UNIVERSITÀ
DI
PISA
DIPARTIMENTO DI INGEGNERIA CIVILE ED INDUSTRIALE Corso di Laurea Magistrale in Ingegneria Aerospaziale
MASTER THESIS IN AEROSPACE ENGINEERING
DEVELOPMENT OF PROGNOSTIC MODEL-BASED
ALGORITHMS FOR FREEPLAY IDENTIFICATION IN
ELECTROMECHANICAL FLIGHT ACTUATORS
Supervisors: Candidate:
Prof. Ing. Gianpietro Di Rito
Silvio Akitani
Prof. Ing. Roberto Galatolo Prof. Ing. Eugenio Denti Ing. Francesco Schettini
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This master thesis focuses on the development of a prognostic algorithm, in order to evaluate the mechanical freeplay evolution of an electromechanical actuator for aircraft control surface, through a model-based approach.
A characterisation of freeplay increase effects over the actuator system performances has been carried out with a detailed Matlab-Simulink® model of the EMA, developed in previous and parallel works. An additional freeplay model has been inserted within the mechanical section of Simulink blocks and, subsequently, the freeplay has been injected gradually through an aging factor related to the dead zones parameters.
A particular attention has been paid on the development of a normalization approach able to energise the fault’s limit cycles amplitudes at characteristics frequencies, in terms of FFT analysis results. Therefore, a comparative analysis has been made to justify the usefulness of the technique. Subsequently, appropriates prognostic models have been achieved in order to perform the health-monitoring and determine the freeplay entity in the actuator.
Finally, random simulations have been carried out to validate the algorithm and, therefore, uncertainties have also been taken into account to demonstrate its robustness, accuracy and limitations.
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ABSTRACT ... I
LIST OF CONTENTS ... II
LIST OF FIGURES ... V
LIST OF TABLES... XI
LIST OF SYMBOLS ... XII
LIST OF ACRONYMS ... XV
INTRODUCTION ... 1
CHAPTER 1 OVERVIEW ON PROGNOSTICS AND HEALTH MANAGEMENT OF ELECTRO-MECHANICAL ACTUATORS ... 3
1.1 Electromechanical Actuators for Flight Controls ... 3
1.1.1 More-Electric and All-Electric Aircraft ... 3
1.1.2 Flight Control Surface Actuation Systems ... 7
1.1.3 Typical EMA solutions ... 15
1.2 EMA Basic Fault Modes ... 22
1.3 Importance of Health-Management in EMAs ... 26
1.3.1 Monitoring sensors issues ... 27
1.3.2 Prognostic Approaches to the EMA Health-Management ... 28
CHAPTER 2 ELECTROMECHANICAL ACTUATOR DYNAMIC MODEL DESCRIPTION 34 2.1 Dynamic system model description ... 35
2.1.1 Brushless Motor ... 38
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2.1.4 Mechanical Transmission ... 45
2.2 Freeplay modelling ... 49
2.3 Flight Control Actuation System Definition ... 52
2.3.1 Mechanical Section ... 52
2.3.1.1 Clutch ... 52
2.3.1.2 Gearbox ... 53
2.3.1.3 Output Lever ... 53
2.3.2 Actuator Electrical and Electronic section ... 54
2.3.2.1 Sensors ... 54
2.3.2.2 Motor ... 55
CHAPTER 3 DEVELOPMENT OF MODEL-BASED PROGNOSTIC ALGORITHMS ... 56
3.1 Maintenance Test Simulation ... 57
3.1.1 Test definition ... 58
3.1.2 Available sensors ... 59
3.1.3 Expected results ... 61
3.2 Signal analysis for freeplay identification via FFT ... 69
3.3 Normalisation approaches ... 74
3.3.1 Normalization with input signal FFT ... 74
3.3.2 Normalization factor definition via residual signal frequency response .. 76
3.3.2.1 Frequency response evaluation... 78
3.3.2.2 Normalization process ... 81
3.3.3 Comparison between two normalization techniques ... 84
3.4 Prognostic models analysis ... 86
3.4.1 Freeplay-induced limit cycles analysis ... 86
3.4.2 Data fitting and uncertainties definition ... 91
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3.5.2 Robustness of the defined MBIT ... 98
CHAPTER 4 ROBUSTNESS CONCERNS AND LIMITATIONS OF THE APPROACH ... 104
4.1 Parameters uncertainties effect on prognostic accuracy ... 104
4.1.1 Prognostic accuracy ... 104
4.1.2 Uncertainty by considering a different motor ... 108
4.2 Correlation between freeplay and age for RUL definition ... 110
CONCLUSIONS AND FUTURE WORK ... 111
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Figure 1.1 Schematic of conventional power distribution, [3]. ... 4
Figure 1.2 Moving towards a More-Electric Aircraft, [4]. ... 4
Figure 1.3 Comparison between conventional aircraft and MEA systems, [6]. ... 6
Figure 1.4 Example of flight control surfaces - commercial airliner (A380). . 7
Figure 1.5 Configuration of flight control system. ... 8
Figure 1.6 Block diagram and energy transmission of EHA, [2]. ... 10
Figure 1.7 Block diagram and energy transmission of EMA, [2]. ... 11
Figure 1.8 EMA and EHA architectures, [5] ... 12
Figure 1.9 Development from early FBW system to recent applications, [10]. ... 14
Figure 1.10 Scenario of the EMA introduction in aircraft flight control systems, [8] ... 15
Figure 1.11 Typologies of flight control EMA, [12]. ... 15
Figure 1.12 Schematic and some application of EMA. ... 16
Figure 1.13 Exploded view of a brushless motor, [13]. ... 18
Figure 1.14 Example of planetary gearbox. ... 19
Figure 1.15 Planetary roller-screw, [14]. ... 20
Figure 1.16 3-phase motor connected to a 6-switches power electronics, [15]. ... 21
Figure 1.17 EMA fault tree: system top-level, [19]. ... 25
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Figure 1.20 Hierarchy of prognostic approaches, [16]. ... 30
Figure 2.1 Sectional view of the EMA, [21]. ... 35
Figure 2.2 Overall Simulink model ... 37
Figure 2.3 3-phase PMSM schematics (one pole pair), [21]. ... 38
Figure 2.4 3-phase motor dynamics structure. ... 40
Figure 2.5 Park transform Simulink block. ... 41
Figure 2.6 Reverse Park transform Simulink block. ... 42
Figure 2.7 Control electronics model. ... 43
Figure 2.8 Quadrant control regulator dynamics. ... 43
Figure 2.9 Direct control regulator dynamics. ... 44
Figure 2.10 Speed regulator dynamics. ... 44
Figure 2.11 Position regulator dynamics. ... 45
Figure 2.12 FCSA system mechanical schematics with vibrating modes. .... 45
Figure 2.13 FCA mechanical system model. ... 48
Figure 2.14 Clutch dynamics. ... 49
Figure 2.15 EMA system including mechanical imperfections, [22]. ... 49
Figure 2.16 Freeplay mechanism. ... 50
Figure 2.17 Freeplay modelling. ... 50
Figure 2.18 Freeplay Simulink® model. ... 52
Figure 2.19 Cinematics of the output lever. ... 54
Figure 3.1 Prognostics approach selection. ... 56
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Figure 3.4 Output lever position response at nominal condition. ... 62
Figure 3.5 Quadrant current response at nominal condition. ... 62
Figure 3.6 Motor revolutions at 1/2 of EoL freeplay condition. ... 63
Figure 3.7 Output lever position response at 1/2 of EoL freeplay condition. ... 63
Figure 3.8 Quadrant current at 1/2 of EoL freeplay condition. ... 64
Figure 3.9 Motor revolutions at EoL freeplay condition. ... 64
Figure 3.10 Output lever position response at EoL freeplay condition. ... 65
Figure 3.11 Quadrant current response at EoL freeplay condition. ... 65
Figure 3.12 Motor position residue at EoL freeplay condition. ... 67
Figure 3.13 Output lever position residue at EoL freeplay condition. ... 67
Figure 3.14 Illustration of expected RUL estimation with Prognostic Models. ... 68
Figure 3.15 FFT spectrum of position command. ... 69
Figure 3.16 FFT spectrum of motor position (Nominal vs Freeplay conditions). ... 71
Figure 3.17 FFT spectrum of output lever position (Nominal vs Freeplay conditions). ... 71
Figure 3.18 FFT spectrum of quadrant current (Nominal vs Freeplay conditions). ... 72
Figure 3.19 FFT spectrum of motor position residue (Nominal vs Freeplay conditions). ... 73
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Freeplay conditions). ... 73
Figure 3.21 Motor position residue normalized FFT. ... 75
Figure 3.22 Output lever position residue normalized FFT. ... 75
Figure 3.23 Quadrant current normalized FFT. ... 76
Figure 3.24 Frequency response of measured motor position residue. ... 80
Figure 3.25 Frequency response of output lever position residue. ... 80
Figure 3.26 Frequency response of measured quadrant current. ... 80
Figure 3.27 Normalization factor for motor position residue. ... 82
Figure 3.28 Normalization factor for output lever position residue. ... 82
Figure 3.29 Normalization factor for quadrant current. ... 83
Figure 3.30 Normalized/Amplified FFT spectrums - motor position residue. ... 84
Figure 3.31 Normalized/Amplified FFT spectrums - output lever position residue. ... 85
Figure 3.32 Normalized/Amplified FFT spectrums – quadrant current. ... 85
Figure 3.33 Normalized/Amplified FFT spectrums - Prognostics Models. .. 87
Figure 3.34 Prognostics Models FFT spectrums corrected with normalization factor - Envelopes of peaks. ... 88
Figure 3.35 Prognostic models FFT spectrums in limit cycles’ frequencies observation window. ... 89
Figure 3.36 Smallest limit cycle remarkable on motor position residue (ε=1% vs ε=5%). ... 90
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identification. ... 91
Figure 3.38 Prognostic models based on normalized/amplified motor position
residue. ... 92
Figure 3.39 Prognostic models with thresholds. ... 94 Figure 3.40 Prognostic validation test - random aging factor identification.
... 97
Figure 3.41 MBIT defined with a high-amplitude input command. ... 98 Figure 3.42 Position response to large-amplitude command at nominal
conditions. ... 99
Figure 3.43 Comparison low/large-amplitude command responses at 3/4EoL
freeplay condition. ... 99
Figure 3.44 Comparison low/large-amplitude command responses at EoL
freeplay condition. ... 100
Figure 3.45 Quadrant current response to large-amplitude command at
nominal condition. ... 100
Figure 3.46 Quadrant current for large-amplitude command at 3/4EoL
freeplay condition. ... 101
Figure 3.47 Quadrant current for large-amplitude command at EoL freeplay
condition. ... 101
Figure 3.48 FFT spectrum of position response to large-amplitude command.
... 103
Figure 3.49 FFT spectrum of normalized position response to large-amplitude
command. ... 103
x
... 109
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Table 1.1 Summary of each technology innovation of actuator, [8]. ... 10
Table 1.2 Features of EHA and EMA systems, [8] ... 11
Table 1.3 Summary of property of FBW actuators, [9] ... 13
Table 1.4 EMA typical failure modes, [19]. ... 24
Table 2.1 Clutch data, [21] [22]. ... 53
Table 2.2 Gearbox data. ... 53
Table 2.3 Output lever data, [22]. ... 54
Table 2.4 Sensors data, [21] [22]. ... 54
Table 2.5 Motor data,[22]. ... 55
Table 3.1 Available sensors for freeplay identification, [22]. ... 60
Table 3.2 Loops design bandwidths. ... 77
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Symbol
Description
ᵃᵉᵇ Freeplay age prognosticated
ᵃᵉᵇ Minimum freeplay age prognosticated
ᵃᵉᵇ Maximum freeplay age prognosticated
ᵃᵉᵇ Mean freeplay age calculated
ᵃ Amplitude of input signal at j-frequency
ᵃ Amplitude of normalized/amplified signal at j-frequency ᵃ Amplitude of monitored signal at j-frequency
ᵃ Amplitude of prognostic model
ᵅ Control surface damping coefficient
ᵅ Gearbox damping coefficient
ᵅ Output lever damping coefficient
Δ Motor position residue
Δ Output lever position residue
Ε
Error on freeplay age evaluationFreeplay angle
Gearbox section freeplay Output lever section freeplay
Error associated to command position measurement Error associated to motor position measurement
; End-of-life freeplay
Error associated to a prognostic model Maximum freeplay
Minimum freeplay Aging factor
Limit cycle amplification factor i-Frequency
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Frequency of prognostic model
ᵅ Current on the direct axis
ᵅ Current on the quadrant axis
ᵅ Requested direct current
ᵅ Measured direct current
ᵅ Requested quadrant current
ᵅ Measured quadrant current
ᵋ Motor peak current
ᵋ Motor nominal current
ᵋ Motor continuous current
ᵋᵕ Model integration step
ᵌ Clutch inertia
ᵌ Control surface inertia
ᵌ Gearbox inertia
ᵌ Output lever inertia
ᵌ Motor rotor inertia
ᵍ Control surface stiffness
ᵍ Gearbox stiffness
ᵍ Output lever stiffness
ᵍ Motor torque constant
ᵰ Magnetix flux linkage
ᵊ Number of bit
ᵳ Motor nominal speed
ᵳ Motor no-load speed
Motor terminal resistance
ᵱ Gearbox reduction ration
ᵱ Output lever reduction ratio
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ᵖ Friction torque of the output lever
ᵖ Motor continuous torque
ᵖ Motor peak torque
ᵖ Motor nominal torque
ᵐ Clutch activation time
ᵐ Input command initial delay time
ᵐ Maintenance test duration
ᵲ Control surface position
ᵲ Motor electrical angle
ᵲ Motor mechanical position angle
ᵲ Output lever position
ᵲ Control surface requested position
ᵲ Motor measured position
ᵲ Output lever measured position
ᵘ DC voltage supply
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Acronym
Description
AEA All-Electric Aircraft
APU Auxiliary Power Unit
ANN Artificial Neural Networks
BIT Built-in Test
BLDCM Brushless DC motor
CBM Condition Based Maintenance
DFT Discrete Fourier Transform
DoF Degree of freedom
ECS Environmental Control System
ECU Electric Control Unit
EHA Electro-Hydrostatic Actuator
EMA Electro-Mechanical Actuator
EoL End-of-Life
EPU Electric Power Unit
FCSA Flight Control Surface Actuator
FFC Flight Control Computer
FFT Fast Fourier Transform
FTA Fault Tree Analysis
GB Gearbox
IDG Integrated Drive Generation
JAA Joint Aviation Authority
LTI Linear Time Invariant
LVDT Linear Variable Differential Transformer
MEA More-Electric Aircraft
MMI Man-Machine Interface
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PFC Primary Flight Control
PHM Prognostic and Health Management
PM Prognostic Model
PMSM Permanent Magnet Synchronous Motor
PoF Physics of Failure
PWM Pulse Width Modulation
QI Quantization Interval
RC Relative Criticality
RL Rate Limiter
RP Relative Probability
RUL Remaining Useful Life
RVDT Rotary Variable Differential Transformer
TF Transfer Function
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Introduction
The present thesis has been carried out, during the research activities at “Dipartimento
di Ingegneria Civile ed Industriale” of the University of Pisa, on the study of
Electro-Mechanical Actuation systems for aerospace application. According to the so-called “More-Electric and All-“More-Electric Aircraft” concepts aiming at replacing hydraulic and pneumatic systems with electrical ones, the development of these systems requires accurate simulation models of the actuators to predict performances at different working conditions. After that, a suitable Prognostic and Health Management system is required to estimate the progression of components degradation, thereby generating a continuously updated prediction of their remaining useful life. The EMA Matlab-Simulink® dynamics modelling has been object of previous research activities on the nose-wheel steering of a light military trainer; and the aim of the present work is the development of model-based prognostic algorithms for mechanical freeplay identification, taking care first all of adapting the model for addressing the flight control application.
Monitoring and maintenance have been always around. Due to rapid increase in engineering systems complexity, an accurate system for fault detection, failure prognostics and maintenance planning was needed and became a huge challenge. Prognostics is one of the most difficult and challenging aspects in PHM approaches. The word “prognostics” is originally a Greek word, “progignôskein”, which means “to know in advance”. In engineering, prognostics can be defined as the process of RULs estimation of system/subsystem/component that is degrading under either nominal operational condition or detected fault condition. This health state estimation should:
guarantee safe operation of the EMA to End-of-Life; output RUL due to mechanical freeplay failure mode; combine RUL with an uncertainty index to be trusted.
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After a brief description of the prognostics approaches and the EMAs system PHM in Chapter 1, the Flight Control Actuator System (FCAS) used in this work is presented in Chapter 2, by describing the subsystems that compose it and their dynamics. In the same chapter, the freeplay modelling implemented within the mechanical section of the system is illustrated; this is necessary to simulate the aging of the actuator and, consequently, faulted operational conditions.
In Chapter 3, prognostic model-based algorithms have been developed starting from the definition of an appropriate maintenance built-in test (MBIT) which, with the aid of available sensors for signals monitoring, is able to highlight the freeplay-induced increase limit cycles. The selected signals are so processed by Fast Fourier Analysis (FFT) to carry out the most possible informations about the characterisation of the freeplay phenomenon and, after that, some normalisation approaches are defined to energise the limit cycles in order to differentiate it from other non-linearities of the system. Always in the same chapter, many prognostic models are carried out and permits to achieve a prognostic on the health state of the actuator; these models are validated by the simulation of various faulted tests and the prognostic ends by giving out a range of probable age of the actuator.
Finally, the robustness and the limitations of the approach are determined by considering parameters uncertainties effect on the prognostic accuracy and the correlation between freeplay and age is carried out.
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Chapter 1
Overview on Prognostics and
Health
Management
of
Electro-mechanical Actuators
1.1 Electromechanical Actuators for Flight
Controls
1.1.1 More-Electric and All-Electric Aircraft
Over the last few decades, there has been tremendous progress in the efforts to move towards “More-Electric Aircraft” (MEA) philosophy that will represent one of the major challenges for the aerospace community [1]. The concept of “All Electric Aircraft” (AEA) was put forward in the 1970s. Economical and environmental constraints (like fuel burn particles rejection or use of pollutant hydraulic fluids) impose a need for more electrification and energy optimization in the onboard systems of the aircraft [2].
In the conventional architecture, fuel is converted into power by the engines and most of this power is used as propulsive power to move the aircraft. The remainder is converted into four main forms of non-propulsive power: pneumatic, mechanical, hydraulic and electrical power (Figure 1.1). Each system has become more and more complex, and interactions between different pieces of equipment have reduced the efficiency of the whole system. So, the trend is to move towards AEA which means that all the power off-takes from the aircraft are electrical in nature, thus removing the need for on-engine hydraulic power generation (Figure 1.2) [3]. The potential results found on an all-electric aircraft can be summarized as follows:
4 Reduction of overall weight; Reduction of costs;
Reduction of fuel consumption;
Increase reliability and maintainability; Expansion of flight envelope.
Figure 1.1 Schematic of conventional power distribution, [3].
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Many subsystems that conventionally use hydraulic, mechanical, and pneumatic power will be fully or partially replaced with electrical systems. Major subsystems and trends of MEA are:
Electric Power System; Main Engine Start; Auxiliary Power Units;
Environmental Control Systems;
On-Board Inert Gas Generation System;
Electrification of Hydraulically-powered systems (flight actuators, brakes, landing gears, nose-wheel steering, etc.)
A relevant example in the evolutionary changes for newer commercial transport aircraft has been the elimination of the integrated drive generator (IDG), which had been used to change the variable speed of the jet engine to constant speed via hydro-mechanical means. This system provided constant voltage and constant frequency to the aircraft’s electric bus. In some of the most recent commercial transport aircraft, including Boeing 787 and Airbus A380, the main engine generator is directly coupled to the jet engine via gearbox. Hence, the frequency of the electrical power is proportional to the engine speed. The engine characteristic and gearbox ratio determine the variation of electrical frequency. So, many loads that have run at a constant frequency in the traditional aircraft with an IDG would now require additional provisions to convert power from one form to another, i.e., ac-dc and dc-ac. This trend makes power electronics and electric machines very important for the aircraft industry.
A further example of the expanding use of electrical systems includes the elimination of the bleed air use for environmental control systems (ECSs), which are used to achieve passengers comfort by regulating the cabin temperature and pressure. Bleed air had been obtained from one of the compressor stages of the main engine; however, in the Boeing 787, instead of tapping the bleed air from the engine, it is used a set of compressors utilizing
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electric power to regulate the temperature and pressure in the cabin, eliminating the pneumatic system and air ducts from the engine. An additional example of electrification is the use of electrical power to start the main engine, instead of using compressed air from the auxiliary power unit (APU), ground cart, or the other main engines. The electric start of the main engine further eliminates pneumatic systems in the aircraft as well. These are just a few examples of the transition from various other systems in newer aircrafts to pure electric systems, as it can be seen in Figure 1.3 [5].
Figure 1.3 Comparison between conventional aircraft and MEA systems, [6].
One of the main lever to reduce the fuel consumption at the aircraft level is the increase in efficiency of actuation systems. Today, those are mainly supplied by hydraulic and pneumatic circuits. These circuits supply permanently a level of power and moreover they have a quite poor efficiency ratio: this conducts to some large energy loss. Replacing those circuits with new electrical networks permits to increase considerably the aircraft systems efficiency, and as a consequence to diminish fuel consumption at engine level, especially if it is possible to integrate “power on demand” strategies at the electrical systems level. On the other hand, flexibility, the easy installing and the possibility of self-monitoring of electrical systems permit to target important gains about acquisition and exploitation costs.
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1.1.2 Flight Control Surface Actuation Systems
The control surface is typically the trailing edge of a wing, tail, or vertical stabilizer, that rotates about a hinge line parallel to it and the actuator provides the force to rotate it against the aerodynamic loads. In some cases, it is the leading edge that rotates, in others it is the entire surface that rotates and not just the edge. The rotation of the surface changes the airflow around the aircraft and creates the aerodynamic forces and moments needed to trim and control the flight vehicle. Flight controls of the aircraft are performed with a variety of control surfaces or mechanisms. As pictured in Figure 1.4, some controls dedicated to the control of the roll, yaw and pitch attitudes and to the trajectory of the aircraft, such as ailerons, rudder, elevators, landing gear, are called the primary flight controls (PFC).
Secondary flight controls make it possible to modify the aerodynamic configuration during
particular flight phases and are dedicated to the control of the lift of the wing, such as spoilers, flaps, slats, landing gears and some trim controls, [2].
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These surfaces are driven by actuators and their operational architecture is shown in Figure 1.5. It can be represented considering the signalling and powering flows. Following these two lines, there are four main sections: man-machine interface (MMI), flight control computer (FCC), power source and actuators. MMI is the interface between pilots and aircraft, like the control sticks, pedals and display screens. It is in charge of communicating with pilots, receiving orders and displaying the aircraft operating information. The autopilot is a common device on modern aircrafts used to substitute pilots who controll the flying trajectory and keep the stabilization during cruise. The pilots and the autopilot give out the position demand for actuators according to flight attitude and transfer it to the FCC. The latter collects the position demand and sensors’ signals and calculates the control orders for power modulating device. Meanwhile the FCC supplies the flight envelope protection to prevent the pilots from controlling commands that would force the aircrafts to exceed its structural and aerodynamic operating designs. In the end, the actuator drives the flight control surface to the demanded position in response to the demand signals [7].
Figure 1.5 Configuration of flight control system.
As the actuator is the mechanical executive device in this flight control actuation system, its static and dynamic behaviors have significant effects on making the upper performance to be satisfied. The selection of an actuator device is imposed mainly by the
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power requirement of the load, which is determined by the aerodynamic forces and the speed of response. A flight vehicle can be better controlled when its static stability is marginal. If the vehicle is passively unstable and it diverges too fast, then the actuator has to respond sufficiently fast in order to catch up with the instability and prevent it from diverging. If the vehicle is too stable, on the other hand, it requires a lot of actuator power in order to manoeuver it. Other factors to be considered for the selection of an actuator include the dynamic characteristics, the power sources available, the reliability of the equipment, and other physical and economic limitations. Therefore, sustained efforts are given on the technology innovation of actuators.
In the conventional aircraft, the actuation system of the flight control surfaces is realized by a centralized hydraulic system, constituted by an hydraulic pump and hydraulic motor drives positioned in the fuselage, plus several fluid pipelines and hydraulic actuators positioned in the wings and tail surfaces. The control of the hydraulic actuators is realized with the well-established “fly-by wire” technology, where no mechanical links between the control surfaces and the cockpit handles are present. But, the current trend is to replace those hydraulic systems with the most important technologies used to pursue MEA path:
“Electro-hydrostatic Actuators” (EHA) and “Electro-Mechanical Actuators” (EMA). In
Table 1.1, is summarized the history of actuator innovations on commercial aerospace and it is also forecasted the future developing [8].
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Table 1.1 Summary of each technology innovation of actuator, [8].
The idea to control each surface with an own directly coupled EMA is a must, and this concept is defined as “power-by-wire” [8]; in fact, EMA and EHA are also called as Electrically Powered Actuators (EPA) which are actuated by electric power. The two actuation systems have the same energy source, electric control unit (ECU), electric power unit (EPU) and motor. The unique difference between EHA and EMA is that EHA uses hydrostatic transmission to take the place of mechanical transmission in EMA (Figure 1.6-Figure 1.7).
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Figure 1.7 Block diagram and energy transmission of EMA, [2].
At the state of art, electro-hydrostatic actuators appear to be a more mature and more reliable technology than electro-mechanical ones; for these reasons, in more electric aircrafts, the firsts are preferred to the seconds in most of the important applications such as primary flight controls. In the Table 1.2 are shown the features of EM and EH actuation systems.
Both EMAs and EHAs require an electric motor and an inverter. In a self-contained unit, EHAs include a reversible hydraulic pump, a cylinder, and a reservoir of hydraulic
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fluid. EHAs are attractive in future aircraft, as they eliminate the external hydraulic source and piping systems. Hence, EHAs are considered advantageous because of weight, volume, dispatch reliability, and cost advantages. Conversely, EMAs do not use any hydraulic power, but instead a gearbox and/or mechanical system to transfer rotary motion to linear motion, similar to a jack screw. This allows the EMA motors to run as reversible hydraulic pump directly. Fig.1.8 shows a comparison of the EMA and EHA systems .So, compared to an equivalent EHA, EMA has other advantages:
It is lighter, smaller, and less complex;
It tends to be stiffer, since there are no hydraulic fluid in the load path, and more efficient, because there are no winding losses or pump inefficiencies; It is better suited to long-term storage or space applications, since there is no
potential leak.
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Table 1.3 Summary of property of FBW actuators, [9]
As summarized in Table 1.3, EMAs are still not mature enough to totally replace the SHAs in primary flight control systems, at least in front line. So, the actual development trend concerns a “point to point replacement”. As said previously, in a few applications, EMAs have been implemented mainly for the secondary flight controls, and more recently 5 EMAs were involved in the spoilers and THS (Trimmable Horizontal Stabiliser) on Boeing 787. The figure 1.9 shows this development.
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Figure 1.9 Development from early FBW system to recent applications, [10]. In Fig. 1.10 is illustrated the future vision concerning the introduction of the EMAs in aircraft flight control systems; power source types are located in the vertical axis on the left (M=Mechanical, H=Hydraulic, E=Electrical), actuator type on the right.
As a result, compared to an EHA, EMA is more efficient and is a better option for leak-free operation. The fundamental aspects that characterize the safety critical systems of the aeronautical components are the stringent reliability requirements, such as those established by the JAA (Joint Aviation Authority). However, due to safety and reliability reasons, mainly concerning the jamming vulnerability (gearbox or ballscrew for rotary-to-linear movements), the air framers have still now some concerns using EMAs for primary flight control surface preferring the most reliable electric-hydraulic actuators (EHA). In the EHAs there is still an hydraulic circuit, but it is just confined in each actuator to transmit power from the electric motor to the surface. This is a major challenge that needs to be addressed if EMAs are to become a viable option for critical safety applications, such as primary surfaces and landing gear deployment [5].
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Figure 1.10 Scenario of the EMA introduction in aircraft flight control systems, [8]
1.1.3 Typical EMA solutions
According to the motion transfer way, currently, two main types with linear (geared or direct drive) and rotary output EMAs are in the focus of research and development activities (Fig.1.11).
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The main components of electromechanical actuator are listed hereafter and the interaction between them is shown in Fig 1.10.
Electric motor; Gearbox;
Screw jack (for Linear EMAs) or output shaft (for Rotary EMAs); Sensors;
Power electronics; Control electronics.
Figure 1.12 Schematic and some application of EMA.
Linear EMAs can be divided into two types: direct drive and gear drive. In the direct drive, the nut/screw is directly driven by the motor and stiffly connected to its rotor or stator; with the rotation of the motor, the screw is driven to extend and retract. In gear drive, the nut/screw and motor are individually installed and a gearbox is used to connect motor and nut. Generally, the direct drive type is more compact and lighter. The gear drive type is more maintenance friendly. A current amplifier supplies the DC current required to drive the motor. The motor generates the power to rotate the load. At the end of the motor’s rotor there is a small gear driving a gearbox producing a higher torque. The gearbox is connected to a screw gear that has a spiral screw type of mechanism that rotates. When the
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screw mechanism rotates, it converts the rotational motion from the motor to translation that extends or retracts the shaft and pushes against the control surface. One side of the actuator is attached to a stiff point on the aircraft structure and the other end of the shaft is attached via a linkage mechanism to the surface and causes it to pivot on the hinge.
Electric Motor
For the electric motor, the technology used in EMAs applications is a three-phase synchronous brushless DC electric motor (BLDCM) ,with integrated power electronics, that operates the motor from a direct current supply. It is within the family of “Permanent
Magnet Synchronous Motor” (PMSM); in other words, it is an electric machine with
windings on the stator and permanent magnets on the rotor. Permanent magnets and windings generate two magnetic fields, and their interaction involve a torque generation and then the motor shaft rotation (Figure 1.13). In the BLCDM, the switching logics performed on the power bridges is simpler and the overall reliability is higher. On the other hand, the phase currents are characterised by higher harmonic components and the torque ripple can be an issue, it depicts a limitation of motor performances related to thermal aspects: torque implies current and the heat generated for Joule effect can induce malfunctions.
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Figure 1.13 Exploded view of a brushless motor, [13].
Mechanical transmission
The mechanical transmission of the motion from the motor shaft to the control surface takes place through the use of a gearbox and/or a jack-screw. It can be said that the performance of a control surface of an aircraft is characterized by high hinge moments and low angular speed so the main problem is the coupling with the high powers of electrical motor .For EMAs, comes the need to combine a high power electric motor with a low power mechanical transmission. As a solution, the use of planetary gearbox coupled with a roller screw can lead to excellent results.
Gearbox -
The gearbox has the function of connection between the motor and the output, introducing a reduction ratio and allowing optimum motor operation. This involves that the motor can rotate at different angular velocity compared to the output. In some19
cases, moreover, the presence of gearbox becomes necessary to obtain in output high torques that the motor would not be able to provide. For example, in rotary application, output angular velocity is often less than motor one; consequently output torque results greater than torque generated by the motor. In Fig 1.14 is shown an example of planetary gearbox with a detailed view on the two stage mechanism which consists of planet gear, sun gear, ring gear and planet carrier.
Figure 1.14 Example of planetary gearbox.
Screw Jack -
A screw jack is necessary to convert rotational motion to linear motion. The common used screw mechanism are ball-screw and roller-screw. The ball-screw has lower friction but with lower load capacity. The roller-screw has better load capacity but with higher friction. Anyhow, these typologies differ for the architecture but not for the working principle [9]. Screw jacks are susceptible to jamming, particularly when operating under vibration and dynamic loads, so many research efforts have been made on the developing and testing roller-screw solutions. The roller screws are divided into planetary and recirculating; the main difference between these two types is the fact that in the first the rollers do not rotate around the screw’s axis but only around their own axis. There are also differences in the contact surfaces because in one case they are helicoidals (planetary) and in the other case they are just perpendicular to the roller axis (recirculating). But there20
are more contact points with these configurations than ball screw. Planetary roller-screws is based on the kinematics that emulate a planetary gearbox. The roller are screwed and they are coupled with both the screw jack and the screwed nut. The motion of the rollers is like that of a satellite in a planetary gear: the screw jack acts as the sun of the planetary gear transmitting the rotation to the rollers which move as satellites for the ring gear connection, and the nut moves axially thanks to the screws transmission of the rollers.
Figure 1.15 Planetary roller-screw, [14].
Power and control Electronics
The power electronic s constitute the heart of motor drives; it works between the control electronic and the motor. The power electronic comprehends all the electronic components and devices used for generating the phase currents starting from the electrical voltage supply; it has the task of evaluate the signals deriving from control electronic and amplify them to drive the motor phases with congruent voltage amplitude, referred to its operating characteristics.
The coil drive in the motor phases can be obtained via three-state PWM (Pulse Width Modulation) technique. The voltage applied to the motor coil is modulated by switching the DC voltage supply (Vsupply) between three states: +Vsupply, 0 and −Vsupply. To accomplish this task, a switch circuit and a three-phase power inverter can be used; the structure is shown
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in Fig. 1.16 where VA, VB and VC are the voltages applied to the star-connected motor windings and Vsupply is the continuous inverter input voltage [15].
Figure 1.16 3-phase motor connected to a 6-switches power electronics, [15]. The PWM coil drive is characterised by high-frequency switching cycles associated with elevated levels of electrical power in the circuits. In other words, this is obtained by electrically switching the DC power supply through a power bridge network composed of semiconductor devices, also called “power switches”. The switches usually used in this kind of application are Metal-Oxide Semiconductor Field-Effect Transistors (MOSFET), which are unipolar voltage-controlled devices that guarantee the characteristics of high-reliability and high-performance required. The PWM duty cycle, that is the time duration and the sign of the voltage level applied to the coil, causes a current in the motor and consequently a torque generation.
The mathematical models used to apply and to analyse PWM duty cycle are Clarke and Park transformations. The Clarke transformation is used in the transition from the stator (A,B,C) system to a two DOF (α, β) system; it has the task to command the activation of the 6-switches in such a way as to generate a voltage space vector used in SVPWM technique (Space Vector PWM). The Park transformation is used in the transition from the stator (A,B,C) system to a three DOF (d,q,0) system; it allows you to control the three-phase motor like a mono-phase equivalent motor [16].
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The EMA control electronics comprehends all the electronic components and devices used to implement closed-loop control functions (e.g. on currents, motor speed, and actuator position) and to provide the necessary signals for health monitoring functions [14].
1.2 EMA Basic Fault Modes
Actuator failure modes vary depending on application and actuator type and are manifested by output responses that shift over time from expected values for given input (command) signals. However, engineering experience indicates that there are some common failure modes of specific interest for the diagnostics and prognostics. In the case of EMA system, three categories of failure modes can be defined, depending on the type of system loss of functionality:
Mechanical/structural failure; Electric failure;
Electronic failure.
The dominant failure mechanisms are generally mechanical in nature. EMAs are the power execution and output mechanism of the servo actuation subsystem and their failure usually have the big relationship with the working condition of the system and intrinsic factors [19]. Each loss of functionality can derive from different types of fault to components or assemblies, which are characterised by different probability of occurrence and safety effects at EMA system level.
Through an exhaustive research including the Fault Tree Analysis (FTA) method, an EMA failure modes analysis were performed in [19] (which are referred to a linear direct drive ball-screw EMAS); the results are summarized in Table 1.4 where only mechanical/structural failures are shown, considering that in this work we are interesting in mechanical Freeplay (Backlash) fault. Three qualitative parameters were also used: RP (Relative Probability) and RC (Relative Criticality), scored from 1 (low probability/criticality) to 10 (high probability/criticality), and = [( ∙ )/100]
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accounting for the relevance of the component/assembly fault for the system safety assessment. Hence, a fault tree were established for the system top-level by differentiating two types of loss of functionality (loss of performance and loss of control); the Figure 1.17 and Figure 1.18 show the fault trees where, once again, is highlighted only the mechanical part.
24 . Table 1 .4 E MA typic al fai lure mode s, [1 9] .
25
Figure 1.17 EMA fault tree: system top-level, [19].
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1.3 Importance of Health-Management in EMAs
The integration of EMAs in commercial aircrafts, as said previously, is still reduced to non critical applications. For a more general use of EMAs in commercial aircrafts, the latter must prove to achieve the same level of safety and reliability as systems based on hydraulics actuators. In spite of the fact that only a few jams have been reported, jamming is one of most feared fault modes in EMAs. Jamming occurs because the load is transmitted through mechanical contacts under very high Hertz stresses, thus fatiguing the materials, especially on the races where balls roll. This fatigue induces the degradation of the contact surfaces, leading to increased power consumption first and finally causing a mechanical jam. The jamming represents a catastrophic failure that makes useless any strategy based on either parallel or grouped actuators topologies.
A variety of mechanical and electrical failure modes can be found in EMAs. Most of the failure modes lead to the loss of control but not to an actuator jam. Depending on the architecture of the EMA, there are several components which can potentially cause a jamming failure: primary bearings that support directly the actuation loads, secondary bearings used to support the rotor or included in the gearbox, gears, as well as screw-nut assemblies. To overcome these issues, which are inherent to the mechanical transmission of loads, two different types of strategies are nowadays being investigated. On one hand, strategies based on isolating the jam failure inside the actuator, either by adding another mechanical channel (duplex actuator) or by the integrating an unlocking device. On the other hand, strategies based on failure anticipation, based on health-management algorithms.
Therefore, the application of electromechanical technology to civil aviation in critical primary flight controls raises a lot of challenges, one of them is the development of HM fault anticipating EMAs system. It is expected that PHM systems will position EMAs closer to achieve the demanded safety requirements. The main benefit of PHM systems is to increase the overall system reliability. PHM systems have two main benefits; on the one hand
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increasing the overall system reliability and, on the other hand, allowing a more efficient maintenance task programming, thus minimizing corrective actions during the actuator service life. Nevertheless, reaching the same level of maturity as for other mechanical systems, such as bearings or gears, will still require an additional research effort in monitoring techniques for EMA assemblies. More specifically regarding linear EMAs, the development of monitoring systems for screw-nut assemblies has recently been demanded by the aerospace industry. These efforts to reach the necessary product maturity regarding the reliability requirements have been oriented basically in two directions. The first direction focuses on the development of specific components for aircraft applications; including power converters, bearings, roller/ball screw assemblies, electrical motors, lubricants or sealing. The second one aims to develop PHM systems capable of anticipating system failures [17].
1.3.1 Monitoring sensors issues
Reliability aspects should also be taken into account when adding new components for PHM in EMAs. Safety cannot be affected due to the introduction of new elements in EMA systems. In fact, additional sensors integrated into the actuator are also prone to failure. Integrating new sensors and electronics, also increases manufacturing costs and EMA complexity, thus reliability of the actuator can be affected. Moreover, the cost of PHM systems, increased by adding new elements, should not be as high as to exceed maintenance cost savings.
For these reasons, a common trend is based on the use of sensors and signals that are already integrated in the EMA, such as consumed currents, rotation and position sensors. Regarding position sensor, these are generally used for two different purposes; both as absolute position feedback for the control and to commutate the motor windings both in case of PMSM or switched reluctance motors. The most used position sensors in EMAs are linear variable differential transformers (LVDT), resolvers, magnetic encoders and hall sensors. The measurement of the currents injected into the motor is easily realizable based on the voltage drop across a sensing resistor. The analogue voltage signal is proportional to the current and can be sampled by a microcontroller/DSP/FPGA based system. A set of
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advanced sensor system of EMA is composed of these sensors. This system shows robustness, simplicity and cost effectiveness, reducing the cost of the monitoring functionality and minimizing the overall EMA reliability. The monitor is completed by this sensor system [17].
1.3.2 Prognostic Approaches to the EMA
Health-Management
Aircraft actuation systems provide critical functionality in a variety of utility, propulsion system and flight control applications. Reliable and consistent function of actuators is vital for the safe, efficient and cost effective operation of the aircraft. Conventional actuator maintenance procedures often rely upon time-based service or replacement of fielded units. This approach in the worst case can result in loss of aircraft due to failure occurring before the end of the estimated component life span. However, since component life is generally estimated in a conservative manner to avoid catastrophic failure, maintenance actions are often performed when not warranted by the actual condition. Modern health monitoring techniques that provide an accurate diagnostic assessment of the current component health enable a transition to Condition Based Maintenance (CBM) where decisions to service or replace components are made according to the current estimated health state. Prognostic Health Management (PHM) systems go beyond purely diagnostic approaches and estimate the progression of component degradation, thereby generating a continuously updated prediction of remaining component life. A PHM approach offers additional benefits beyond purely diagnostic systems by allowing advanced scheduling of maintenance procedures, proactive replacement part allocation, and enhanced fleet deployment decisions based upon the estimated progression of component life usage. Prior studies have demonstrated the process of applying PHM techniques to aircraft hydraulic actuator systems and the resulting benefits. As the role of EMAs in aircraft applications continue to increase, PHM technologies will be a vital part of the Condition Based Maintenance strategy. Prognostics is very essential for PHM, it plays the most effective rule because it represents the predictive part in PHM, which enables no surprises for PHM users especially the maintainers. The location of prognostics in PHM is shown in Figure 1.19.
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Figure 1.19 Prognostics in PHM process, [16].
Prognostics approaches are classified in different ways. Sometimes, the classification is based on the type of available data and knowledge about the system. The prognostics system developers can benefit from these classifications in algorithm selection based on available background about the system and suitable forecasting techniques. Prognostics approaches classification also helps in identifying what techniques from other technologies can be used in prognostics algorithms development. A key point about prognostics approaches classification is building a way to obtain a standard methodology for prognostics applications development within a standard framework. In general, prognostics approaches can be classified into four types:
Reliability based approach; Physics-based approach; Data-driven approach; Hybrid approach.
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The complexity, cost, and accuracy of prognostics techniques is inversely proportional to its applicability (Figure 1.20). Increasing prognostics algorithm accuracy with low cost and complexity is a big challenge.
Figure 1.20 Hierarchy of prognostic approaches, [16].
Reliability-based approach
This approach is used mainly for uncritical, unmonitored components that do not have a physical model and are mass produced. In this approach, assessing the health of individual components in real time considering the operating and environmental conditions is not considered. It depends only on massive historical data about the same components population and its average rate of failure. MTBF was obtained mainly from the original equipment manufacturer and updated during the field operation. This method can be used to be the driver for scheduled maintenance, the maintenance interval of which can be calculated based on the historical usage of a large set of components or on the accelerated tests in case of insufficient data about MTBF of newly used components. Techniques used for this method are solely based on statistics, e.g., Weibull analysis and log-normal and Poisson laws. The advantages of this approach dwells in its simplicity and can be easily
31
applied. It does not require any knowledge about failure modes or system operation. Although the simplicity of this method, it has many drawbacks. The main problem about replacing a part at every fixed interval is that the component-specific conditions are not considered causing either early replacement of working component or late replacement that implies component failure before replacement. It is also hard and inaccurate to apply this approach to newly developed components, because it requires massive failure historical data.
Physics-based prognostics
Physics of failure (PoF) based prognostics is one of the major methodologies used for prognostics and it is located on the top of the pyramid of prognostics approaches as seen in Fig. 1.16. In this approach, a physical model for the system or component is developed. This physical model is a mathematical representation of failure modes and degradation phenomenon. To establish this model, a thorough understanding of the system/component physics is required. In addition to knowledge about the system, knowledge about operating conditions and life cycle loads applied to the system/component are also required. Modelling of the system can be at a micro or macro level. A macro-level model is based on the first principle knowledge about the system to model the relation between its component parts and modelling is performed by mathematical. After establishing the system model, an in situ monitoring of the system is performed, then system diagnosis is used to assess its performance. The model can use the knowledge about the current system health and future scenario about the load exposure to forecast the Remaining Usefull Life (RUL).
Physics-based prognostics has been applied to the systems in which their degradation phenomenon can be mathematically modeled such as in gearbox prognostic module. This methodology is very efficient and descriptive because system degradation modelling depends on laws of nature. It is also accurate and precise, but accuracy and precision depend on model fidelity.
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Data-driven prognostics
Data-driven prognostics approach is the recommended technique when the feasibility study implies a difficulty of obtaining a PoF degradation model. The idea about this approach is to use the measured performance parameters of the system, e.g., pressure, temperature, speed, vibration, current etc. to create a model that correlates these parameters variation to system degradation and fault progression and then use this model for RUL estimation. The creation of this model is solely based on techniques from soft computing, e.g., artificial neural networks (ANN), fuzzy logic, neuro-fuzzy etc., and sometimes techniques from statistics such as regression analysis. Techniques from soft computing are preferable than statistics because of their ability for noise rejection and learning hidden relations between parameters. The key requirement for data-driven prognostics algorithm development is the availability of multivariate historical data about system behavior. These data must cover all phases of system normal and faulty operation as well as degradation scenarios under certain operating condition. Availability of these data for algorithm training is a challenging task, but once the data are available, the creation of the algorithm will not be a matter.
Although the physics-based approach is preferable because of its accuracy, precision, and real-time performance, the data-driven prognostics is more widely spread than the physics-based one in the PHM community. This wealth of available applications based on data-driven prognostics is due to its quick implementation and deployment. Data-driven approach mainly relies on techniques from AI which has its readymade tools that could be applied directly with minor modifications. The low cost of algorithms development and no or little knowledge required about system physics make this approach preferable by prognostics system developers.
As mentioned above, each technique, either PoF or data driven, has some limitations. A fusion approach is combining both data-driven and PoF approaches together to get the best from each, i.e., PoF can compensate the lack of data and data driven compensates the
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lack of knowledge about system physics. This fusion can be performed either before RUL estimation which is called pre-estimate where PoF and data driven are fused to perform RUL estimation or after RUL estimation by fusing the results from each individual approach to obtain the final RUL called post-estimate. Although this approach is used to eliminate the drawbacks of PoF and data-driven methods and gain their benefits, it also carries the disadvantages of both methods to a certain extent, but of course not by the same level if each technique is used individually. The Kalman filter which is adaptive in nature and particle filter are used for the implementation of this methodology.
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Chapter 2
Electromechanical Actuator
Dynamic Model Description
This chapter illustrates the model of the EMA dynamics used as reference for this work. The model, developed in parallel research activities [21], has been used for the design and performance analysis of the actuation system of the nose-wheel steering of a light military trainer, and is characterised by a high level of detail, allowing to simulate failures, malfunctions and non-linearities.
The model has been used as reference for the mechanical, electrical and electronic sections and has been adapted for addressing the flight control application: the mechanical part have been modified with the introduction of mechanical freeplay modelling (which is the focus of the prognostic algorithm that will be discussed in the next chapter), while the loads section is strongly simplified.
The electromechanical actuator main components are (Figure 2.1):
Brushless DC motor; Electro-magnetic clutch; Spur reduction gearbox;
Three stage planetary reduction gear; Resolver;
Current sensors.
As it can be observed in Figure 2.1 the motor with the clutch and the three-stage planetary reduction gear with the output shaft are mounted on two different parallel axis. The spur gearbox transmits motion from the motor axis to the output shaft axis. The spur
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gearbox does not introduce a reduction ratio. The electro-magnetic clutch located between the motor and the spur gearbox has been introduced to comply the flight safety requirements of the actuator and functions as a backup disconnect mechanism in case of mechanical failures in the drive system. In fact, in case of failures, the opening (release) of the clutch allows
Figure 2.1 Sectional view of the EMA, [21].
to disconnect the two components. These failures can be the actuator jamming, the lost of electrical supply or the control unit failure.
2.1 Dynamic system model description
The developed EMA overall Simulink® model is shown in Figure 2.2. Hereafter, it will be described in detail the principal blocks composing this model, which are:
Three-phase motor;
Park transform and inverse Park transform; Power electronics;
36 Digital control loops;
37 Figu re 2 .2 Overa ll Sim ulink mode l
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2.1.1 Brushless Motor
The 3-Phase BLDCM model has been developed on rotor reference frame as shown in Figure 2.3, where only a couple of magnetic poles is depicted to simplify the sketch. For this, the following assumptions have been considered:
Hysteresis, saturation, and others motor magnetic non-linearities are neglected; The motor is magnetically symmetrical with respect to its phases;
Permanent magnets are made of rare-earth materials and their magnetic reluctance along the quadrant axis is infinite with respect to the one along the direct axis;
Motor phases are magnetically decoupled;
Reluctances due to others motor ferromagnetic parts are neglected.
Figure 2.3 3-phase PMSM schematics (one pole pair), [21]. The motor electrical equations are given by Eq. (2.1).
⎩ ⎨ ⎧ ᵘ = ᵔᵅ + ᵎᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ sin(ᵊ ᵲ ) ᵘ = ᵔᵅ + ᵎᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ sin(ᵊ ᵲ − 2ᵰ 3) ᵘ = ᵔᵅ + ᵎᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ sin(ᵊ ᵲ + 2ᵰ 3 ) (2.1)
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where ᵊ is the number of pole pairs, ᵔ is the phase resistance, ᵎ is the phase self-inductance, ᵰ is the magnetic flux linkage and ᵲ is the motor mechanical angle.
To determine the torque provided by the motor, it is necessary to multiply each electrical equation by the respective phase current. This operation produces the system power balance. In reference to Eq. (2.2) it is possible to define the electrical power input (terms at the left hand of Eq. (2.2)), the Joule losses (first terms at the right hand), the electrical power exchanged through the inductances (second terms) and the mechanical power output (third terms).
⎩ ⎨ ⎧ ᵘ ᵅ = ᵔᵅ + ᵎᵅ ᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ ᵅ sin(ᵊ ᵲ ) ᵘ ᵅ = ᵔᵅ + ᵎᵅ ᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ ᵅ sin ᵊ ᵲ − 2ᵰ 3 ᵘ ᵅ = ᵔᵅ + ᵎᵅ ᵠᵅ ᵠᵐ − ᵰ ᵊ ᵲ ̇ ᵅ sin ᵊ ᵲ + 2ᵰ 3 (2.2)
From the mechanical terms of Eq. (2.3), it is determined the motor torque by eliminating the rotor speed term and obtaining:
ᵖ = −ᵰ ᵊ ᵅ sin(ᵊ ᵲ ) + ᵅ sin ᵊ ᵲ − 2ᵰ
3 + ᵅ sin ᵊ ᵲ + 2ᵰ
3 (2.3)
Applying the Park Transform it is possible to express the torque referring to the rotor magnetic system (ᵅ , ᵅ , ᵅ ) with ᵅ obtaining the Eq. (2.4) which is also useful to
determine the value of ᵰ .
ᵖ = 3
2ᵰ ᵊ ᵅ = ᵍ ᵅ (2.4)
The above equation shows that the torque depends on the current on the quadrant axis (ᵅ ), so, this is the parameter to control and that allows the control of the torque and then the motor. This statement allows to understand the meaning and the great usefulness of the
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Park transform. In Figure 2.4, is shown the 3-phase motor implementation in the Simulink overall model [21].
Figure 2.4 3-phase motor dynamics structure.
2.1.2 Park Transform
The Park space, as already said, is a three DOF time-invariant system in which the stator (A,B,C) is transformed into a three DOF (d,q,0) rotor magnetic system; it is used to control the spatial relationship between the stator vector current and the rotor flux vector. In the Simulink model (Figure 2.5), the Park transform is used to transform the current phases sensor signals (ᵅ , ᵅ , ᵅ ) relative to the motor phases, into the set of three current (ᵅ , ᵅ , ᵅ ). The firsts two represent respectively the feedback of the quadrant current regulators and of the direct current regulator.
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Figure 2.5 Park transform Simulink block.
The equation containing in the above Matlab function block of Simulink and related to the Park transform are the following:
⎩ ⎨ ⎧ ᵅ = 2 3 ᵅ cos ᵲ + ᵅ cos ᵲ − 2ᵰ 3 + ᵅ cos ᵲ + 2ᵰ 3 ᵅ = − 2 3 ᵅ sin ᵲ +ᵅ sin ᵲ − 2ᵰ 3 + ᵅ sin ᵲ + 2ᵰ 3 ᵅ = 1 3(ᵅ + ᵅ + ᵅ ) (2.5)
It is worth noting that the Park transform needs information regarding the motor electrical angle ᵲ , that is related to the motor mechanical angle ᵲ by the following relation:
ᵲ = ᵊ ᵲ (2.6)
The inverse Park transform is used in the Simulink model (Figure 2.6) to generate the three voltage amplitudes ᵘ , ᵘ , ᵘ to provide to the power electronics; these are determined starting from the quadrant voltage amplitude signal ᵘ and the direct voltage amplitude signal ᵘ , provided by the respective current regulator.
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Figure 2.6 Reverse Park transform Simulink block.
Like for the Park transform, the equation containing in the above Matlab function block of Simulink and related to the reverse Park transform are the following:
⎩ ⎨ ⎧ ᵘ = 2 3 ᵘ cos ᵲ − ᵘ sin ᵲ ᵘ = 2 3 ᵘ cos ᵲ − 2ᵰ 3 −ᵘ sin ᵲ − 2ᵰ 3 ᵘ = 2 3 ᵘ cos ᵲ + 2ᵰ 3 −ᵘ sin ᵲ + 2ᵰ 3 (2.7)
2.1.3 Digital Control Loops
The control electronics architecture implemented in Simulink is based on four items control regulators related to the four closed loops of the system realized in [21] and which are: the current loop (direct and quadrant), the speed loop and the position loop (Figure 2.7). Each closed loop works at the same frequency of 10 kHz. It can be observed that, due to the presence of the three-phase motor, it is required control on the quadrant current and on the direct current. For this reason, there are two current closed loops and then two current regulators.
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Figure 2.7 Control electronics model.
The quadrant current regulator, shown in Figure 2.8, have as input the quadrant current measured by the sensor, i_q_sens, and the quadrant current requested, i_q_dem that derives from the upstream speed regulator. The output of this regulator is the requested quadrant voltage amplitude V_q_dem.
Figure 2.8 Quadrant control regulator dynamics.
The direct current regulator is shown in Figure 2.9. It can be remarked on how it has the same architecture of the quadrant current one, and the same values of the gain and the zero of the PI control. The difference is that its input reference i_d_dem is always equal to zero.
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Figure 2.9 Direct control regulator dynamics.
The speed regulator model schematics is shown in Figure 2.10 where omega_m_dem represents the reference input derived from the upstream position regulator and
omega_m_sens represents the motor velocity measured by the resolver. It is worth noting
that in reality the resolver measures the motor angular position; this data must be derived to obtain the angular velocity. For this purpose, as seen previously in Figure 2.2, it is used a discrete filter instead of a discrete derivative Simulink block because it is noted by experimental evidence that the filter generates a lower noise compared to the derivative.
Figure 2.10 Speed regulator dynamics.
Finally, it is shown in Figure 2.11 the position regulator model. The inputs are
theta_out_i which is the command signal derived from the pedals sensor i.e. the requested
control surface position, and theta_out_sens which is the signal measured by the RVDT. The output is the requested motor speed omega_m_dem. In this regulator, it is also present the discrete implementation of the AntiWindup system.
