a simpliﬁed model of a fueldraulic xx(x):1–12 the author(s

A simplified model of a fueldraulicactuation system with application toload estimation

Journal TitleXX(X):1–12c©The Author(s) 2017

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Tomas Puller1 and Andrea Lecchini-Visintini2

AbstractIn this work, a simplified model of the compressor variable stator vane fueldraulic actuation system of a jet engineis presented. The actuation system is a sub-assembly of the engine’s Hydro-Mechanical Unit (HMU). A uniquecharacteristic of the actuator is an internal cooling flow which prevents the overheating of fuel. It is shown that theeffect of the cooling flow is well represented by a static input nonlinearity. The resulting model is of the Hammersteinstructure. It is then shown that the model can be used for the estimation of the actuator’s external load. The results arevalidated using an accurate real system simulator.

KeywordsHydraulic actuators, Fueldraulic systems, Position control, Hammerstein model, Aerospace simulation

Introduction

Hydraulic servo-systems are characterised by highpower-to-weight ratios, and the ability to generateforces in locations which are remote and difficult toreach. For these reasons hydraulic servo-systems arewidely used in aviation for the actuation of controlsurfaces and other moving parts. An introductionto hydraulic systems, hydraulic components, physicalmodels, and linearisation techniques, can be foundin Merritt 1 and Jalali and Kroll 2 . Modelling andcontrol applications for hydraulic systems have beenreported under different approaches. These include:control-oriented models,3–6 and PID,7–9 robust,10–17

adaptive and nonlinear18–26 control designs. In some ofthese contributions, full position and pressure feedbackis adopted. However, in aerospace applications,requiring low complexity and high reliability, the use ofpressure sensors within the actuators is often avoided.

In this work, the modelling aspects of the VariableStator Vanes (VSV) fueldraulic actuation system ofa Rolls-Royce Trent 1000 jet engine are developed.Here, the term fueldraulic indicates that, in order toreduce overall weight, the actuator uses pressurisedfuel in place of an hydraulic fluid. The purpose ofthe VSV actuator is to position the jet engine statorvanes in such a way that they attain an optimalangle of attack in all engine operating conditions. Thevanes are mounted in a casing, so that rotation alongtheir shroud-tip axis is enabled, and are joined in aunison ring which enables their uniform actuation.The actuator is located on the intermediate pressurecompressor case, which, during engine operation, is arelatively high temperature zone. As a consequence,a unique feature of this actuator is that its pistonhas an orifice whose purpose is to establish a coolingflow inside the actuator in order to prevent fuel insidethe actuator from overheating. The cooling flow has

a substantial effect on the behaviour of the actuator,similar to that of a sizeable internal leakage. Theactuator is also characterised by asymmetric profiles ofits servo valve’s orifices, resulting in separate low- andhigh-flow zones, which induce a safe slow retraction ofthe actuator in the case of electric power loss.

The internal leakage is a feature in many hydraulicactuators’ models. In the context of QFT and LPVrobust control design,10–13,17 previous contributionshave taken into account the effect of the internalleakage on the linearised dynamics of the hydraulicactuator for the design of the local controllers. Inmore complex adaptive and nonlinear design methodsbased on the use of global nonlinear models18–22,24,25

the internal leak is simply included in the full setof nonlinear equations of the model. In contrast withprevious works, in this contribution, a simplifiedmodel of the global dynamics of the actuation systemis developed, in which the effect of the cooling flowis well represented by a static input nonlinearity. Theresulting model is of the Hammerstein structure, seee.g. Giri and Bai 27 . The input nonlinearity turns outto be either a ‘deadzone’ or a ‘preload’ nonlinearitydepending on the actuator’s external load. To theextent of the authors knowledge, such representationof an internal flow or leakage on the global input-output dynamics of the actuator is a new insightinto the modelling of hydraulic actuators. In theliterature concerned with the modelling for controlof hydraulic actuators, deadzone nonlinearities havebeen considered before, but only to take into account

1, 2 University of Leicester, UK

Corresponding author:Andrea Lecchini-Visintini Department of Engineering, University ofLeicester, University Road, Leicester, LE1 7RH, UK.Email: [email protected]

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2 Journal Title XX(X)

Figure 1. The actuation system: two-stage servo valve andVSV actuator depicted in extending mode.

manufacturing imperfection such as valve overlaps(see e.g. Liu and Daley 7 , Lee et al. 8 , Ye et al. 9 , Mohantyand Yao 20 ). It will be shown that the simplified modelcan be used to estimate the actuator’s external load.This task turns out to be a special case of identificationof a Hammerstein system with an input nonlinearity ofknown structure28. In Bai 28 the identification methodis developed for a one-dimensional parametrisationencompassing different types of input nonlinearities.Here, the algorithms are tailored to the estimation ofthe two-parameter asymmetric input nonlinearity ofthe VSV actuation system model.

The actuation system considered in this work ismanufactured by Rolls-Royce Control Systems (RRCS)in Birmingham, UK. The simplified model and loadestimation algorithm developed in this work areobtained and validated using the Trent 1000 RealSystem Simulator (RSS) implemented in Simulink.The simulations generated by the Trent 1000 RSS areconsidered to be very accurate and are employed byRRCS as surrogate experimental data for developmentand certification purposes. It will be shown that thesimplified model achieves excellent performance witha low computational load.

Fueldraulic servo valve and actuatorThe fueldraulic actuation system treated in this workcomprises a two-stage electro-hydraulic servo valveand an hydraulic actuator. A schematic representationof the system is given in Figure 1. The first stageservo valve, together with a mechanical feedback loopbetween the first and the second stage servo valves,establishes a proportional relation between the controlvariable TMC (variable stator vanes Torque MotorCurrent) and the position of the piston of the secondstage servo valve. The second stage servo valve, basedon the openings of its orifices, establishes supply flows,from a high-pressure manifold at pressure Hp, andreturn flows, to a low-pressure manifold at pressure Lp,to and from the actuator’s chambers. These pressuresare determined by the engine speed and can beassumed to be constant in a given flight condition (e.g.‘Ground idle’, ‘Cruise’, etc..). In extension, orifices 1and 4 are open, and orifices 3 and 6 are closed, while, inretraction, orifices 3 and 6 are open and orifices 1 and4 are closed. Orifices 2 and 5 are always open. In turn,the supply and return flows alter pressures in the head-end (PH) and in the rod-end (PR) chambers causingmovement of the piston. The position of the piston isthe measurable output of the system and is denoted byXVSVA. In the diagram of Figure 1, note the presence ofthe cooling flow orifice.

In this section, the equations that represent the sys-tem in the Trent 1000 RSS are provided. In a prelim-inary conference contribution,29 a simplified versionof the actuation system was considered which omit-ted the cooling flow. Here, a complete representationof the system is provided, with additional technicalexplanations, and, crucially, including the cooling flow,which, as it will be shown in the following sections,has a substantial effect on the system’s behaviour. It ispointed out that some characteristics of the actuationsystem are omitted due to confidentiality. However,these characteristics are entirely outside the scope ofthe analysis and the equations provided constitute arealistic description of the system. In addition, a full setof representative values of the parameters is providedin the section “Simulation results”, which would allowthe interested reader to simulate the simplified model.

The movement of the piston is described by:

xVSVA =1M

(FP + FL) (1)

where M is its mass and FP and FL are internal andexternal loads. The convention adopted is that forcesacting on the piston take a positive sign when directedtowards extension. The force FP is developed by theinternal pressures acting on the piston. It is given by:

FP = AH · PH − AR · PR (2)

where AR and AH are the rod-end and head-endpiston’s surfaces. Note that AH > AR (see Figure 1).The force FL is an exogenous variable which actsalways against the actuator’s movement. In addition,according to performance data, FL is stronger in

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Puller and Lecchini-Visintini 3

retracting mode than in extending mode. This isexplained as follows. The external load is interpreted tobe the sum of aerodynamic (FA) and friction (FF) loads:

FL = FA + FF. (3)

The aerodynamic load FA acts on the stator vanesand is always positive (i.e. supporting extension).The friction FF acts against the actuator movementand is mainly developed in the vanes’ pivots andin the transmission from the actuator to the vanes.This is a complex mechanical linkage, containing alarge amount of moving joints. In comparison, thefriction forces inside the actuator result to be negligible.Hence, the aerodynamic load can be assumed to bealways lower than the friction. Finally, in a given flightcondition, FA and the modulus of FF are assumed tobe constant (see more details at the end of the section).Hence, FL assumes only two possible values: FE

L(negative, in extension) or FR

L (positive, in retraction).The pressures PH and PR are described by compress-

ible flow equations:

PH =B

VH(QH + QHd −QC) (4)

PR =B

VR(QR + QRd + QC) (5)

where QR and QH are flows through the second-stage servo valve and into or from the rod-end andhead-end chambers respectively, QRd and QHd aredisplacement flows caused by the piston’s movement,and QC is the cooling flow. All flows, apart fromthe cooling flow, take positive sign when incoming(i.e. raising pressures). In extension, QH is positive(flow through orifices 1 and 2) and QR is negative(flow through orifices 5 and 4). In retraction, QH isnegative (flow through orifices 2 and 3) and QR ispositive (flow through orifices 6 and 5). The coolingflow QC is considered positive from head-end to rod-end, regardless of the piston’s motion. In addition,B is bulk modulus, which characterises the fuel’scompressibility, and VH and VR are the actuatorchambers’ volumes. These volumes are function ofthe piston position, but their variation is assumed tobe negligible. This can be done because the servo-valve is located on the fan case, while the actuatoris on the compressor case. The manifold betweenthese two elements is relatively long, and contains ahigh volume of fluid, in comparison to the volumeof fluid in the chambers. This assumption, whichin some cases has been already adopted in theliterature see e.g. Thompson et al. 11 , Karpenko andSepehri 13 , introduces a considerable simplification ofthe equations.

Flows QH and QR are determined by the flownum-bers of the respective servo valve orifices. Theflownumber is a parameter integrating the physicalcharacteristics of the orifices with those of the fluid intoa single coefficient in the flow equations (see e.g. Jalaliand Kroll 2 where the term ‘flow coefficient’ is used

Figure 2. Servo valve flownumbers, with highlighted orifices’profiles for the high-flow extension and low-flow retractionmodes

instead). The orifices’ flownumbers for QH and forQR in both retraction and extension are approximatelyequal. Hence, the same variables f R and f E are used todenote the flownumbers, in retraction and in extensionrespectively, for both QH and QR. The resulting flowequations are:

QH =

f E√Hp− PH , in extension,

− f R√PH − Lp, in retraction,(6)

QR =

− f E√PR − Lp, in extension,

f R√Hp− PR, in retraction,(7)

where f R and f E are determined by the openings ofthe servo valve orifices as described in the ensuingequations (11), (12), and Figure 2. The remaining flowsare described by:

QHd = −AH · xVSVA, (8)QRd = AR · xVSVA, (9)

QC = fC sgn(PH − PR)√|PH − PR|. (10)

Note that the superscripts E and R distinguish betweenextending and retracting modes (as in f E and f R) whilesubscripts R and H distinguish between the rod-endand the head-end chambers (as in PH and PR).

The steady-state relations between input currentTMC and the flownumbers f E and f R are describedby:

f E =

KE(TMC− TMC0), TMC ≥ TMC0,

0, TMC < TMC0,(11)

f R =

0, TMC ≥ TMC0,

KR(TMC0 − TMC), TMC < TMC0,(12)



as displayed in Figure 2. The dynamics of the servovalve includes the drive circuit and motor lags and themotion of the piston. This is represented by a dampedthird order system with a cutoff frequency at around10Hz.

The flownumbers profiles depicted in Figure 2implement the safety requirement that the VSVactuator should slowly retract in case of a powerinterrupt. This loads the compressor and slows downthe engine, thus preventing an engine surge in caseof electrical power loss. This behaviour is obtainedby means of a positive TMC0 value, i.e. the currentcorresponding to all orifices closed, and by meansof asymmetric profiles of the orifices. In particular,the reduced gain of the flownumber profile in theretracting mode allows for a slow retraction in the casethat TMC = 0, i.e. a power interrupt.

In summary, the dynamics of the VSV actuationsystem in the Trent 1000 RSS is described by a non-linear dynamical system (equations (1)-(12)) with threestates (velocity xVSVA, head-end pressure PH androd-end pressure PR), one input (the control inputTMC) and three exogenous variables (high-pressureHp and low-pressure Lp, entering in (6) and (7),and the actuator’s loading FL in (1)). Note that thenonlinearity of the system is due to the flow equations(6-10). The Electronic Engine Controller (EEC) of Rolls-Royce engines maintains accurate estimates of Hpand Lp (which are needed for the control of the fueldistribution). Hence these variables can be assumedto be known with sufficient accuracy. Instead, in theTrent 1000 RSS, the aerodynamic loading FA andthe modulus of the friction force FF are calculatedas functions of the engine speed on the basis of anominal relation. Hence, they can also be assumed tobe constant in a given flight condition. However, in realoperating conditions, the relation with engine speed issubject to variations caused by air properties, engineconditions, and other factors. Hence, in a given flightcondition, FA and the modulus of FF can be consideredto be constant but uncertain.

Operating points and linearisation

In this section, in view of the formulation of asimplified model, a linearisation based analysis of thesystem is developed. In order to find the operatingpoint xVSV , PH , and PR are set to 0. The derivationsare carried out separately for the extending andretracting modes because different flow equationsapply. In addition, since the input TMC affects theactuator only through the static relations (11) and(12), in this section, in order to simplify the notation,the flownumber f E (in extending mode), or f R (inretracting mode), are considered to be the actuator’sinput. The subscript 0 denotes input and state variablesat the operating point. In addition, v0 denotes xVSVA atthe operating point. The exogenous variables Hp, Lpand FE

L (in extending mode) or FRL (in retracting mode)

are assumed to be constant. Recall that FEL is negative

and FRL is positive, i.e. always opposing the actuator’s

movement.In the following subsections, the operating points for

the extending and retracting modes are obtained andthen the linearised dynamics is analysed.

Extending modeFrom equations (4), (5) and (6) - (10) one obtains

f E0√

Hp− PH0 − AHv0−

− fC sgn(PH0 − PR0)√|PH0 − PR0| = 0 (13)

− f E0√

PR0 − Lp + ARv0+

+ fC sgn(PH0 − PR0)√|PH0 − PR0| = 0, (14)

and from equations (1) - (3) one obtains

AH PH0 − ARPR0 + FEL = 0. (15)

From equations (13) and (14), one obtains that the ratioof the head-end and rod-end flows can be expressed as√

PR0 − Lp√Hp− PH0

=

=ARv0 + fC sgn(PH0 − PR0)

√|PH0 − PR0|

AHv0 + fC sgn(PH0 − PR0)√|PH0 − PR0|

. (16)

It is now assumed that if v0 > 0 then the cooling flowbecomes negligible with respect to the displacementflow. The assumption is justified by considering thesmall flownumber of the cooling orifice. Under thisapproximation, from equation (16) one obtains that√

PR0 − Lp√Hp− PH0

≈ ARAH

. (17)

The approximate operating pressures PER0 and PE

H0 arenow defined as the solution obtained from equations(15) and (17) (the latter with an equals sign). Theexpressions of the approximate operating pressures are

PER0 =

A2R AH Hp + A3

H Lp + A2RFE

LA3

H + A3R

, (18)

PEH0 =

A3RHp + AR A2

H Lp− A2H FE

LA3

H + A3R

, (19)

and the corresponding cooling flow is given by

QEC0 = fC sgn(PE

H0 − PER0)√|PE

H0 − PER0|. (20)

Expressions (18) and (19) are valid provided thatAH Hp − ARLp + FE

L > 0 which ensures that Hp >

PEH0 and PE

R0 > Lp. Note that for given Hp and Lpthe inequality provides the maximum loading againstwhich the extending mode can be established.

From the equations above, it can be noticed that,under the approximation introduced, the operating



pressures PEH0, PE

R0 depend on Hp, Lp and FEL but

are independent from the input f E0 . Then, for a

given flownumber f E0 , one obtains the operating point

velocity v0 from equations (13) and (14). However, notethat, since PE

R0 and PEH0 were based the approximation

(17), they would not fulfil (13) and (14) for the same v0.Thus, an approximate expression vE

0 of the operatingvelocity v0 is obtained as the arithmetic mean of theoperating velocities obtained from (13) and (14). This isgiven by:

vE0 =

1AH

√Hp− PE

H0( f E0 − f E

S ) (21)

where

f ES =

12

AR + AHAR

QEC0√

Hp− PEH0

. (22)

In (21), f ES represents explicitly the minimum value

of f E0 corresponding to a positive vE

0 . Note that, sincein the derivations a positive velocity is assumed, theexpression on the right-hand side of (21) is meaningfulonly for positive values of vE

0 . Hence, it can beconcluded that, for given Hp, Lp and FE

L , the extendingmode is established for f E

0 > max(0, f ES ).

In extending mode, the two cases PEH0 > PE

R0 andPE

H0 < PER0 can arise. For given Hp and Lp, the actuator

loading FEL discriminates between the two cases. From

(18) and (19) one obtains that PEH0 = PE

R0 when theactuator loading is equal to

FEL =

(AR − AH)(A2RHp + A2

H Lp)A2

H + A2R

. (23)

Note that FEL is negative, since AH > AR. Since FE

L isalso negative, the two cases can arise: FE

L < FEL and

FEL > FE

L . If FEL < FE

L , then PEH0 > PE

R0, QEC0 is positive

(i.e. from head-end to rod-end) and f ES > 0. If FE

L > FEL ,

QEC0 is negative (i.e. from rod-end to head-end) and

f ES < 0. The difference between the two cases is now

illustrated. If FEL < FE

L and 0 < f E0 < f E

S then the valveopening is not enough to establish an incoming flowwhich is bigger than the cooling flow and so vE

0 = 0.Hence, if FE

L < FEL , the extending mode is established

only for f E0 > f E

S . If FEL > FE

L then the flow coming intothe actuator has direction opposite to that of the coolingflow. In this case any f E

0 > 0 is sufficient to establish theextending mode. In particular, a strictly positive vE

0 isestablished for f E

0 = 0+.Illustrative examples of the relation between f E

0and vE

0 are shown in Figure 3 (b) for selectedflight conditions: ‘Ground idle’, ‘Take-off’, ‘Cruise’and ‘Descent idle’. In each case, the correspondingvalues of Hp, Lp, and FE

L were obtained from theTrent 1000 RSS. In the case denoted ‘Cruise outlier’the actuator loading is 20% lower than the nominalactuator loading. In the other cases the loading takesnominal values. It can be seen from the figure thatf ES > 0, in the four cases corresponding to nominal

conditions, while f ES < 0 in the case ‘Cruise outlier’.

In addition, note that the slope of the linear part isdifferent for each flight condition.

Retracting modeFollowing a derivation similar to that presented for theextending mode, with the obvious modification in thenotation, one obtains the following expressions whichdefine the operating point in the retracting mode:

PRR0 =

A3H Hp + A2

R AH Lp + A2RFR

LA3

R + A3H

, (24)

PRH0 =

AR A2H Hp + A3

RLp− A2H FR

LA3

R + A3H

, (25)

QRC0 = − fC

√PR

R0 − PRH0, (26)

vR0 = − 1

AR

√Hp− PR

R0( f R0 − f R

S ), (27)

f RS =

12

AH + ARAH

−QRC0√

Hp− PRR0

. (28)

In this case the expressions are valid provided thatARHp− AH Lp− FR

L > 0 which ensures that Hp > PRR0

and PRH0 > Lp.

In the retracting mode, in contrast to the extendingmode, the actuator’s movement can be established onlyif PR

H0 < PRR0. This is because the rod-end area of the

piston is smaller than its head-end area (see Figure 1).Therefore, since FR

L is positive, the rod-end pressuremust be greater than the head-end pressure in order toenable retraction. This fact can be recovered from theequations. Using (24)-(28) it can be shown that PR

H0 =

PRR0 is obtained when the actuator’s load is equal to

FRL =

(AR − AH)(A2H Hp + A2

RLp)A2

H + A2R

. (29)

Note that FEL is negative, since AH > AR. However FR

Lis positive. Hence only the case FR

L > FRL is possible

which, in turn, corresponds to having f RS > 0. Hence,

vR0 = 0 for 0 < f R

0 < f RS , and the retracting mode is

established for f R0 > f R

S . The expression of FRL in

(29), which appears to be of theoretical interest only,nevertheless will be used to shorten the expressionsused to define the simplified model in the next section.The relation between f R

0 and vR0 is illustrated in Figure

3 (a) for the same flight conditions considered in Figure3 (b).

Linearised modelsGiven Hp, Lp and FE/R

L , linearised models aroundoperating points [PE/R

H0 , PE/RR0 , f E/R

0 ] are obtained bylinearising the flow equations (6), (7) and (10). Thelinearised system has a pair of high-frequency lightly-damped poles (≈ 103Hz). In addition, it can be seenthat the choice of the operating points has verylittle effect on the linearised dynamics since it affectsonly the amplitude of the high-frequency resonance



(a) retracting mode (b) extending mode

Figure 3. Relation between flownumber and velocity in extending and retracting modes for different flight conditions and actuatorloadings. (The profiles shown are for two actuators in parallel in accordance with the simulation cases presented in the last section.)

Figure 4. Bode plots of the linearised dynamics betweenflownumber and velocity in extending mode for the same flightconditions considered in Figure 3(b). The vertical lines indicatethe bandwidth of the VSV actuation control system and thesampling frequency.

peak. This is illustrated in Figure 4 where the Bodeplots of the linearised dynamics from f E to xVSVAcorresponding to the flight conditions considered inFigure 3(b). In each flight condition, changing f E

0 doesnot cause noticeable changes in the Bode plots. In eachBode plot, the low-frequency gain corresponds to theslope of the linear part of the corresponding graph inFigure 3 (b).

High-frequency lightly-damped poles are a com-mon occurrence in hydraulic systems, as shownin e.g. Fales 4 , Thompson et al. 11 , Karpenko andSepehri 14 and Rubagotti et al. 21 . Here, the bandwidthof the VSVA control system is 10rad s−1/1.6Hz and theavailable sampling frequency is 40Hz. Hence, the highfrequency resonance peak is well beyond the controlbandwidth (see Figure 4).

Simplified model

In this section, a simplified control-oriented model ispresented, which approximates the dynamics betweenthe control input ∆TMC = TMC − TMC0 and theactuator’s position xVSVA. The rationale behind thesimplified model is that, following the linearisation-based analysis at different operating points performedin the previous section, the high-frequency dynamicscan be neglected in order to represent the behaviourof the actuator in the frequency range of interest. Inparticular, over the frequency range up to the samplingfrequency 40Hz, it can be assumed that ∆TMC is linkedto xVSVA by a delay plus a static nonlinearity.

In order to simplify the notation, the ‘signedflownumber’ f is introduced to represent bothextending and retracting flownumbers with one singlevariable. In addition, the dynamics of the servo valveinside the bandwidth is well represented by a puredelay Td = 0.025s. Hence, from (11) and (12) oneobtains the static relations

f =

KE∆TMCd, ∆TMCd ≥ 0,

KR∆TMCd, ∆TMCd < 0.(30)

where ∆TMCd is the delayed ∆TMC. Then, one canlink f to xVSVA through the non-linear static relation

xVSVA =

NE ( f − f ES ), f ≥ max(0, f E

S ) ,

0, − f RS < f < max(0, f E

S ),

NR ( f + f RS ), f ≤ − f R

S ,

(31)

where NE and f ES are functions of FE

L , Hp, Lp andNR and f R

S are functions of FRL , Hp, Lp as follows.



Figure 5. Input nonlinearity for selected flight conditions. Notethe different scalings for positive and negative values of∆TMCd (compare with Figures 2 and 3).

Figure 6. Simplified model of the actuation system

Substituting (18) in (21) and (24) in (27), one obtains

NE =

√AH Hp− ARLp + FE

LA3

H + A3R

, (32)

NR =

√ARHp− AH Lp− FR

LA3

H + A3R

. (33)

Similarly, using (22) and (28) and taking into accountthat in extension the cooling flow can be positive ornegative, one obtains

f ES = sgn(FE

L − FEL )×

× fC2

AR + AHAR AH

√(A2

H + A2R)|FE

L − FEL |

AH Hp− ARLp + FEL

, (34)

f RS =

fC2

AR + AHAR AH

√(A2

H + A2R)(FE

L − FEL )

ARHp− AH Lp− FRL

. (35)

Instances of the static nonlinearity obtained bycombining (30) and (31) are shown in Figure 5.

In conclusion, the simplified model of the VSVactuator linking ∆TMC to xVSVA is composed of apure delay, an input static nonlinearity, and a linearintegrator plant (see Figure 6). The coefficients of thestatic nonlinearity include some physical parametersof the actuator and the exogenous variables Hp, Lpand FE/R

L . Some other parameters of the full nonlinear

model become irrelevant in the simplified model, theseare: the head-end and rod-end volumes of the actuator(VH/R) and the bulk modulus (B). However, it isremarked that VH/R and B were needed to perform thelinearisation analysis of the previous section which ledus to the simplified model.

Estimation of the actuator’s loadingIn a given flight condition, as discussed in Section 2,FE

L and FRL can be considered to be uncertain constants,

while accurate values of Hp and Lp are available in theEEC. Here, It is shown that FE

L and FRL can be estimated

by a simple extension of the method presented in Bai 28 .In this section, in order to simplify the notation, thesymbols u = ∆TMCd, v = xVSVA, and y = xVSVA areused.

To start with, the parametrisation of the ‘deadzone’and ‘preload’ nonlinearities of Bai 28 is adopted toexpress the static nonlinearity in the model. In orderto do this, the following coefficients are defined

ME = NEKE, MR = NRKR, (36)

uE = f Es /KE, uR = − f R

s /KR. (37)

Then, by combining (30) and (31) one obtains

v =

ME

2[1 + sgn(u− uE)

] (u− uE) , u ≥ 0

MR

2[1− sgn(u− uR)

] (u− uR) , u < 0.

(38)

In the above expressions ME and uE are functions ofFE

L and MR and uR are functions of FRL . Note that

ME and MR are always positive. The coefficient uR

is always negative (deadzone in retraction), while uE

can be positive (deadzone in extension) or negative(preload in extension).

Given a set of input (u) and output (y) data onecan use (38) to compute an estimate of the actuator’svelocity v(u, FE

L , FRL ) as a function of FE

L and FRL .

Then, estimates FEL and FR

L can be obtained by directminimisation of a least-squares criterion. In general theproblem is not convex but is two dimensional and,thus, is not computationally intensive. In addition, aspointed out in Bai 28 , the estimate is consistent and hasgood properties when the data are affected by noise.In particular, if the data are affected by i.i.d. zero-mean Gaussian noise then FE

L and FRL are a maximum

likelihood estimator. Here, this property is particularlywell suited since the noise affecting the data is low-intensity electrical noise which is well described by thei.i.d. Gaussian assumption (see illustrative results inthe following section).

Simulation resultsIn this section, the simplified VSVA model isassessed in a comparison with the Trent 1000 RSS.The Trent 1000 RSS is a large Simulink modelwhich includes: Pumping unit, Hydro-Mechanical Unit(HMU), Electronic Engine Control (EEC), and Engine.



KR = 4.36 mm3s−1Pa−1/2mA−1 M = 0.90 kgKE = 32.97mm3s−1Pa−1/2mA−1 Hp = 2061 kPaAH = 5748 mm2 Lp = 358 kPaAR = 4940 mm2 FE

L = -1664 NfC = 0.582 mm3s−1Pa−1/2 FR

L = 4430 NTable 1. Representative values of parameters in ‘ground idle’.

In the RSS, the VSVA component includes the servovalve and two actuators in parallel. In the RSS VSVAcomponent, the actuation system is implemented bythe full non-linear equations (1)-(12). In Table 1numerical values of the parameters of the RSS VSVAcomponent, which are representative of a ’groundidle’ state, are disclosed. Note that Table 1 includesall parameters which appear in the simplified model.For confidentiality, the parameters’ values in the otherfight conditions are not disclosed. In order to generatethe simulations presented in this section, RSS VSVAcomponent was isolated from the rest of the RSS. HenceHp , Lp, FA and FE/R

L were set at constant valuescorresponding to the given flight condition. In orderto generate the closed-loop simulations, the existingPI controller from the EEC module was included.The simulations of the RSS VSVA component weregenerated using the Simulink Runge-Kutta solver witha 10−6s fixed-step size compiled in rapid acceleratormode. The reason for the choice of such a shortstep size is that the RSS VSVA component includesstiff differential equations (see the high-frequencyresonance peak shown in Figure 3). In order to generatea 10s response, the solver required approximatelytwo minutes of computational time. In contrast, thesimplified model was simulated using a variable-stepsolver requiring a comparatively negligible time.

In Figures 7 and 8 the position and velocity responsesgenerated by the RSS VSVA component are comparedwith the responses generated by the simplified model.It can be seen that the responses provided by thesimplified model mostly overlap those generatedby the RSS. Hence, the simplified model providescomputationally light yet accurate simulations. Forcompleteness, the mean squared error (mse) betweenthe two responses, computed with sampling time0.025s, is reported for each plot. For the positionresponses of Figure 7 the values are mse = 3.66× 10−3

and mse = 1.77× 10−5 for the open and closed-loopresponses respectively. For the velocity responses ofFigure 8 the values are mse = 1.388× 10−3 and mse =9.51× 10−3 for the open and closed-loop responsesrespectively. Note that the mse of the closed-loopposition responses is much lower than the mse of theopen-loop position responses. This is expected sinceposition is the controlled variable in the closed-loopsystem. In all cases, the mse values, which are verylow in comparison with the excursion of the responses,confirm the accuracy of the simplified model. It canalso be seen that the velocity responses generated bythe RSS VSVA component are characterised by burstsof high-frequency oscillations at the transition points

(see magnified inset in Figure 8). These oscillationsmatch the frequency of the resonance peak seen inFigure 4. The oscillations are smoothed by integrationand do not appear in the position responses. It canbe seen, by comparing the velocity responses, thatthe velocity generated by the simplified model at thetransition points follows a smoothed version of thevelocity response generated by the RSS.

In Figure 9, the evolution of the TMC inputs isdisplayed. In the open-loop simulations, the inputs tothe RSS and to the simplified model were the same.In the closed-loop simulations, the TMC inputs weregenerated by two independent closed-loop systemsfed by the same reference signal. Note that the TMCinputs are still almost overlapping. In Figure 9 thevalue of TMC0 and the limits of the input deadzoneof the simplified model are also displayed. Note thatthe deadzone is smaller on the positive side (comparewith Figure 5). Comparing Figure 9 with Figure 8, it canbe seen that the time intervals in which TMC is insidethe dead-zone of the simplified model coincide withtime intervals in which the velocity is null. This is moreevident in the open-loop simulations, in which theinput TMC is inside the deadzone for longer intervals.

In Figure 10, the evolution of PH and PR in thesimulation generated by the RSS is displayed. In thefigure, the operating pressures PE/R

H0 and PE/RR0 are also

displayed and are plotted only over the time intervalsin which the actuators are moving. From the figures itcan be seen that the pressure PH and PR converge veryrapidly to the operating values whenever the actuatoris moving independently of the attained velocity. Inthis respect, recall that the independence of operatingpressure from the velocity was a key point in theformulation of the simplified model. In addition, notethat PH and PR are subject to the same bursts ofoscillations seen in the velocity plots. However, in thecase of pressures, the amplitudes of the oscillations arerelatively too small to be seen in the plots.

To conclude, the results of the estimation ofthe actuator’s loads are illustrated. The estimateswere obtained using sampled open-loop and closed-loop data generated by the RSS and acquiredwith sampling time 0.025s. The open-loop andclosed-loop inputs were those used to generate thesimulations in Figures 7-10. The acquisition of datawas simulated by including the transducer componentwhich includes a realistic source of low-intensityelectrical noise. The velocity of the actuators wasthen reconstructed in discrete-time using a backwarddifference discretisation scheme.30 The optimisation ofthe least-squares estimation criterion was performedby a simple grid search. The estimates, and relativeerrors with respect to the true values in Table 1, wereFE

L = −1721 N(3.5%) and FRL = 4423 N(0.2%) obtained

from the open-loop data, and FEL = −1664 N(0%) and

FRL = 4430 N(0%) obtained from the closed-loop data.

Note that the relative errors range from negligible to3.5%. Thus, the estimated loads can be considered tobe very accurate. The contour plots of the least-



Figure 7. Position responses in open-loop (left) and in closed-loop (right).

Figure 8. Velocity responses in open-loop (left) and in closed-loop (right).

Figure 9. TMC inputs in open-loop (left) and in closed-loop (right).



Figure 10. Pressure responses in open-loop (left) and in closed-loop (right).

Figure 11. Estimation criterion using open-loop data (left) and using closed-loop data (right).

-squares criteria in both cases are shown in Figure 11.Note how the cost functions are such that the optimumis easily determined. The estimation of the actuator’sloads was repeated for all flight conditions consideredin Figure 3, which correspond to significantly differentshapes of the input nonlinearity in the simplifiedmodel, leading to similar results in each case.

Conclusions

In this paper, a simplified model of the compressorvariable stator vanes (VSVA) actuation system ofthe Rolls-Royce Trent 1000 engine was presented.The actuator is characterised by the presence of acooling flow orifice which significantly affects itsbehaviour. It has been found that the behaviour ofthe actuator is accurately represented by a static inputnonlinearity followed by a linear system. The accuracyof the simplified model was verified using the Rolls-Royce Trent 1000 Real System Simulator. The VSVAsimplified model has enabled us to develop a fastalgorithm for computing a snapshot estimate of the

actuator’s external load in a given flight condition.The external load is by far the largest uncertaintyaffecting the actuation system. In our current workwe are developing a continuous estimator suitablefor changing flight conditions with a focus on faultdetection31–34.

Acknowledgement

The authors gratefully acknowledge the technical inputof Martin Kirkman (Rolls-Royce Control Systems). Thiswork was supported by Rolls-Royce Control Systems,Birmingham, UK.

References

1. Herbert E Merritt. Hydraulic control systems. John Wiley& Sons, 1967.

2. Mohieddine Jalali and Andreas Kroll. Hydraulic servo-systems. Modeling, Identification and Control, Springer,2004.



3. Bora Eryilmaz and Bruce H Wilson. Unified modelingand analysis of a proportional valve. Journal of theFranklin Institute, 343(1):48–68, 2006.

4. Roger Fales. Stability and performance analysis of ametering poppet valve. International Journal of FluidPower, 7(2):11–17, 2006.

5. Davide Cristofori and Andrea Vacca. Modeling hydraulicactuator mechanical dynamics from pressure measuredat control valve ports. Proceedings of the Institution ofMechanical Engineers, Part I: Journal of Systems and ControlEngineering, 229(6):541–558, 2015.

6. Amin Maghareh, Christian E Silva, and Shirley J Dyke.Parametric model of servo-hydraulic actuator coupledwith a nonlinear system: Experimental validation.Mechanical Systems and Signal Processing, 104:663–672,2018.

7. GP Liu and S Daley. Optimal-tuning nonlinear pidcontrol of hydraulic systems. Control Engineering Practice,8(9):1045–1053, 2000.

8. Ill-yeong Lee, Dong-hun Oh, Sang-won Ji, and So-namYun. Control of an overlap-type proportional directionalcontrol valve using input shaping filter. Mechatronics, 29:87–95, 2015.

9. Yi Ye, Chen-Bo Yin, Yue Gong, and Jun-jing Zhou.Position control of nonlinear hydraulic system using animproved pso based pid controller. Mechanical Systemsand Signal Processing, 83:241–259, 2017.

10. Frans Wijnheijmer, Gerrit Naus, Wil Post, MaartenSteinbuch, and Piet Teerhuis. Modelling and lpvcontrol of an electro-hydraulic servo system. In IEEEInternational Conference on Control Applications, Munich,Germany, 2006.

11. David F Thompson, John S Pruyn, and Amit Shukla.Feedback design for robust tracking and robust stiffnessin flight control actuators using a modified QFTtechnique. International Journal of Control, 72(16):1480–1497, 1999.

12. M Karpenko and N Sepehri. Robust position control ofan electrohydraulic actuator with a faulty actuator pistonseal. ASME Journal of Dynamic Systems, Measurement, andControl, 125(3):413–423, 2003.

13. Mark Karpenko and Nariman Sepehri. Fault-tolerantcontrol of a servohydraulic positioning system withcrossport leakage. IEEE Transactions on Control SystemsTechnology, 13(1):155–161, 2005.

14. Mark Karpenko and Nariman Sepehri. On quantitativefeedback design for robust position control of hydraulicactuators. Control Engineering Practice, 18(3):289–299,2010.

15. Vladimir Milic, Zeljko Situm, and Mario Essert. Robusth position control synthesis of an electro-hydraulic servosystem. ISA transactions, 49(4):535–542, 2010.

16. Lisandro J Puglisi, Roque J Saltaren, Cecilia Garcia, andIlka A Banfield. Robustness analysis of a pi controllerfor a hydraulic actuator. Control Engineering Practice, 43:94–108, 2015.

17. G. Ren, M. Esfandiari, J. Song, and N. Sepehri. Positioncontrol of an electrohydrostatic actuator with toleranceto internal leakage. IEEE Transactions on Control SystemsTechnology, 24(6):2224–2232, 2016.

18. J. E. Bobrow and K. Lum. Adaptive, high bandwidthcontrol of a hydraulic actuator. ASME Journal of DynamicSystems, Measurement, and Control, 118(4):714, 1996.

19. Mete Kalyoncu and Mustafa Haydim. Mathematicalmodelling and fuzzy logic based position control ofan electrohydraulic servosystem with internal leakage.Mechatronics, 19(6):847–858, 2009.

20. Amit Mohanty and Bin Yao. Integrated direct/indirectadaptive robust control of hydraulic manipulatorswith valve deadband. IEEE/ASME Transactions onMechatronics, 16(4):707–715, 2011.

21. Matteo Rubagotti, Marco Carminati, GiampieroClemente, Riccardo Grassetti, and Antonella Ferrara.Modeling and control of an airbrake electro-hydraulicsmart actuator. Asian Journal of Control, 14(5):1159–1170,2012.

22. Kai Guo, Jianhua Wei, Jinhui Fang, Ruilin Feng, andXiaochen Wang. Position tracking control of electro-hydraulic single-rod actuator based on an extendeddisturbance observer. Mechatronics, 27:47–56, 2015.

23. Hai-Peng Ren and Pei-Fen Gong. Adaptive control ofhydraulic position servo system using output feedback.Proceedings of the Institution of Mechanical Engineers, Part I:Journal of Systems and Control Engineering, 231(7):527–540,2017.

24. Noah D Manring, Laheeb Muhi, Roger C Fales, Viral SMehta, Jeff Kuehn, and Jeremy Peterson. Using feedbacklinearization to improve the tracking performance of alinear hydraulic-actuator. Journal of Dynamic Systems,Measurement, and Control, 140(1), 2018.

25. Yong Li and Qingfeng Wang. Adaptive neural finite-time trajectory tracking control of hydraulic excavators.Proceedings of the Institution of Mechanical Engineers, Part I:Journal of Systems and Control Engineering, 2018.

26. Zhikai Yao, Yongping Yu, and Jianyong Yao. Artificialneural network–based internal leakage fault detectionfor hydraulic actuators: An experimental investigation.Proceedings of the Institution of Mechanical Engineers, Part I:Journal of Systems and Control Engineering, 232(4):369–382,2018.

27. Fouad Giri and Er-Wei Bai, editors. Block-orientedNonlinear System Identification. Springer London, 2010.

28. Er-Wei Bai. Identification of linear systems with hardinput nonlinearities of known structure. Automatica, 38(5):853–860, 2002.

29. Tomas Puller and Andrea Lecchini-Visintini. Modellingfor control of a jet engine compressor variable statorvanes hydraulic actuator. In 2016 European ControlConference (ECC), 2016.

30. Karl Johan Astrom and Bjorn Wittenmark. Computer-Controlled Systems. Dover Publications Inc., 2011.

31. Murat Arcak and Petar Kokotovic. Nonlinear observers:a circle criterion design and robustness analysis.Automatica, 37(12):1923–1930, 2001.

32. J. Voros. Recursive identification of hammersteinsystems with discontinuous nonlinearities containingdead-zones. IEEE Transactions on Automatic Control, 48(12):2203–2206, 2003.

33. W.-H. Chen. Disturbance observer based controlfor nonlinear systems. IEEE/ASME Transactions onMechatronics, 9(4):706–710, 2004.



34. Rishi Relan and Johan Schoukens. Recursive discrete-time models for continuous-time systems under band-limited assumptions. IEEE Transactions on Instrumentationand Measurement, 65(3):713–723, 2016.


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