Scholarly article on topic 'Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows'

Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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{"Bond Graph" / "Electro-hydrostatic actuator" / "Electromechanical actuator" / "More electric aircraft" / Modelling / Power-by-wire / "Power loss" / Simulation}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Fu Jian, Jean-Charles Maré, Fu Yongling

Abstract In the aerospace field, electromechanical actuators are increasingly being implemented in place of conventional hydraulic actuators. For safety-critical embedded actuation applications like flight controls, the use of electromechanical actuators introduces specific issues related to thermal balance, reflected inertia, parasitic motion due to compliance and response to failure. Unfortunately, the physical effects governing the actuator behaviour are multidisciplinary, coupled and nonlinear. Although numerous multi-domain and system-level simulation packages are now available on the market, these effects are rarely addressed as a whole because of a lack of scientific approaches for model architecting, multi-purpose incremental modelling and judicious model implementation. In this publication, virtual prototyping of electromechanical actuators is addressed using the Bond-Graph formalism. New approaches are proposed to enable incremental modelling, thermal balance analysis, response to free-run or jamming faults, impact of compliance on parasitic motion, and influence of temperature. A special focus is placed on friction and compliance of the mechanical transmission with fault injection and temperature dependence. Aileron actuation is used to highlight the proposals for control design, energy consumption and thermal analysis, power network pollution analysis and fault response.

Academic research paper on topic "Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows"

Chinese Journal of Aeronautics, (2016), xxx(xx): xxx-xxx

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics

JOURNAL OF

AERONAUTICS

cja@buaa.edu.cn www.sciencedirect.com

REVIEW ARTICLE

Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows

Fu Jian a'b'*, Jean-Charles Mareb, Fu Yonglinga

a School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China b Institut Clement Ader (CNRS UMR 5312), INSA-Toulouse, Toulouse 31077, France

Received 12 January 2016; revised 22 March 2016; accepted 22 April 2016

KEYWORDS

Bond Graph;

Electro-hydrostatic actuator;

Electromechanical actuator;

More electric aircraft;

Modelling;

Power-by-wire;

Power loss;

Simulation

Abstract In the aerospace field, electromechanical actuators are increasingly being implemented in place of conventional hydraulic actuators. For safety-critical embedded actuation applications like flight controls, the use of electromechanical actuators introduces specific issues related to thermal balance, reflected inertia, parasitic motion due to compliance and response to failure. Unfortunately, the physical effects governing the actuator behaviour are multidisciplinary, coupled and nonlinear. Although numerous multi-domain and system-level simulation packages are now available on the market, these effects are rarely addressed as a whole because of a lack of scientific approaches for model architecting, multi-purpose incremental modelling and judicious model implementation. In this publication, virtual prototyping of electromechanical actuators is addressed using the Bond-Graph formalism. New approaches are proposed to enable incremental modelling, thermal balance analysis, response to free-run or jamming faults, impact of compliance on parasitic motion, and influence of temperature. A special focus is placed on friction and compliance of the mechanical transmission with fault injection and temperature dependence. Aileron actuation is used to highlight the proposals for control design, energy consumption and thermal analysis, power network pollution analysis and fault response.

© 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/

licenses/by-nc-nd/4.0/).

Corresponding author at: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China. E-mail addresses: fujianbuaa@126.com (F. Jian), jean-charles.mare@insa-toulouse.fr (J.-C. Mare), fuyongling@126.com (F. Yongling). Peer review under responsibility of Editorial Committee of CJA.

http://dx.doi.Org/10.1016/j.cja.2016.07.006

1000-9361 © 2016 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

CJA 726

10 November 2016

2 F. Jian et al.

25 1. Introduction

26 In recent years, increases in fuel costs, a focus on reduced car-

27 bon footprint and the emergence of new competitors have dri-

28 ven the aerospace industry to take steps towards creating

29 greener, safer and cheaper air transport.1 The concepts based

30 on extended use of electricity in "More Electric Aircraft"

31 (MEA) and ''All Electric Aircraft" (AEA) have logically

32 defined the technological shift towards greening aviation oper-

33 ations.2'3 Currently, numerous research activities strive to

34 widen the use of electrical power networks for electrically sup-

35 plied power users (Power-by-Wire or PbW) as a replacement of

36 conventional hydraulic, pneumatic and mechanical power net-

37 works.4 At the same time, PbW actuators have become suffi-

38 ciently mature to be introduced in the latest commercial

39 programmes:

40 - Electro-hydrostatic actuators (EHAs) as backup actuators

41 for primary and secondary flight controls in the Airbus

42 A380/A400M/A350.

43 - Electromechanical actuators (EMAs) as frontline actuators

44 for several secondary flight controls and landing gear brak-

45 ing in the Boeing B787.

47 Although they remove central hydraulic power distribution,

48 EHAs still use hydraulics locally to maintain the major advan-

49 tages of conventional actuators with regard to secondary func-

50 tions (e.g. back-driving, overload protection, and damping)

51 and in response to failure (i.e. easy hydraulic declutch and

52 extremely low risk of jamming). EMAs, however, remove both

53 central and local hydraulic circuits by transmitting motor

54 power to the load through mechanical reducers (e.g. gearbox,

55 nut-screw). Nevertheless, EMAs are not yet sufficiently mature

56 to replace conventional hydraulic servo-actuators (HSA) in

57 normal mode for safety-critical functions such as flight con-

58 trols. Several technical challenges still need to be overcome:

59 weight and size constraints for integration, voltage spikes

60 and current transients affecting the pollution and stability of

61 electrical networks, heat rejection for actuator thermal bal-

62 ance, reduced reflected inertia for dynamic performance,

63 increased service life and fault tolerance or resistance (e.g.

64 for jamming or free-run) for safety.5'6

65 A model-based and simulation-driven approach can

66 unquestionably provide engineers with efficient means to

67 address all these critical issues as a whole. In particular, it facil-

68 itates and accelerates the assessment of innovative architec-

69 tures and concepts,7,8 and their technological embodiments.

70 Introducing all or more electrical actuation raises new

71 challenges:

72 (a) Heat rejection - the temperature of motor windings and

73 power electronics is a key element affecting service life

74 and reliability. Thus, thermal balance is an important

75 issue in PbW actuators. Unlike in HSAs, where the

76 energy losses is taken away by fluid returning to the

77 reservoir, the heat in PbW actuators has to be dissipated

78 locally into surroundings or a heat sink. Simulation of

79 lumped parameter models can provide a detailed view

80 of the temperature and heat flow fields.9,10 Unfortu-

81 nately, these methods are too time-consuming for mod-

82 elling and simulation at the system-level. In addition,

they cannot be used in the early design phases because 83

they are too detailed and require numerous parameters 84

that are not yet known. The heat generated in EMAs 85

comes from a multiplicity of sources: electronic (switch- 86

ing and conduction losses), electrical (copper losses), 87

magnetic (iron losses) and mechanical (friction losses). 88

Accurately quantifying this heat during a reference flight 89

cycle helps determine the operating temperature of the 90

actuator components. 91

(b) Response to failure - safety-critical functions like pri- 92 mary flight controls must have extremely low failure 93 rates (e.g. 10~9 per flight hour). This is achieved through 94 installation of multiple channels for redundancy. How- 95 ever, each channel must have fail-safes to enable the 96 remaining channels to operate correctly. This require- 97 ment introduces another challenge in EMAs, where jam- 98 ming and free-run faults of mechanical components are 99 considered. In HSAs, a fail-safe response to failure (free, 100 damped or frozen) is easily obtained at low mass and 101 low cost by resorting to bypass valves, restrictors, pilot 102 operated check valves or isolation valves. Unfortu- 103 nately, it is no longer possible to transpose the needs 104 in the hydraulic domain to EMAs where clutches, 105 brakes, dampers and torque limiters may be required. 106 Virtual prototyping at the system-level therefore 107 becomes a focus, not only to support conceptual design 108 but also to verify control and reconfiguration strategies. 109

(c) Electrical pollution: the power control of electrical 110 machines (e.g. actuator motor) is based on high fre- 111 quency on/off switching (e.g. 8-16 kHz) of power 112 semi-conductors through pulse width modulation 113 (PWM). Although power is controlled with very low 114 energy losses, it generates high transients in the electrical 115 supply bus and can affect the stability of the electrical 116 network. Moreover, regenerative currents need to be 117 managed properly under aiding-load conditions. This 118 is another reason why model-based systems engineering 119 (MBSE) of PbW actuators calls for more realistic 120 models. 121

All these considerations support developing high fidelity 123

models with a transverse view of the physical domains 124

involved in EMAs. These models have to be properly struc- 125

tured in order to support the MBSE development process 126

and the associated engineering needs: they must be energy bal- 127

anced, replaceable and incremental. This paper reports 128

research that has contributed to this goal. It makes wide use 129

of the Bond-Graph methodology for graphical and qualitative 130

modelling. Bond-Graph modelling11'12 explicitly displays mul- 131

tidisciplinary energy transfers, and the structure and calcula- 132

tion scheme for simulations. Incidentally, it facilitates the 133

design of a model structure that enables incremental or even 134

decremental modelling. In the following sections, the models 135

are developed at a system-level to support various major engi- 136

neering tasks such as control design, component sizing, ther- 137

mal management, power budget and network stability for 138

flight control EMAs. Their main contribution concerns model 139

decomposition versus EMA architecture from a multidisci- 140

plinary point of view and with special consideration of power 141

flows and response to failure. 142

Section 2 describes the EMA under study, focusing on 143

power and signal architecture, coupled physical effects and 144

Modelling and simulation of flight control electromechanical actuators 3

power flows. In Section 3, the EMA power components are modelled with the support of Bond-Graph formalism, paying particular attention to the various sources of energy loss. Section 4 illustrates how the modelling proposals can be implemented in a commercial simulation environment with the example of aileron actuation. In Section 5, the implemented model is simulated in order to highlight its interest for various engineering activities. Finally, the conclusion summarizes the main advances and indicates plans for future work.

2. EMA system description

This study deals with a direct-drive linear EMA. In such an "in-line" EMA, the motor rotor is integrated with the rotating part of the nut-screw. The absence of gear reduction saves weight and offers a high potential for geometrical integration. This design is attractive for aerospace applications because the actuator is compact and easily integrated within the air-frame when the available geometrical envelope is limited. Such an EMA is shown schematically by Fig. 1. When it is applied to flight controls, the load is the flight control surface to which the aerodynamic forces apply. This scheme can also address landing gear actuation applications. In this case, the load is the landing gear leg for extension/retraction or the turning tube for steering.

2.1. Basic components

In this paper, the flight control EMA actuation system consists of the following components:

• actuator control electronics (ACE), which perform closed loop position control

• power drive electronics (PDE), which control the amount of power flowing between the electrical supply and the motor

• an electric motor (DC or 3-phase BLDC/PMSM) that transforms power between the electrical and the mechanical rotational domains

• a nut-screw (NS) mechanical transmission that transforms power between the high speed/low torque rotational and the low velocity/high force translational domains

• sensors of current, speed, position and force if necessary

• a flight control surface, which transforms power between rod translation and surface rotation, through a lever arm effect. This surface is acted on by the aerodynamic forces.

2.2. Control structure

The EMA is position servo controlled. It follows pilot or autopilot demands (pursuit) and rejects the disturbance (rejection) that is generated by the air load. The common way to control the EMA is to use a cascade structure that involves three nested loops: the current (inner) loop, the velocity (middle) loop and the position (outer) loop. If needed, a force sensor can be inserted between the EMA rod and the flight control surface in order to meet the rejection performance requirements through additional force feedback.13 The controller design is generally based on the linear approach and involves proportional and integral serial correctors. However, particular attention has to be paid to structural compliance and power saturation (voltage and current).14

As EMAs naturally include the above-mentioned sensors for the control loop, it becomes possible to develop and implement Health and Usage Monitoring (HUM) functions. In EMAs, different sensors are required to perform the closed-loop position control and protections: motor current and temperature, motor speed, load position and even force to load. The signals delivered by these sensors enable usage monitoring functions to be implemented, without increase in recurrent costs, simply by logging (e.g. peak and mean values). For the same reason, HUM functions can be implemented at a reduced cost: diagnostics detect abnormal levels and determine a faulty device according to its fault signature; prognostics predict the remaining life before a fault generates a failure. HUM is currently investigated for two reasons. First, by enabling on-condition maintenance instead of scheduled maintenance, it contributes to cut operating costs. Second, it is looked at as an attractive means to deal with reliability issues regarding jamming. Although a lot of research effort has been placed on health monitoring of the PDE and EM, robust solutions for health monitoring of the MPT are still at a very low level of maturity. The proposed model of MPT with jamming/ free-run/backlash fault injection provides the designers with a significant added value. It allows the assessment of health monitoring algorithms through virtual prototyping since the effect of faults can be observed without intrusive or destructive effects on real hardware. Therefore, the actuator control electronics (ACE) is also in charge of running the HUM algorithms and reporting the EMA faults to the flight control computers (FCCs).

An overview of an EMA control structure is shown in Fig. 2, where signal and power flows are explicitly differentiated. Xc is

Fig. 1 Schematic of a flight control EMA actuation system.

Fig. 2 Synoptic control structure of an EMA system.

231 the position command (m), C* is the torque reference for motor

232 control (N-m), the Us and Is are the voltage (V) and current (A)

233 of the electric supply, respectively. FL and VL are the force (N)

234 and velocity (m/s) from EMA to drive the load, respectively. Fex

235 and Vex are the disturbance of aerodynamic force (N) and

236 velocity (m/s), respectively. The i, x, x, F are the current (A),

237 rotational velocity (rad/s), position (m), force (N) feedback

238 loops variables, respectively.

239 According to Bond-Graph formalism, power flows are rep-

240 resented using a single-barbed arrow that carries the two

241 power variables (e.g. voltage and current, force and velocity).

242 Full arrows indicate a signal flow that carries only one type

243 of information. Typically, the EMA is position servo-

244 controlled. Usually, position feedback involves a linear vari-

245 able displacement transducer (LVDT) that measures rod

246 extension. The load angular position is used for monitoring

247 purposes. The motor angular position and velocity can be

248 measured by an integrated resolver (sinusoidal commutation)

249 or by Hall sensors (triangular modulation).

250 2.3. Multidisciplinary domain coupling

251 Designing an EMA system requires multidisciplinary

252 approaches for preliminary power sizing and estimation of

253 the mass and geometrical envelope. Unlike an HSA, an

254 EMA generates heat by energy losses, which has to be dissi-

255 pated or stored at the actuator level (except in very specific

256 applications where the actuator can be cooled by a dedicated

257 liquid circuit). Energy is lost in transistor switching (commuta-

258 tion losses), the electrical resistance of wires/windings and

259 power electronics (copper and conduction losses), eddy cur-

260 rents and magnetic hysteresis (iron losses) in the motor, and

261 friction losses between moving bodies. Most of these losses

262 govern the thermal balance of an EMA and are sensitive to

263 temperature. This generates a strong multidisciplinary cou-

264 pling among physical domains, as depicted by Fig. 3. 0 is

265 the temperature (0C), S is entropy flow rate (J/K) and the 0e

266 0c 0i 0f and Se, Sc, Si, Sf are the temperatures and entropy

267 flow rates of the conduction, copper, iron and friction loss,

268 respectively.

269 2.4. Functional power flows

270 In a direct-drive in-line EMA, there are two functional types of

271 motion on the same axis: rotation of the motor rotor and

272 translation of the nut-screw rod. In order to increase the

273 fidelity of the EMA, these two degrees of motion should be

274 considered for any of its components. This enables the rod

275 anti-rotation function and the rotor axial thrust bearing

276 functions to be modelled. In this way, it is possible to consider

Fig. 3 Multi-domain coupling of an EMA for thermal balance.

imperfect bearings (e.g. compliance and friction) and access 277

the reaction forces, e.g. the force and torque at the interface 278

between the EMA housing and the airframe. A second key 279

idea for structuring the EMA model consists of keeping the 280

same topology as the cut-view of the EMA. These two princi- 281

ples are illustrated in Fig. 4. The C and x are power flows of 282

torque (N-m) and rotational velocity (rad/s) for mechanical 283

rotational motion, respectively. The F and V are the power 284

flows of force (N) and velocity (m/s) for mechanical transla- 285

tional motion. The torque and Cm are the motor shaft torque 286

(N-m), xm is the motor rotor velocity (rad/s), xr is the relative 287

rotation velocity in the mechanical power transmission system 288

(rad/s), Ft and Vt are the MPT output force (N) and velocity 289

(m/s). Um and Im are the voltage (V) and current of motor elec- 290

tric supply, respectively. 291

It is important to note that the proposed model architecture 292

also enables the thermal flows to appear explicitly. In the fig- 293

ure, only one thermal body is considered that receives the heat 294

generated from power losses and exchanges it with the sur- 295

roundings. However, the model structure enables individual 296

thermal bodies to be considered for each component or zone 297

of the EMA.10 The detailed modelling of power flows is 298

addressed in Section 3.6. 299

2.5. Model architectures V.S. engineering needs

At the system-level of EMA modelling and simulation, the 301

model depends strongly on the needs of the current engineering 302

task; the best model is never the most detailed one. For this 303

reason, it is particularly important to properly select the phys- 304

ical effects to be considered in order to get the right level of 305

model complexity. Typically, the EMA model can be devel- 306

oped for simulation aided conceptual design (architectures 307

and function), control design, thermal balance, mean and peak 308

power drawn. Since the level of detail is not obviously identical 309

for each component, the EMA should be decomposed into 310

three package models: power drive electronics (PDE), electric 311

motor (EM) and mechanical power transmission (MPT). 312

Table 1 links the engineering tasks to the physical effects to 313

be considered following the proposed decomposition. 314

This approach requires the components' models to be made 315

replaceable, whether each physical effect is considered or not. 316

In the well-established simulation environments, this raises 317

causality issues that are addressed in Section 4. 318

Modelling and simulation of flight control electromechanical actuators

Fig. 4 Functional architecture of EMA model topology with power flows.

Table 1 Model architecture vs. engineering needs.

Model Engineering needs

architecture Functional Power Thermal Natural Stability Consumed Failure Load Reliability

sizing balance dynamics accuracy energy response propagation

Perfect Y Y Y Y Y Y Y Y Y

transformer

Dynamic Y N/A N/A P Y N/A N/A N/A N/A

function

With power N/A Y Y N/A N/A Y P N/A N/A

Perfect Y Y Y Y Y Y Y Y Y

converter

With power N/A Y Y Y Y Y N/A N/A N/A

Advanced N/A Y Y P P Y N/A P N/A

Perfect Y Y Y Y Y Y Y Y Y

transformer

With friction N/A Y Y Y Y Y Y P P

With N/A P N/A P P N/A P P P

compliance

With fault N/A N/A N/A N/A P N/A Y N/A Y

Note: Y means yes; P means possibly but depends on relative level; N/A means not applicable.

319 3. System-level modelling of physical effects

320 The physical effects in EMA are complex and multi-domain:

321 electric, magnetic, mechanical and thermal. Energy balanced

322 modelling is considered an imperative requirement here

323 because of its importance for assessing coupled thermal effects.

This is why Bond-Graph formalism particularly suits the first 324

step of model structure definition. The second step includes 325

re-using (or adapting) models from the standard libraries of 326

commercial simulation software in order to save time and 327

reduce risk (models are assumed to have been tested, validated, 328

documented, and supported and be numerically robust). 329

330 3.1. Power drive electronics (PDE)

331 The function of the power drive electronics is to modulate the

332 power transferred between the supply bus and the motor by

333 actions on the motor winding voltages according to the switch-

334 ing signals sent to the power transistors. Consequently, the

335 PDE can be seen as a perfect power transformer in which

336 power losses come from switching and electrical resistance.

337 3.1.1. Perfect transformer

338 Functionally, the PDE operates as a perfect modulated power

339 transformer, an MTF in the Bond-Graph, between the electric

340 power supply and motor windings. It is driven by the actuator

341 controller, the pulse width modulation function of which out-

puts the duty cycle a, a 2 [—1; 1]

Um = aUs

Im = Is/a

346 3.1.2. Dynamics of the torque control

347 For preliminary design of controllers, it may be advantageous

348 to develop a simplified model that merges the PDE and the

349 motor: the motor current Im is linked to the motor electromag-

350 netic torque Cr through the motor torque constant Km and the

351 dynamics of the current loop, which is modelled as an equiva-

352 lent second order model. Therefore, the electromagnetic torque

353 can be calculated as

s2 + 2^iœis + «2

357 where s is the Laplace variable, and the two parameters

358 xi = 2pf and ni are the current (torque) loop natural

359 frequency (rad/s) and the dimensionless damping factor,

360 respectively. These parameters can be provided by the PDE

361 supplier (typically f is in the range 600-800 Hz while ni is in

362 the range 0.6-1).

363 It is important to note that this model implicitly assumes

364 that the current loop perfectly rejects the disturbance coming

365 from the motor back electromotive force (BEMF). In practice,

366 torque response to torque demand requires a more complex

367 model, including the structure of the controller (e.g. PI control

368 plus BEMF compensation), noise filtering, sampling effects,

369 parameter variation under temperature, and Park transforma-

370 tion for 3-phase electric motors. Some of these effects are

371 introduced into the model implemented in Section 4.3.1. There

372 are no special issues raised by adding the remaining effects.

373 3.1.3. Conduction losses

374 In most chopper and inverter bridge circuits, the basic commu-

375 tation cell involves a solid-state switch (e.g. IGBT) and a diode

376 that serves for free-wheeling by an anti-parallel structure.

377 These components generate energy losses, the R effect in the

378 Bond-Graph, which can be divided into three types: on-state

379 conduction losses, off-state blocking (leakage) losses, and

380 turn-on/turn-off switching losses.15

381 In practice, the off-state blocking losses can be neglected

382 because leakage currents are extremely low.15 When a power

383 transistor or a diode conducts, it generates a voltage drop that

384 is given in its datasheet as a current/voltage characteristic.16

385 This characteristic can be modelled by combining an on-state

zero-current forward threshold voltage Uth (V) and an internal resistance Ron (X). Consequently the voltage drop Ud (V) is expressed versus the root mean square (RMS) current Idrms (A)

Ud — Uth + Ron Idrms

Eswfsw (Eon H" Eoff)fsw

sw Us Us

Therefore, the switching power loss PSw (W) is

Psw — (Eon H" Eoff )fsw

3.2. Electric motor (EM)

At system-level, the electric motor can be seen as a perfect

power transformer in which the torque balance

Cm Cem Cj Cd Ccg

3.2.1. Perfect power converter

The electric motor is an electromechanical power transformer that functionally links current to torque and voltage to velocity (a gyrator GY in the Bond-Graph)

xm — Um/Km

where Km is the motor electromagnetic constant (N-m/A).

389 391

and the associated average power loss Pd (W) is as follows: 392

Pd = Ud/drms (4) 395

For example, the conduction loss Pd of the IGBT men- 396

tioned in Table 4 at rated current is 88.3 W. This corresponds 397

to 2.6% of the rated power. At rated output power, the 398

efficiency of the power switch is therefore 97.4% when only 399

conduction loss is considered. 400

3.1.4. Switching losses 401

At each switching, a phase lag occurs between current and 402

voltage within the electronic component. This induces a very 403

small energy loss at turn-on Eon (J) and at turn-off Eoff (J). 404

However, the resulting power loss cannot be neglected when 405

the switching frequency fsw (Hz) is high (typically in the range 406

of 10 kHz for aerospace EMAs). This effect can be viewed as a 407

current leak Isw (A) that is directly proportional to the switch- 408

ing frequency 409

414 416

To illustrate the order of magnitude, the IGBT mentioned 417 * in Table 4 produces a switching loss Psw of 106.4 W, when 418 fsw is 8 kHz. This represents 3.1% of the rated power. When 419

combined with the conduction loss at rated current, the overall 420

efficiency of the IGBTs (electric power delivered to motor/con- 421

sumed electric power) is 94.3%. 422

At this level, it is important to keep in mind that the effec- 423

tive values of Ron, Uth, Eon and Eoff depend on the temperature 424

of the junction. This may cause a snowball effect. In practice, 425

there is no problem in reproducing this dependency in the 426 model through a look-up table or a parametric model as long 427

as the temperature is available as an input of the model. 428

where Cem is the electromagnetic torque (N-m), Cj is inertial 435 torque (N-m), Cd is the dissipative torque (N-m) and Ccg is 436 the compliance torque (N-m). 437

Cem Km Im

Modelling and simulation of flight control electromechanical actuators

3.2.2. Inertial effect

The rotor inertia Jm (kg m2), an inertance I element in the Bond-Graph, generates an inertial torque

C, = J.^ (9,

Attention must be paid to the fact that the inertial torque involves the absolute velocity of the rotor, which is a time derivative with respect to the earth frame of reference. The inertial torque cannot be neglected for three reasons. Firstly, in very demanding applications, e.g. fighter aircraft or space launchers, the inertial torque takes the ma,or part of the electromagnetic torque during transients (high rate of acceleration or deceleration). Secondly, under aiding load conditions, it impacts the transient back-drivability of the actuator by opposing torque to the load acceleration. Lastly, the kinetic energy stored by the inertial effect must be absorbed when the end-stops are reached in such a way as not to generate excessive force. For example, EMAs reflect a huge inertia at the load level, typically 10-20 times greater than the load itself. Conversely, HSAs only reflect a few per cent of the load inertia.14'17

3.2.3. Dissipative effects

Energy dissipation, modelled by R elements in a Bond-Graph, comes from copper, iron and friction losses.

(1) Electric domain: Copper loss - The primary power loss in the electric domain of a motor (also called Joule loss). Copper loss comes from the voltage drop Uco (V) in motor windings due to their resistance Rs (X) to a current Is (A)

Uco — Is Rs

The associated power loss Pœ (W) is given by

For example, the copper loss Pco of the motor mentioned in Table 4 at rated current is 194.4 W. This represents 5.6% of the rated output power. The associated efficiency is 94.4%.

(2) Magnetic domain: Iron loss - The variation of the flux density in the magnetic circuit of the motor generates eddy current and hysteresis losses. The reversing magnetic field in iron induces a voltage that produces eddy currents due to the electrical resistance of iron. As there is no access to the magnetic quantities during measurements, the effect of eddy currents is commonly expressed as an equivalent power loss. This power loss Ped (W) is modelled by the first member of the Steinmetz equation18 as a function of the eddy current constant ked, the magnetic flux density Bs (T) and the velocity «m

Ped = kedBlat

As a result, the torque loss Ced (N-m) due to eddy currents takes the form of an equivalent viscous friction torque that is given by

Magnetic hysteresis appears within ferromagnetic materials between the remanence flux density and the coerciv-ity (B-H curve). The area of the hysteresis domains represents the work done (per unit volume of material). For each cycle, the magnetic hysteresis generates an energy loss that depends directly on the motor electrical frequency. The hysteresis power loss Phy (W) can be modelled using the second member of the Steinmetz equation18 that links the hysteresis constant khy and the magnetic flux density Bs

Phy — khyBla,

where y is the Steinmetz constant, typically in the range 1.5-2.5.

According to Eq. (14), the hysteresis effect can be modelled globally as pure Coulomb friction

Chy — khyBl

To illustrate the order of magnitude, when the motor mentioned in Table 4 operates at the maximum velocity «max of 314rad/s (3000 r/min), the power loss Ped by eddy current is 14.7 W and the hysteresis loss Phy is 29.1 W. These effects represent 1.2% of the rated output power of the motor.

If a more detailed description is required, hysteresis has to be modelled as a function of the instantaneous magnetic field, e.g. by using switched differential equations.19

(3) Mechanical domain: Friction loss - Power loss Pfm (W) in a motor comes from friction at bearings and drag due to shear within the rotor/stator air gap. The friction torque generated by the hinge bearing is addressed in the next section. The drag friction torque can be modelled as proposed in Ref. 20

3.2.4. Capacitive effect

The variation of the air gap permeance of the stator teeth and slots above the magnets during rotor rotation generates a torque ripple21: the cogging (or detent) torque. This is an energy storage effect that is equivalent to a spring effect, a C element in Bond-Graph. Modelling the cogging effect may be important for two reasons. The cogging torque can be used in some applications as a functional effect to avoid back-drivability. Also, as cogging generates a torque ripple, the frequency of which depends on the relative velocity of the rotor, it may excite the natural dynamics of EMAs and its mechanical environment, potentially leading to vibrations and noise emission.

A system-level representative model of cogging torque Ccg can be expressed versus rotor/stator relative angle hm (rad). It is parameterized by the number np of motor pole pairs and by the cogging torque factor k at motor rated torque Cn (N-m)18

Ccg — kCn sin(wp0m

Ced — kedB^m

The maximum cogging torque can be reduced to 1% or 2% of the rated torque in today's high performance motors22 when it appears as a parasitic effect. Cogging torque in the motor mentioned in Table 4 has a maximum magnitude of 0.1 N-m, which represents 1% of the rated motor torque.

Pco - UcoIs - Rs1

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8 F. Jian et al.

572 3.2.5. Magnetic saturation

573 At flux densities above the saturation point, the relationship

574 between the current and the magnetic flux in ferromagnetic

575 materials ceases to be linear: a given current generates less

576 magnetic flux than expected, as illustrated by the magnetiza-

577 tion curve given in Fig. 5. Consequently, the motor constant

578 drops in the saturation domain. In addition, the inductance

579 of motor windings is also affected by magnetic saturation.

580 Magnetic saturation can therefore be modelled by modulating

581 the motor constant and the windings' inductance as a function

582 of current. For example, the electric motor of an EMA (GSX-

583 40 series) in Ref. 23, the maximum permitted current is twice

584 the steady state current but generates only 30% more than

585 the rated torque. Modelling and simulation of magnetic satu-

586 ration are well documented in bibliography, e.g. in Refs. 24,25

587 3.3. Mechanical power transmission (MPT)

588 The mechanical transmission appears as a rotary to linear

589 power transformer, a TF element in Bond-Graphs. In direct-

590 drive linear EMAs, this transformation is obtained by using

591 a nut-screw. For lumped parameter modelling purposes, the

592 real nut-screw can be decomposed into three parts, as shown

593 in Fig. 6: a perfect nut-screw, a friction loss and a compliance

594 effect (that can represent preload, backlash or pure compli-

595 ance). In the proposed EMA model architecture, the bearings,

596 joints and end-stop are not explicitly considered to be part of

597 the nut-screw model. Consequently the nut-screw model

598 involves 4 mechanical power ports (rotation and translation

599 of nut and screw). An additional heat port enables the nut-

600 screw model to output the heat generated by its power losses.

601 This port also gives temperature to the nut-screw model in

602 order to reproduce its influence on friction and compliance.

603 The order or decomposition has been chosen according to

604 the engineering needs.26

Fig. 5 Magnetic saturation effects on an electric motor.

3.3.1. Perfect transformer 605 When the nut-screw is considered perfect, it achieves pure 606 power transformation between the electric motor and the load 607

with a ratio (2p/p) 608

(Fl = > Cm (17)

[ Vl = ¿«m 611

where p is the pitch (m) of nut-screw. 612

3.3.2. Friction losses 613 The friction of the mechanical transmission mainly comes 614 from bearings, joints and the nut-screw. Friction loss is a very 615 complex phenomenon that is highly dependent on velocity, 616 external load and temperature. This explains why there are 617 numerous types of friction models.27'28 618

(1) Velocity dependent - From the control designer's point of 619 view, the LuGre model is an accurate model of velocity- 620 friction characteristics that has capability to capture static 621 and dynamic friction behaviours.29 However, for a prelim- 622 inary control study, the friction is always modelled as a 662236 pure viscous effect that makes the friction force propor- 624

tional to the sliding velocity. This gives 662257

662278

Ff = feVr (18) 630

where Ff is the nut-screw pure viscous friction force (N), 631

fe is the coefficient of viscous friction (N/(m/s)), and vr is 632

the relative velocity (m/s) of nut-screw. 633

(2) Velocity and load dependence - Friction can be 635 represented in a more realistic way by introducing its 636 dependence on load. For a nut-screw, a five parameter 637 model, Eq. (19), has been identified from experiments 638 for nut-screws by Karam.30 It introduces a constant 639 Coulomb friction (first part), a Stribeck effect (second 640 part) and a load and power quadrant dependent 6431 Coulomb effect (last part): 642

Ff =[Fd +Fste-W="s* + |Fl |(a + bsgn(FLVr)]sgn(vr) (19) 647

where Fcl and Fst respectively are the Coulomb force and 648

the Stribeck force (N), vst is the Stribeck reference veloc- 649

ity (m/s), a is the mean coefficient of external force and b 650

is the quadrant coefficient. 651

(3) Load dependent and load independent - In this 653 approach, friction is decomposed into load dependent 654 and load independent components.16 This model is con- 655

Fig. 6 Proposed model of the MPT.

CJA 726 10 November 2016 ARTICLE IN PRESS No. of Pages 19

Modelling and simulation of flight control electromechanical actuators 9

656 sistent with nut-screw suppliers' datasheets, which pro-

657 vide efficiency (the load dependent friction), as well as

658 the no-load friction under opposite load and the no-

659 drive friction under aiding load (the load independent

660 friction). The velocity effect is added in a second step

661 by introducing its influence on these parameters. The

662 details of this modelling approach have been presented

663 in Ref. 28

Fc, x<0 / / *«>0

Preload F*=KX, Ar

¡/ j/

_J *o '

Backlash: 2*(l

/ / / / Preload

Both types of models are able to reproduce the load effect that is the main contributor to friction in mechanical transmissions like a nut-screw. For any friction model for mechanical transmission, the power loss Ptf (W) is calculated as

Ptf — FfVr

Fig. 7 Compliance model with backlash and preload.

3.3.3. Compliance effect

Obtaining a realistic model of compliance is of particular importance because compliance significantly impacts the dynamic performance14 and the service life of the EMAs. Within EMAs, the mechanical transmission is not infinitely rigid. This makes it compliant due to the elastic deformation of solids under mechanical and thermal stress, in particular at contact locations. In the absence of preload and backlash, the axial mechanical stiffness decreases around the null transmitted force where not all the contacts are fully loaded. This generates the so-called lost motion. When they exist, backlash or preload can also be considered as a compliance effect, a C element in Bond-Graphs, because they algebraically link force and relative motion, as elasticity does (see Fig. 7). Fc is the elastic force (N), F0 is the preloading force (N), ks is the stiffness (N/m), xr is the relative displacement (m), x0 is a proposed single parameter (m) and can be used to reproduce backlash as well as preload in the compliance model.

668 669

680 681 682

688 689

(c) Causal Bond-Graph model of MPT Fig. 8 Causal Bond-Graph modelling of the EMA.

(1) using x0 = 0 models a pure spring effect. The elastic force Fc is purely proportional to the xr, and can be given by

(2) using x0 > 0 models a backlash effect. It displays a total dead-zone of 2x0 and the elastic force Fc is

ks(Xr — X0) Xr > X0

Fc — { 0 I Xr I 6 X0

• ks(xr + X0) Xr < —X0)

(3) using x0 < 0 models a preload effect. The preload force is | F0 | = ks | x0 | and the elastic force Fc is

ks (xr — X0) Xr > —X0 Fc — { 2ksXr | xr | 6 I X0 |

. ks (xr H X0) Xr < X0

For numerical stability and rapidity, the compliance model is implemented by combining Eqs. (21)-(23) in such a way as to avoid switches or "if" functions. The elastic force Fc can be expressed as

Fc — ksjXr — X0 (1 — sign( IX0 I — I Xr I)sign(Xr) — X2rsign(x0)[1 — sign( I Xr I —

Although it is low, structural damping must be considered with compliance in order to avoid unrealistic simulated oscillations. As the physical knowledge about it is very poor, structural damping is usually considered as a linear function of the relative velocity and of damping coefficient ds (N-m—^s)). In order to avoid discontinuities when contact is made or broken, the damping force Fd (N) acting in parallel with the elastic force Fc has to be bounded:

{min(Fc, dsvr) xr > x0

0 | xr | 6 X0 (25)

max(-Fc, dsVr) Xr < — X0

Therefore, the contact force Fct (N) for MPT compliance is the sum of elastic force Fc and damping force Fd:

Fct = Fc + Fd (26)

The power loss due to structural damping Psd (W), 733

although negligible in general, can be calculated to make the 734

nut-screw model exactly balanced with respect to energy: 735

Psd = Fdvr (27 ) 738

3.4. Modelling of faults 739

Simulating the response to failure of EMAs is mandatory if 740

flight control systems are to be verified through virtual integra- 741

tion, particularly to assess the merits of health monitoring fea- 742

tures or reconfiguration after failure has occurred. The main 743

feared events in the power path of an EMA are summarized 744

by Balaban.31 Faults of PDE (e.g. open circuit) and of EM 745

(e.g. winding short circuits or demagnetization) are not consid- 746

ered below because they are addressed in numerous publica- 747

tions.32-34 For this reason, the focus is on major faults that 748

may occur in the mechanical transmission: jamming, increased 749

backlash or reduced preload or free-run. Jamming can be mod- 750

elled by increasing the friction model parameters in order to 751

force stiction. According to the proposed model of compliance, 752

reduction in preload, augmentation of backlash and even free- 753

run can be modelled by increasing the backlash parameter x0. 754

3.5. Sensitivity to temperature 755

The heat flow generated by internal energy losses makes EMA 756

temperature increase. In turn, temperature impacts the energy 757

losses that affect heat flow. This produces a looped effect that 758

cannot be neglected when the intention is to assess the thermal 759

equilibrium or service life of an EMA. The proposed model 760

architecture involves a thermal port for any component. Con- 761

sequently, it can easily enable the temperature to be used as a 762

time variable input in the models of energy losses. 763

3.5.1. Influence on electric parts 764

The on-state resistances, forward voltage drop and switching 765

loss of IGBTs (diodes and transistors) in PDE and the winding 766

resistances in EM increase when the temperature increases. 767

The effect of temperature is rarely documented in suppliers' 768

datasheets or product catalogues. As the energy loss grows 769

accordingly, it causes a snowball effect. However, in the 770

absence of more accurate data, the forward voltage drop and 771

switching loss can be assumed to linearly depend on tempera- 772

ture, like the electric resistance but by a different temperature 773

coefficient: 774

R1 — R0 [1 + £r(@1 — 00 )]

Fc ks Xr

Fig. 9 Schematic of the EMA classical control design.

Modelling and simulation of flight control electromechanical actuators

Fig. 10 Basic EMA model for flight surface control in AMESim.

free-run translation feedback

Fig. 11 Realistic EMA model implemented in AMESim.

where R and R0 are the component resistance (X) at actual operating temperature H (0C) and at reference temperature 00 (0C) respectively, and et is the temperature dependence coefficient of the material resistance (eRon is for the IGBTs ''on" resistance and eRw is for the stator wingdings resistance). The temperature coefficients of IGBTs forward voltage and switching loss can be respectively introduced by eu and es.

3.5.2. Influence on magnets

The increase in motor temperature may decrease the performance of magnets, which lowers the Km. This also can be modelled in a first step as a linear dependency on temperature:

Km1 = Km(1 + £m(©1 — ©0)) (29)

where Km1 is torque constant (N-m/A) at the actual operating temperature, and em is the negative temperature dependence of the magnetic material. This sensitivities of common magnetic materials are illustrated in Ref. 35

3.5.3. Influence on friction

It is well known that friction depends heavily on temperature, represented by Ff (N). Modelling this effect at system-level has been addressed in detail by Mare;.28 A simple approach may consist of using weighting friction as a function of a temperature-dependent factor ~f(0) to modify the advanced friction model in Eq. (19).

Ff = ~f(0)Ff

However, it has to be kept in mind that the effect of temperature on friction is poorly documented, including in suppliers' datasheets.

3.5.4. Influence on dimensions

Temperature variation causes solids to dilate. This leads to variations in dimension and impact preload, backlash and friction. Once again, if a model of dilation is developed, this effect can be easily introduced using the temperature variable of the heat port. For example, the temperature introduced parameter X0 (m) used to present the temperature sensitivity to x0 of MPT compliance model, which can be described by using a temperature-dependent factor ~x(0).

X0 = ~x(©)x0 (31)

This effect can be significantly reduced in design by adequate selection of materials to avoid differential dilation.

3.6. Causal Bond-Graph model

All the above-mentioned physical effects can be considered in a causal Bond-Graph model (see Fig. 8). The Bond-Graph is consistent with incremental modelling objectives that facilitate the progressive development of increasingly complex models. As shown in Fig. 4, the EMA model can be split into three parts in order to explicitly display the physical architecture: power drive electronics, electric motor and mechanical transmission. The Bond-Graph model is augmented by causal marks36 that graphically display the model calculation structure. In this way, it can be verified that the proposed model is consistent with numerical implementation in the commercial simulation software, which still requires algebraic loops and time derivation to be avoided.

The Bond-Graph model of the PDE is shown in Fig. 8(a). The basic element is the perfect and modulated power

Jamming

(c) Advanced mechanical power transmission (MPT) submodel Fig. 12 Advanced supermodels of the EMA in AMESim.

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Modelling and simulation of flight control electromechanical actuators 13

Table 2 EMA controller and load parameters. Parameter

Position loop proportional gain Kp (rad-s_1-m_1) Velocity loop proportional gain Kv (N m s/rad) Velocity demand saturation rnam (rad/s) Torque demand saturation Clim (N m) Current loop proportional gain Kip (V/A) Current loop integral gain Ks (V-ms^/A) Ideal structural stiffness kt (N/m) Ideal structural damping dt (N-s/m) Common surface reflected mass Ms (kg)

4500 0.47 314 10 67.8 17.7 5 x 109 1 x 104 600

Table 3 Motor basic parameters of an EMA.23

Parameter Value

Bus voltage Um (V) 400

Continuous rating current In (A) 6.05

Continuous motor torque Cn (N m) 9.89

Rated speed ron (r/min)) 3000

Torque constant Km (N-m/A) 1.65

Stator resistance Rs (X) 1.77

Stator inductance Ls (H) 0.00678

Lead of screw p (mm) 2.54

Rod mass Mr (kg) 1

Mass of magnetic material MB (kg) 4

Magnetic flux density Bs (T) 2

Rotor inertia Jm (kg-m2) 0.00171

Number of pole pairs np 4

transformer (MTF). The current (or torque) loop can be included as a dynamic function that affects the torque demand. The power losses of conduction and switching can be represented by two dissipative modulated resistor fields (MRS) which link to the thermal port. The switching loss (Rsw) is modelled as a leakage current on the power supply side and is fixed by the switching frequency fsw of the PWM. The conduction loss (Rcd) is modelled as a voltage drop on the motor side, which is affected by temperature as mentioned in Section 3.5.

The Bond-Graph model of the EM is presented in Fig. 8(b). The element GY corresponds to the perfect power transformation between the electrical and mechanical domains. Global inertia (rotor and screw) and motor friction are modelled as mechanical inertance J and resistance Rfm, respectively. The magnetic saturation can potentially be introduced as a modulating signal by its effects on the perfect power transformation between the current in the field windings and the magnetic flux (gyrator GY becomes MGY), where the current is introduced by the flow detector DF element. This can also occur from its effect on the inductance of motor windings (inertance I becomes MI). Copper losses are introduced as a resistance element that generates a voltage drop (1 junction) in the electrical domain. In accordance with the models proposed by Eqs. (13) and (15), iron losses are introduced as the friction loss, so two resistance elements generate torque losses (1 junction) in the mechanical domain. According to Eq. (16), the cogging torque is represented by a nonlinear mechanical capacitance (Ccg). Any power loss (electromagnetic, electric and mechanical) adds to the heat flow at the motor heat port. Only one thermal

node (0 junction) is considered in order to make the model simple. Consequently all effects are subjected to the temperature that is sensed by the effort detector, DE element. However, if a detailed thermal model of the motor is developed, there is no particular issue connected with splitting the thermal nodes into different parts associated with windings, magnets, housing, etc.

The causal Bond-Graph model of MPT is given in Fig. 8(c). A perfect nut-screw is presented as a modulated power transformer (MTF) that operates on the relative rotational and translational velocities of the nut and screw. For this purpose, two 0 junctions are used to generate these relative velocities in case the support motion has to be considered. Inertial effects can be optionally considered so as to meet the causal constraints imposed by the motor or the load model. The friction loss is presented as a dissipative modulated resistor field (MRS) that links to the thermal port. Structural damping in the compliance model is introduced with a resistor field (RS) that also links to the thermal port. The temperature imposed on these RS fields enables the friction losses to be easily made sensitive to this variable. In addition, an effort detector (De) is introduced to obtain the temperature variable for the dilatation model that is ready for implementation within the compliance sub-model. Jamming can be forced by increasing the load independent force that affects the friction loss. A reduction in the preload or an increase in backlash/free-run can also be introduced to model wear or faults by increasing the compliance parameter x0.

4. Virtual prototype and model implementation

The former sections presented the EMA model architecture and multidisciplinary effects that are highly nonlinear. Therefore, analytical studies are no longer adequate and numerical simulation becomes mandatory for assessing architectures and analysing power flows. In this section, a virtual prototype model of a flight control EMA system is built in the multidomain system-level simulation, AMESim, environment. The available libraries offer validated submodels and expert management of integration solvers to give accurate and robust simulation. Re-using the as many available sub-models as possible is an efficient solution that enables the engineer to concentrate on design and not on detailed model making or even on numerical issues. The following sections illustrate how the proposed model architecture and structure enable incremental modelling of the power elements of the EMA during the different phases of development. For this reason, no specific attention is paid to advanced control. The effects of digital control (sampling, quantization and computer time cost) and measurements (sensors, signal conditioning and filtering) are not considered, though they can be introduced easily as reported in Ref. 37

4.1. Control structure

The block-diagram of the EMA control structure under study is shown in Fig. 9. The PDE is a four-quadrant three-phase inverter, and the motor is of the PMSM type. The motor rotor is rigidly connected to the nut of an inverted roller-screw. The flight control surface, not part of the EMA model, is simply modelled as an equivalent translating mass to which the air

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14 F. Jian et al.

Table 4 Advanced parameters of an EMA model.23'40'41'18'42

EMA devices Parameter Value Source

DC supply voltage Us (V) 565 Test bench installation

PWM frequency/sw (Hz) 8000 _r datasheets23 and setting

Transistor resistance in "on" state (Î2) 0.036 -

Transistor forward voltage drop Uilh (V) 0.9

Power Drive Electronics (PDE) Diode "on" resistance fidon (£2) 0.087

(Conduction and switching losses) Diode forward voltage drop f/dth (V) Total referenced switching energy Esw (J) Temperature coefficient êr„„ (1/°C) Temperature coefficient ^ (1/°C) Temperature coefficient e, (1/°C) 1 0.013 0.0042 0.003 0.005 Referenced from IGBT datasheets40'41

Steinmetz constant of hysteresis loss khy 5.8x10 3-

Steinmetz constant of eddy current loss k^ 9.3X10"6

Electric Motor (EM) (iron losses, cogging torque) Steinmetz constant y Factor of the maximum cogging torque X Temperature coefficient êrw (1/°C) 2 0.01 0.0039 Referenced from literature18

Nut-screw stiffness ks (N/m) 3x10s } From suppliers' data-

Nut-screw damping ds (Ns/m) lxlO4 sheets

Mechanical Power Transmission Coulomb friction force Fcl (N) 7590

(MPT) Stribeck friction force F, (N) 4702

(compliance, friction loss) Reference Stribeck speed vst (m/s) 0.035 - Scaled from former experiments42

Mean coefficient of external force a 0.218

Quadrant coefficient b 0.13 -1

Fig. 13 Surface position response simulation.

926 load is applied. Structural compliances at the anchorage of the

927 EMA housing to the wing and at the EMA rod to load connec-

928 tion are merged into a single spring-damper model that is

929 inserted in series between the rod and the load. The controller

930 model implements the common structure of EMA controllers

931 that was introduced in Section 2.2. Two saturation functions

932 are generally inserted to limit the speed and the torque

933 demands, possibly versus flight conditions. Gp(s) and Gv(s)

934 are the position controller and velocity controller, respectively.

935 The current controller Gj(s) is integrated in the PDE model.

936 The s is the Laplace variable. Position feedback is rod displace-

937 ment Xt (m), and the surface/load displacement is Xs (m).

Fig. 14 Motor shaft torque simulation.

4.2. Basic model for control synthesis 938

The basic model has to be simple and linear enough to facili- 939

tate the first step of control synthesis. At this level, thermal 940

effects, electrical supply and fast dynamics are not considered. 941

The PDE and EM make a pure electromagnetic torque 942

generator. The dynamics of the current loop is introduced as 943

a well-damped second order transfer function between the 944

torque setpoint and the electromagnetic torque. Inertia and 945

friction are not detailed at EMA component levels but merged 946

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Modelling and simulation of flight control electromechanical actuators 15

(b) Simulation results in load rejection stage Fig. 15 Comparison of different energy losses.

25 20 15 10 5 0 -5 -10

0.8 0.6 0.4 0.2

1 1 Pursuit Rejection

1.0 Time (s)

20 30 Frequency (Hz) (a) PWM switching simulation and FFT

^ 0.18 <

t 0.12 tu

— FFT of pursuit

— FFT of rejection

: I 1,1 1 1 J . 1 1 1 1 1

Frequency (Hz) (b) PWM average simulation and FFT

Fig. 16 Current pollution network comparison, PWM switching and PWM average.

into global effects. The EMA mechanical compliance is not introduced because it is not a major driver for control design. The resulting basic EMA model implemented in AMESim is presented in Fig. 10.

4.3. Realistic model with physical effects

The causal Bond-Graph of Fig. 8 is used to implement a realistic model considering multidisciplinary effects and power flows. According to the EMA physical architecture, the EMA model, Fig. 11, is split into three main sub-models: PDE, EM and MPT (Fig. 12). It clearly displays the interfaces for power (electric supply, mechanical anchorage and transmission to load, thermal environment), for signal (torque demand, output from sensors) and fault injection (jamming and free-run).

4.3.1. PDE simulation model

The PDE model architecture reproduces the structure of IGBT power management by the usual means of PWM on the DC supply input that provides a variable voltage to the three-arm inverter. The PWM signals are generated by a Clark/Park controller that links the 3-phase (A/B/C alternating current)

reference frame to a rotating frame of two axes, direct and quadrature, in order to implement the field-oriented control38 of the torque loop, as seen in Fig. 12(a). The Idref and Iq are direct and quadrature axes of reference current (A) respectively. In order to make the simulation faster, an average model of the PWM can be used if there is no need to reproduce the dynamics associated with the switching frequency.39 Conversely, at the expense of computer load, the model can be made even more realistic by introducing commutation delays and dead time, passive filters on the supply and motor lines, a supply rectifier and a chopper.

4.3.2. EM simulation model

The standard three-phase PMSM motor model is already integrated into the software model library. However, this model does not consider iron losses, cogging torque, magnetic saturation or hysteresis. Thus, a subcomponent is designed in Fig. 12 (b), which can replace the standard motor model. It implements Eqs. (13)-(16) using standard blocks from the library for signals (functions of one variable) and for mechanics (torque summation, friction, sensors). A specific model is created to provide a speed sum that corresponds to the 0 junctions in Fig. 8(b).

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16 F. Jian et al.

4.3.3. MPT simulation model

On the mechanical side, the perfect roller-screw is modelled using the generic nut-screw element. The friction loss is implemented with a generic piloted translational friction model that handles the numerical issues of breakaway properly. The level of friction force that pilots this element is formed as a function of the transmitted load, the sliding velocity and the temperature. It implements Eq. (19) in the simulation examples. A generic model that can be used to simulate preload or backlash as a function of a single parameter (x0) is not available in the standard library. Such a model can be built according to Eq. (24) (elastic effect) and Eq. (25) (structural damping). The mechanical ports associated with anti-rotation of the screw and anti-translation of the nut are explicitly introduced for connection with the bearing and joint models. Jamming, wear or free-run faults are introduced as signals that can be used to modify the parameters of friction and compliance models. Fig. 12(c) shows the advanced model of MPT.

5. Model simulation for various engineering needs

tasks: control design, energy consumption or thermal balance, pollution of power supply network, response to faults, failure of HUM and temperature sensitivity.

5.1. Control design

The closed-loop performance is usually assessed by quantifying stability, accuracy and dynamics for pursuit (output follows demand) and rejection (output is not affected by disturbances). For this purpose, an aileron position step demand of 10 mm (6% full stroke) is applied at time 0.1 s and then followed by a step aerodynamic force disturbance of 10 kN (40% rated output force) at time 1 s. Fig. 13 compares the simulated responses for three types of EMA models: (a) basic model, (b) advanced PDE and EM model except for MPT (applied by perfect transformer), and (c) full advanced model. Models (a) and (b) output globally the same response with only very little change in overshoot (1% of the step magnitude). Model (c) shows the importance of modelling friction accurately, for pursuit performance in particular. In addition,

In order to highlight the aspects of particular interest in the proposed model architecture and structure, an EMA driven aileron is simulated. The main parameters used in the following simulations are listed in Tables 2-4. The EMA model is run to illustrate how it can support six major engineering

Fig. 17 Surface position response when fault failure occurs for free-run and jamming.

Fig. 18 Surface position response when fault failure occurs for free-run and jamming.

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Modelling and simulation of flight control electromechanical actuators 17

it has to be borne in mind that, due to nonlinearity, responses change with pilot versus airload inputs. Fig. 14 displays the motor shaft torque simulated in four cases: (a) standard model without iron losses or cogging torque, (b) optional advanced model with iron losses only, (c) optional advanced model with cogging torque only, and (d) full advanced model with both iron losses and cogging torque. According to the magnitude of the position step demand, the current is saturated for 70 ms. The motor shaft torque is plotted versus time to highlight the differences, which are torque ripple and torque loss caused by cogging and iron effects, respectively.

5.2. Energy consumption analysis

The same model excitation is used for comparative analysis of energy loss and energy consumption (Fig. 15(a) for pursuit and Fig. 15(b) for rejection). In the absence of motion, when the final load position is reached, iron losses and friction losses become null. Copper and conduction losses remain present when the motor develops torque. Although friction represents the major source of energy loss, the importance of modelling conduction, switching and iron losses is highlighted: they represent up to 11% and 43.5% of total energy loss in the pursuit and rejection modes, respectively.

5.3. Power network pollution analysis

The effect of high frequency switching on driving the inverter arm with PWM is established by comparing the response of the full advanced model, Fig. 16(a) top, to that of a switching

Fig. 19 Temperature sensitivity analysis for heat generation.

model, Fig. 16(b) top, where PWM is replaced by its low frequency equivalent. The PWM generates current spikes on the DC bus, the magnitude of which can reach several times the mean current. Spectrum analysis of the current through a fast Fourier transform (FFT) applied to the time history is displayed on the bottoms of the Fig. 16(a) and (b). For the switching model, it displays the first sub-harmonic and multiple harmonics of the PWM frequency (8 kHz). It should be remembered that the DC bus supply is considered perfect because it is out of the scope of the present work.

5.4. Analysis of wear/ageing and jamming faults

The analysis here focuses on the response to increased backlash and jamming faults. Fig. 17(a) compares the simulated responses of the advanced model for null preload or backlash (0.3 mm backlash), and a preload of 3 kN. Fig. 17(b) displays the simulated surface position when jamming is forced by adding a Coulomb friction (50 kN) at times: (a) 0.22 s (rise stage), (b) 0.27 s (overshoot stage), (c) 0.7 s (stability stage) and (d) 1.2 s (rejection stage). As expected, the position is frozen immediately.

5.5. Analysis of fault to failures for HUM

When focusing on analyses of fault failures to power losses or energy consumption in EMAs, a typical fault of MPT mechanism is selected, which reproduces augmentation of 50% friction force. In order to illustrate the influence of this fault, a specific mission is applied to the models, as shown in Fig. 18 (a), using trapezoidal shapes for position demand (50 mm) and external load (10 kN). Firstly, the simulation result of Fig. 18(a) shows when introducing the fault in MPT, the position error becomes bigger (0.04 mm) than the no fault case. Secondly, as shown in Fig. 18(b), there are an additional 50% friction fault causes: more than 20% power losses and the maximum magnitude of the motor operating current increases nearly 23% for the opposite load (time 1-2 s and time 6-7 s). However, for adding load (time 3-5 s), the power losses increases to 5 times higher, and the motor operating phase current also becomes nearly 5 times larger; thus, the fault influence on an EMA is much more significant.

5.6. Temperature sensitivity analysis

In order to illustrate the ability of the proposed model architecture to simulate the effect of temperature, two figures are plotted below based on the model excitation as directed in Section 5.1. Fig. 19(a) displays the effect of temperature on PDE for heat generated by conduction losses and switching losses that increase by approximately 50% between —40 0C and + 90 0C. Fig. 19(b) shows the effect of temperature on EM for heat generated by copper loss that increases by 67% between the same operating temperature limits.

6. Conclusions

(1) The research presented in this paper is first aimed at architecting models for the system-level virtual prototyping of EMAs. Bond-Graphs were used to graphically

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18 F. Jian et al.

focus on the qualitative dependence between the multi-disciplinary and nonlinear effects that occur in power transmission from supply to driven load. The structure of the model calculation to be implemented in common simulation environments was developed by in-depth consideration of causality, which was facilitated by the introduction of causal marks in the Bond-Graphs.

(2) Since heat rejection is a key issue in the design of aerospace PbW actuators, system-level models were proposed for each source of energy loss in EMAs (power electronics, motor, mechanical transmission). Thermal ports were introduced into the models of components in order to explicitly expel the heat energy loss for each contributor. Additionally, the thermal port enabled models to be made sensitive to temperature and thus reproduce snow-ball effects.

(3) Due to the need to investigate response to failure, verify control robustness and assess HUM strategies, wear and fault models were proposed for mechanical power transmission devices. Jamming was simulated by forcing an increased level of Coulomb friction. Wear (or even free-run) was simulated by action on a single parameter that could be varied continuously to transit from preload to backlash.

(4) The proposed modelling approach was illustrated through the example of aileron actuation for a single-aisle commercial aircraft. The models were implemented in the AMESim simulation environment. It was shown that the above proposals provide engineers with models that can be developed in an incremental way with the advantage of keeping the same model structure during the various steps of simulation-aided development: conceptual design, control design, thermal balance and safety.

Acknowledgements

This study was supported by the Aeronautical Science Foundation of China (No. 2012ZD51) and the authors gratefully acknowledge the support of the China Scholarship Council (CSC).

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Fu Jian is a Ph.D. candidate at the School of Mechanical Engineering and Automation, Beihang University, China. In September 2012, he was financed by the China Scholarship Council (CSC) to pursue his Ph.D studies in France. Currently, he is studying in the Institut Clement Ader (CNRS UMR 5312), INSA-Toulouse, France. His research interests are modelling, simulation and control of PbW actuation systems for aerospace applications.

Jean-Charles Mare is a professor and Ph.D. supervisor at the Institut Clement Ader (CNRS UMR 5312), INSA-Toulouse, France. He received his first degree in mechanical engineering in 1982 and his French Doctorat d'Etat in 1993. His current research activity deals with electrical actuation for flight controls, landing gears and engines. He has been involved in 4 European projects and 5 French competitiveness cluster projects dealing with electrical actuation in aerospace. He works closely with the aerospace industry, including Airbus, Goodrich, Latecoere, Messier and Turbomeca, either for research programs or for scientific support. Since 1995, he has contributed to the design of various actuators test-benches (Eurocopter NH90, Airbus A340-600, A380 and A350, French strategic missile). He is now the chair of the International Conferences on Recent Advances in Aerospace Actuation Systems and Components (R3ASC). Since 1998, he has initiated and organized seven R3ASC conferences.

Fu Yongling is a professor and Ph.D. supervisor at the School of Mechanical Engineering and Automation, Beihang University, China. He received his Ph.D from Harbin Institute of Industry Technology in 1993. His areas of research include aircraft hydraulic transmission control design, industrial robots and efficient high-performance integrated electrohydraulic system manufacturing.