and horizontal CG position and can be fixed to fit in the positions provided by Etkin. Reviewing the approximate equations along with the aerodynamic data obtained from both Etkin and the model generated by CEASIOM, large errors were observed with respect to control coefficients, leading to errors in the trim point obtained or no solution existing. The elevator control coefficient predicted by digital DATCOM is approximately 5 times greater in the aerodynamic data presented in Etkin. To obtain a solution at this trim point, artificially increasing the CM δelv derivative 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 3 and 4, this would not affect the prediction of the short period, as the results obtained for the derivatives involved in prediction of the short period are within the linear region and are unlikely to change with trim angle of attack, but will however be affected by the error in the lift coefficient, and relative error in CG position, CM α and CM q¯ as a result of poor aerodynamic force prediction. Although the error in trim point may not affect derivatives involved in the short period, all approximations indicate that the phugoid is highly dependent on the calculated trim point. This is because derivatives such as CXα are typically non-linear, due to the parabolic relationship between drag and angle of attack through the lift coefficient (CD = CD0 + kCL2 ). Therefore deviations away from the trim point will certainly lead to errors in phugoid prediction, as the linear derivative is only valid for a small perturbation in the trim point parameters. Figure 13- 17 investigates the effects of mass and inertia on the aircraft modes of motion. Mass is a scaler quantity, 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 the aircraft modes of motion. The short period damping is observed to decrease, or where as the frequency appears to be relatively insensitive to variations in mass. 2.5

0.08

Short Period

2

0.06

Phugoid

1.5 Dutch Roll

1

0.02 Roll Subsidence

Spiral

Imag

Imag

0.5

0.04

0 −0.5

0 −0.02

−1 −0.04 −1.5 −0.06

−2 −2.5 −0.5

−0.4

−0.3

−0.2

−0.1 Real

0

0.1

−0.08 −0.014

0.2

(a) Mass effects on short period, dutch roll and roll subsidence modes

−0.012

−0.01

−0.008 −0.006 Real

−0.004

−0.002

0

(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 the frequency 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). Unfortunately dutch roll approximations rely on underlying assumptions for there accuracy, which in the approximation presented by Etkin assumes that sideslip and yaw rate are the dominant modes where roll rate is assumed negligible. As can be observed by investigation of the associated Eigenvector, this is certainly not the case across the flight envelope. Closed form approximations may seem attractive for design purposes, but can become misleading if the assumptions are not treated carefully, implying that there use in design across the envelope may be quite limited, thus supporting the notion of increased fidelity methods to optimise the FCS design according to flight dynamic requirements. The inertial properties affect the mode which is most closely associated to the plane in which the mode acts as will be demonstrated. The results in figure 15 indicate that by increasing the pitching moment of inertia, both the frequency and damping decrease. The result of the decreasing frequency comply with the analytical result obtained from equation 3. Equation 4 indicates that the variation of the short period 2U0 Iyy 2U0 damping is dependent on the proportion of the QS¯ c2 c¯ CZα term. The results would indicate that the contribution of this term on the numerator with variations in Iyy is minimal, and that the damping is dominated by the inverse relationship with the Iyy term, with little contribution from the short period frequency. 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

6 Too rapid an initial response − over sensitive tendency to PIO


5.5 5

Poor

4.5 4


3.5 3


2.5 2 Poor

1.5

Unacceptable

1


0.5 −1

0

10


(a) Effect of mass on the ESDU short period assessment criteria

Min. Frequency

0.2

120

0.15

100

40

Damping Ratio (−)

60

UNACCEPTABLE

Phugoid Period (s)

0.1 80

SATISFACTORY for normal operation ACCEPTABLE for emergency conditions

Clb, Crz and Des zeta x omega = 0.15 Min. Damping

0.05

0

−0.05

20

0 −0.04

T/O, Appr and Land zeta x omega = 0.10

−0.1

−0.02


0.06

0.08

0

0.5


2.5

3

(b) Effect of mass on the ICAO phugoid assessment criteria(c) Effect of mass on the MIL-F-8785C Dutch Roll assessment criteria Figure 14. Effect of mass on the aircraft modes assessment criteria


2.5 2 1.5

Short Period

1

Imag

0.5 0 −0.5 −1 −1.5 −2 −2.5 −0.5

−0.4

−0.3

−0.2

−0.1 Real

0

0.1

0.2

(a) Effect of Iyy on the aircraft pole positions

6

0.08 Too rapid an initial response − over sensitive tendency to PIO

0.06

5

Phugoid 0.04

Poor

4.5 4


3.5 3


2.5

0.02

Imag


5.5

0 −0.02

2 Poor

1.5

−0.04

Unacceptable

1

−0.06


0.5 −1

10

0


−0.08 −2.21

(b) Effect of Iyy on the ESDU assessment criteria

−2.2

−2.19

−2.18

−2.17 Real

−2.16

−2.15

−2.14

−2.13 −3

x 10

(c) Effect of Iyy on the phugoid pole positions

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


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 that for this particular mode, the modal characteristics are more sensitive to variations in Ixx relative to Izz . This suggests that the mode may be predominantly a rolling motion, which is further supported by investigating the eigenvector magnitude, where the ratio is 5:1 when comparing roll and yaw rate normalised eigenvectors respectively. This is further supported by the results presented in Etkin, although the error of the roll rate seems to be far greater than the other normalised states relative to one another. This may suggest that the method prediction has large deficiencies in the modelling of roll damping and stiffness terms. This would also invalidate the assumption of negligible rolling motion in the dutch roll approximation.

Min. Frequency

0.2

1 0.8

0.15 0.6

Increasing I

xx

0.4

0.1

Increasing I

Damping Ratio (−)

zz

Imag

0.2 0 −0.2 −0.4

T/O, Appr and Land zeta x omega = 0.10 Clb, Crz and Des zeta x omega = 0.15 Min. Damping

0.05

0

−0.05

−0.6 −0.1 −0.8 −1 −0.01

−0.005

0

0.005

0.01 Real

0.015

0.02

0.025

0.03

0

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

0.5


2.5

3

(b) Effect of Ixx and Izz on the aircraft MIL-F-8785C Dutch 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 demonstrate 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 characteristics are more sensitive to variations in Ixx , or the rolling moment of inertia. Also, the figure 17(a) implies that increasing 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 figure 17(b), which indicates the mode is more sensitive to variations in yawing moment of inertia. Again, the effect of yawing moment of inertia is observed to increase the modes time constant, however increasing the rolling moment of inertia decreases the modes time constant.


1

1

Increasing I

Increasing I

xx

xx

0.8

Increasing I

zz

0.6

0.6

0.4

0.4

0.2

0.2

Imag

Imag

0.8

0

−0.2

−0.4

−0.4

−0.6

−0.6

−0.8

−0.8 −0.56

−0.54

−0.52

−0.5 Real

−0.48

−0.46

−0.44

−1 −0.012

−0.42

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

zz

0

−0.2

−1

Increasing I

−0.0118

−0.0116

−0.0114 Real

−0.0112

−0.011

−0.0108

(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 software framework capable of analising the flight control system design. Models and systems design were based on a Boeing 747, due to the availability of stability and control data to compare to the aircraft model generated by the CEASIOM software. Investigation of the flight control architecture was based on the control effector layout found in the Boeing 747 technical manual, although the results are derived from a arbitrary control system architecture. The FCSA software interface demonstrated that the flight control system architecture problem could be solved by adopting a novel algorithmic protocol approach to represent the flight control system. This can be used to combine the control effector topology, with the systems architecture of each effector to compute the failure rates, and generate the fault dependence diagram of all control effector combinations. This provides the required framework to develop and analyse all control system configuration setups across the flight envelope, such as take-off, landing and cruise configurations. Results for stability and control analysis to demonstrate the SCAA software interface were based on the trim point of a Boeing 747-100 from Etkin. The software results using the model presented in Etkin produces the same results, suggesting that any variation in the stability and control results are due to the methods used 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 amount of 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 displayed in Etkin, although these may be at different CG positions for other modes. However, the variation is far more significant in the eigenvectors, which defines the mode shape, leading to errors in simulation time histories with respect to relative amplitude and phase of the states. Digital DATCOM was the method used to produce the aerodynamic data, and is proven to yield reasonable results, although closer investigation of the data shows gross underestimated lift coefficients and control derivatives. This may lead to the discrepancies shown in the aircraft modal characteristics. Digital DATCOM is based on HTP aircraft and therefore this is not a feasible option to integrate into a conceptual aircraft design for unconventional aircraft morphologies. The integration of a vortex lattice code to generate the aircraft model has also been considered due to the quick time to a solution, and more analytical approach, increasing the applicability of the model to other design concepts. This has been part integrated into CEASIOM, allowing for generation of the inviscid aerodynamic data, although Mach corrections have not been applied. The SCAA interface provides the means to analyse trim points within the limits of applicability of the model. Linear results are generated at each trim point, which can be used to analyse and assess the design according to a set of assessment criteria. This data can then be used to generate controllers across the flight envelope, to augment the aircraft dynamics and improve the flight handling qualities. Furthermore, each trim point can then be used to simulate a set of inputs to generate time histories, for investigation of the


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 integrate control design into the software framework, although work on a methodology and tools are required for sizing of the control effectors.

References 1 Moir I. & Seabridge A., “Aircraft Systems: Mechanical, Electrical & Avionics subsystems integration”, John Wiley & Sons Ltd., England, Third Edition, 2008. 2 Fabrycky W.J. & Blachard B.S. , “Life-Cycle Cost and Economic Analysis”, Prentice Hall, 1991. 3 Chudoba B., “Stability & Control of Conventional & Unconventional Aircraft Configurations: A Generic Approach”, Collage of Aeronautics, Cranfield University, England, April 2001. 4 Rizzi A. et al, “Annex 1: Description of Work”, July 2006. 5 Jackson S., “Systems Engineering for Commertial Aircraft”, Ashgate Publishing Limited, Hants, England, 1997. 6 US Air Force, “Military Standard, Flying Qualities of Piloted Aircraft”, MIL-STD-1797, 1987. 7 Engineering Science Data Units, “A Background to the Handling Qualities of Aircraft”, ESDU 92006, July 2006. 8 International Civil Aviation Organization, “ICAO Airworthiness Technical Manual”, 1974. 9 Stinton D., “Flying Qualities & Flight Testing of the Aeroplane”, Blackwell Science Ltd., England, 1996. 10 Thomas H.H.B.M. et al, “A background to the handling qualities of aircraft”, ESDU International Plc., Royal Aeronautical Socioty, Issue with Amendment A, May 2006. 11 US Air Force, “Military Specification, Flying Qualities of Piloted Aircraft”, MIL-F-8785C, 1980. 12 Tewari A., “Atmospheric & Space Flight Dynamics”, Birkhauser, Boston, 2007. 13 Etkin B., Reid L., “Dynamics of Flight: Stability & Control”, 3nd Edition, John Wiley and Sons Inc., New Jersey, 1996. 14 Stevens, B., Lewis, F., “Aircraft Control and Simulation”, 2nd Edition, John Wiley and Sons Inc., New Jersey, 2003. 15 Boeing Commertial Airplane Company, “747 Aiplane Characteristics Airport Planning” 16 Lanchester F.W., “Aerodonetics”, A. Constable & Co. Ltd., London, 1908. 17 Kamesh, S., Pradeep S., “Refined Phugoid Approximations for Conventional Aircraft”, AIAA-98-4269, 1998.
