Disturbance Observer Based Control with Anti-Windup ... · windup and subsequent performance degradation. In this work, numerical simulations are conducted com-paring a baseline Linear

J Intell Robot Syst (2017) 88:329–346DOI 10.1007/s10846-017-0534-5

Disturbance Observer Based Control with Anti-WindupApplied to a Small Fixed Wing UAV for DisturbanceRejection

Jean Smith · Jinya Su ·Cunjia Liu ·Wen-Hua Chen

Received: 15 September 2016 / Accepted: 8 March 2017 / Published online: 22 March 2017© The Author(s) 2017. This article is published with open access at Springerlink.com

Abstract Small Unmanned Aerial Vehicles (UAVs)are attracting increasing interest due to theirfavourable features; small size, low weight and cost.These features also present different challenges incontrol design and aircraft operation. An accuratemathematical model is unlikely to be available mean-ing optimal control methods become difficult toapply. Furthermore, their reduced weight and inertiamean they are significantly more vulnerable to envi-ronmental disturbances such as wind gusts. Largerdisturbances require more control actuation, meaningsmall UAVs are far more susceptible to actuator satu-ration. Failure to account for this can lead to controllerwindup and subsequent performance degradation. Inthis work, numerical simulations are conducted com-paring a baseline Linear Quadratic Regulator (LQR)controller to integral augmentation and DisturbanceObserver Based Control (DOBC). An anti-windupscheme is added to the DOBC to attenuate windup

J. Smith (�) · J. Su · C. Liu · W.-H. ChenDepartment of Aeronautical and Automotive Engineering,Loughborough University, Stewart Miller Building,Leicestershire LE11 3TU, UKe-mail: [email protected]

J. Sue-mail: [email protected]

C. Liue-mail: [email protected]

W.-H. Chene-mail: [email protected]

effects due to actuator saturation. A range of externaldisturbances are applied to demonstrate performance.The simulations conduct manoeuvres which wouldoccur during landing, statistically the most danger-ous flight phase, where fast disturbance rejection iscritical. Validation simulations are then conductedusing commercial X-Plane simulation software. Thisdemonstrates that DOBC with anti-windup providesfaster disturbance rejection of both modelling errorsand external disturbances.

Keywords Disturbance observer · UAV · Externaldisturbance · Anti-windup

1 Introduction

The continual growth in the use of Unmanned AerialVehicles (UAVs) has generally been accompanied bya reduction in size and weight of the systems. This hasled to small UAVs being widely used for a range ofapplications (e.g. remote sensing, mapping and traf-fic monitoring among many others [1]). This work isconcerned with fixed-wing UAVs, which are generallyoperated outdoors. Operating outdoors exposes theaircraft to environmental disturbances such as windgusts [2]. This is a challenge which has been stud-ied since the very beginning of aviation [3] and manymodern aircraft are fitted with Gust Load Alleviation(GLA) systems [4]. For large aircraft (e.g. GalaxyC-5a or Boeing 787), the GLA systems are used

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330 J Intell Robot Syst (2017) 88:329–346

to reduce bending and torsional stress allowing forlighter structures and greater passenger comfort.

For small UAVs, however, wind gusts presenta considerably different challenge. The significantreduction in size leads to lower inertia, making smallUAVs more sensitive to disturbance [5]. Moreover,a reduction in aircraft size is generally accompa-nied by a reduction in operating airspeed. This hasreached a critical point for small UAVs where theiroperating airspeeds are of the same magnitude asthe gust disturbances they are subjected to [6]. Asa consequence, in gust alleviation for small UAVs,structural loads are less critical condition than flightperformance. This presents a different problem ofdisturbance rejection, with small UAVs having verydifferent considerations. Flight control can be gener-alised into two categories; outer loop trajectory controland inner loop attitude control. UAV trajectory track-ing in wind has been studied in literature, with arange of methods applied. Vector field guidance hasdemonstrated robustness to wind disturbance by util-ising ground speed and course for navigation [7]. Itwas shown that path planning with a known constantwind can improve mission accuracy and efficiency [8].By using pre-computed information of aircraft turn-ing performance in wind, it has also been shown thatpath following in wind can be improved [9]. Thesemethods demonstrate that using robust methods isfeasible for trajectory tracking in wind. Using infor-mation of the wind improves performance further. Thelimitation being that accurate prior wind knowledgeis not feasible, especially for gust disturbances. Assmall UAVs are highly affected by gusts, it shouldbe considered in their operation. It has been shownthat online estimation of steady wind can be obtainedand used in trajectory following, with some abilityto track variance [10]. Disturbance Observer BasedControl (DOBC) augmentation has shown good per-formance in simulation and flight testing in rejectingdisturbance of an unknown wind in trajectory track-ing [11]. Inner loop control for UAVs is also widelystudied in literature. However, work regarding distur-bance rejection in this area is more sparse, particularlyregarding external disturbances. Disturbance rejectionfor parameter uncertainty has been addressed by var-ious approaches including robust methods [12], Neu-ral Networks (NNs) [13], Support Vector Regression(SVR) [14] and Active Disturbance Rejection Control(ADRC) [15]. While these works were able to account

for modelling uncertainty, they have no active con-sideration of external disturbance rejection. LinearQuadratic Regulator with Integral action (LQI) con-trol has been applied to the problem [16]. This methodis able to compensate for parameter uncertainties andexternal disturbances, through integral action on theoutputs. This method is compared to DOBC in thiswork; as such its drawbacks are discussed in later sec-tions where appropriate. ADRC has been applied toexternal disturbance rejection of a large UAV [17].Although improvement was demonstrated, the effectof the disturbance was not completely removed fromthe output. DOBC has the ability to reject both inter-nal and external disturbances, and has been applied tosmall UAV control [2]. Rejecting internal disturbancesmeans modelling uncertainty, which is likely for smallUAVs, is accounted for. Integral augmentation is alsoable to remove the effect of modelling errors in theoutput. However, DOBC also restores nominal perfor-mance in such cases, which is a feature not shared withintegral augmentation. Integral augmentation is alsoable to remove the effect of external disturbances fromthe output; in this work we aim to further demonstratethat DOBC is faster in this regard.

In practice, every actuator has limited capabili-ties (e.g. a motor with limited torque, an elevatorwith limited deflection angle) [18]. Small UAVs aremore prone to actuator saturation when comparedto their full sized counterparts as the magnitude ofdisturbances relative to the aircraft state are muchhigher, requiring significantly more control deflec-tion for rejection. Under actuator saturation, controlperformance degradation may appear such as largeovershoot or limit circle; in extreme cases, it ispossible for instability to arise. Actuator saturationcan lead to the appearance of the controller windupphenomenon. With windup, internal controller statescontinue increasing in magnitude which can causeovershoot and instability, among other issues. Unlikeconventional approaches which consider saturation incontrol design [19], an anti-windup compensator [18]is employed in this work allowing for nominal controlperformance recovery in the absence of actuator satu-ration. In this work, the classic static anti-windup [20]is exploited. This work is a continuation of the workpublished previously [2], aiming to further develop thetechnique toward the landing control problem.

In summary, small UAVs are more vulnerable togust disturbance than full size aircraft. Furthermore,

J Intell Robot Syst (2017) 88:329–346 331

they are at greater risk of actuator saturation due tothe increased relative magnitude of disturbances. Con-sidering these issues in a situation such as landing,statistically the most dangerous flight phase [21], sig-nificantly increases the risk. The aircraft will be closeto stall speed, so rapid rejection of disturbances isessential, Furthermore, not accounting for the issuesbrought about by actuator saturation increases the riskof aircraft loss. Small UAVs are also more likely tosuffer parameter uncertainty; failure to account forthis can also endanger the aircraft in critical situa-tions. DOBC affords the ability to reject the effectof both external and internal disturbances. The anti-windup scheme proposed within removes the riskbrought about by actuator saturation. This work aimsto demonstrate these advantages.

2 Preliminaries

2.1 Aircraft

This study is based on the Skywalker X8 shown inFig. 1. The X8 is a popular commercially available air-frame in the small UAV category, which has been usedin a number of research papers [22–24]. The aircrafthas no direct yaw control surfaces, whilst pitch androll are controlled by elevons.

2.2 System Dynamics

The coordinate system for the model is shown inFig. 2, where xB and zB represent body axes, xE andzE represent global axes. Moreover, u and w representbody horizontal and vertical velocities, V is the totalairspeed, θ is the flight path angle, M is the pitchingmoment, δε is the control surface deflection and δT

represents throttle setting position. This force is pre-sumed to act directly along the positive xB axis. Thedirectionality of δε is such that a positive deflection

Fig. 1 The Skywalker X8 platform used in this work

Fig. 2 Coordinate system definition utilised in this work

results in a negative pitching moment. The kinematicrelationships for aircraft position are defined as

h = −ze

xE = u cos θ + w sin θ − wx

zE = w cos θ − u sin θ − wh

This system is condensed into a state-space modelof the form given in Eq. 1. Here, X, Z and M arethe non-dimensional stability coefficients due to theirassociated subscripts, q is the pitching rate and g isthe gravitational acceleration constant, x is the systemstate, uδ is the control input matrix and A and B arethe system matrices. Any state denoted further with an∗ represents the state at the linearisation point of themodel.

x =

⎡⎢⎢⎢⎢⎢⎢⎣

Xu Xw Xq −g cos θ∗ 0Zu Zw Zq −g sin θ∗ 0Mu Mw Mq 0 00 0 1 0 0

sin θ∗ − cos θ∗ 0 u∗ cos θ∗+ 0w∗ sin θ∗

⎤⎥⎥⎥⎥⎥⎥⎦

︸︷︷︸A

⎡⎢⎢⎢⎢⎣

u

w

q

θ

h

⎤⎥⎥⎥⎥⎦

︸︷︷︸x

+

⎡⎢⎢⎢⎢⎣

0 Xδt

Zδε 0Mδε 00 00 0

⎤⎥⎥⎥⎥⎦

︸︷︷︸B

[δε

δt

]

︸︷︷︸uδ

.

(1)

As uδ ∈ R2×1, only two reference commands can

be accurately followed. For this work, based on themotivations discussed in the introduction, the states


which are to be controlled are u and h. Therefore, thereference command r is defined as

r =[

ur

hr

](2)

Subsequently, the output equation y can be defined as

y =[1 0 0 0 00 0 0 0 1

]

︸︷︷︸C

x

2.3 System Identification

In this work, the A and B system matrices for the statespace model were obtained from system identifica-tion applied to a model of the X8 in X-Plane. X-Planeis recognised in the industry as a good simulationenvironment [25] providing accurate data. X-Planesimulation is conducted based on a geometrical modelof the X8 using blade element theory to determinethe aerodynamic performance. Using flight data fromthis model, state space system identification methodswere applied to obtain a model of the X-Plane X8.This method is representative of real world applica-tions of the technique in this paper as a linear modelhas been obtained from a non-linear flying platform.It is expected that modelling errors are present whichthe DOBC will be expected to deal with.

2.4 Control and Performance Objectives

The control objectives for the system are to providestate regulation around the trim condition, while alsoallowing for tracking of a desired change in refer-ence command. Furthermore, the controllers shouldbe robust against disturbances, allowing for the con-trol objectives to still be accomplished accurately. Theperformance objectives are defined to satisfy thesecontrol objectives.

2.4.1 Tracks u and h Around a Given ReferenceCommand

This objective is concerned with the controllers beingable to provide sufficient regulation about a referencecommand, as well as good tracking performance to a

changing reference input. The initial reference com-mand will be to maintain the trim condition for theaircraft, which is V = 15m/s and h = 300m. Thisobjective is mainly concerned with the rejection ofinternal modelling errors. That is to say, the ability ofthe linear controllers to control a non-linear plant.

2.4.2 Maintain SafeFlightUnderExternal Disturbances

This objective links with the motivation of the work;the ability of the controller to reject external dis-turbances and maintain a safe flight condition. Thismeans providing rapid disturbance rejection to avoidaircraft stall or excessive loss of height; the twoconditions which are most dangerous in the landingscenario.

3 Nominal Feedback Control Design

Linear Quadratic (LQ) control was selected for thecontrol strategy, as it represents a well understood lin-ear optimal control strategy. Three control schemeswill be compared. A Linear Quadratic Regulator(LQR) will be used as a baseline for comparison tofurther controller augmentations. A reference track-ing Linear Quadratic Regulator with Integral action(LQI) represents classical augmentation for robust-ness. Finally, an LQR with DOBC augmentation willbe used. To ensure comparability, the LQI will bedesigned first; the baseline LQR is extracted from thedesigned LQI. DOBC augmentation is applied to theextracted LQR. This ensures that the state regulationprovided by the LQR in each case will provide compa-rable performance, which allows for accurate study ofthe disturbance rejection of classic LQI augmentationwhen compared to DOBC augmentation.

3.1 Linear Quadratic Integral Control Design

Integral augmentation is the classical method for dis-turbance compensation. The LQI used in this work isbased on previous research [26], and as such the fullderivation is omitted for brevity; a brief overview ispresented. Firstly, a new state es is defined to representthe tracking error for the reference command given inEq. 2

es = r − Cx.


Secondly, define two new states, as the integral of thisreference error

xie =∞∫

0

es(t)dt.

The original system is expanded to include the newstates, given as follows[

x

xie

]

︸︷︷︸xi

=[

A 0−C 0

]

︸︷︷︸Ai

[x

xie

]+

[B

0

]

︸︷︷︸Bi

uδ +[0I

]

︸︷︷︸G

r. (3)

Now the system error can be defined as

ei =[

r − Cx

xie

]= Mr + Hxi, (4)

where

M =[

I

0

], H =

[ −C 00 I

].

Next, we modify the general LQ cost function byinserting the error system in Eq. 4; this is given inEq. 5.

J = 1

2

∞∫

0

(eTi Qiei + uT

δ Ruδ)dt. (5)

Where Qi and R are the state and control weight-ing matrices, respectively. By modifying the systemto include error dynamics, the state regulation gainsare chosen internally by the system once the errorweighting Qi has been selected. Following the stan-dard method, details of which can be found in [26],the Algebraic Riccati Equations (ARE) can be solvedfor the control law (6).

uδ = −Kxixi − Krr. (6)

The controller layout is shown in Fig 3. Kxi∈ R

2×7

contains both the state feedback gain kx ∈ R2×5

and the error integral gain ki ∈ R2×2 of the form

Kxi= [

kx ki

]. The resulting optimal gains depend

only on the system being modelled and the weight-ing matrices Qi and R. The introduced integral actionwill account for modelling errors and external dis-turbances, although it does introduce issues. Integralcontrol is a lagging controller in the sense that an errormust first exist for a period of time for the controllerto generate feedback to eliminate it. Although this can

Fig. 3 The diagram of Linear Quadratic Integral controller

be made to happen quickly with an increased integralgain, this also introduces other problems such as over-shoot, oscillation and control surface saturation; inreality this means that a high integral gain is not a fea-sible solution [27]. The DOBC method proposed inthis work aims to eliminate these errors and improveperformance.

3.2 Linear Quadratic Regulator Control Design

This section details the development of an LQR con-troller with reference tracking. Any matrix associatedexclusively with the LQR will be denoted by a sub-script r . For system (1), one can design an LQRfor state regulation using the approach discussed inSection 3.1; this involves minimising the cost functiongiven by

J = 1

2

∞∫

0

(xT Qrx + uTδ Rruδ)dt,

where the selection of Qr would allow for tuning theweights placed on individual states by the optimisationroutine. However, for a better comparison betweencontrollers in this work, we continue in this section byapplying the state regulation gain kx from kxi in Eq. 6.The control law for this regulator is then given by

uδ = −kxx.

To include reference tracking, a new variable N isdefined as part of the control law, which is the DC gainof the system

uδ = −kxx + Nr, (7)

where the DC gain is the value at which the transferfunction from reference command to system output is


1. To determine the gain N , the transfer function Gry

(from reference to output) for the closed loop system(1) under control (7) can be calculated, given by

Gry = C(sI − (A − Bkx))−1BN.

For a reference with steady state value, the DC gainmatrix N can be calculated by choosing s → 0 andGry being an identity matrix, which is given by

N =[C(−(A − Bkx))

−1B]−1

.

The controller layout is given in Fig. 4. This figurehighlights one of the main issues with this technique:no direct feedback on the reference error. This causestwo problems. First, it relies on A, B and C beingknown exactly; any error will result in steady stateerror. The lack of reference feedback also limits thedegree to which external disturbances can be rejected.In the following section, disturbance observer aug-mentation will be explored, which provides a paral-lel approach to LQI while enabling fast disturbancerejection.

4 Disturbance Observer Augmentation

Adding integral action to an LQR controller allowsfor disturbance rejection through feedback regulation;this approach can remove the effect of nearly con-stant disturbances in steady state but comes at theprice of nominal performance degradation such asovershoot and control saturation in the transit process[27]. DOBC has recently received much attention inboth academia and industry [28] due to its promis-ing features such as the preservation of the nominalcontrol performance and the “separation principle”for the ease of control design [28, 29]. DOBC isusually patched into an existing baseline controller.

Fig. 4 Controller layout under state regulation and with refer-ence command tracking

The baseline controller addressing stability and per-formance specifications. The DOBC augmentation isused to reject disturbances and return the baseline con-troller to nominal performance. In this paper, DOBCis exploited to achieve external disturbance rejectioncontrol for small UAV, where the LQR discussed inSection 3.2 serves as the baseline optimal controlfor nominal performance. DOBC will also be usedto eliminate model uncertainty from the system. Thedetailed design procedure of the DOBC is given asfollows.

4.1 Observer Design

A key feature of DOBC is the ability to accountfor modelling uncertainties as well as external distur-bances. First, we add the external disturbances to thesystem, which transforms (1) to (8).

x = Atx + Btuδ + Bddx. (8)

Where At and Bt are the true matrices which wouldideally describe the system being modelled, Bd =I 5×5 as the disturbances are presumed to act directlyon the states, and the external disturbances dx aredefined as

dx = [ud wd qd 0 hd

]T.

No disturbance is considered on θ as it is a knownkinematic relation to q. In our case we define dlx , thelumped disturbance term, as the sum of the externaldisturbances and the modelling errors,

dlx = (At − A)x + (Bt − B)uδ + Bddx. (9)

It is defined that the lumped disturbances act inthe same channels as the external disturbances, soBld = Bd . This demonstrates how modelling errorsare accounted for as the difference between the true,unknown, matrices (At, Bt ) and the identified matri-ces (A, B) used for control design. Modelling errorsare presumed to be present as it is prohibitively dif-ficult and expensive, if possible at all, to obtain thetrue system matrices for a small UAV. Furthermore,even the ideal system would become inaccurate as theaircraft departs from the linearisation point, which isexpected during operation. Using DOBC accounts forthese issues. With the disturbances defined, it remains


to design an observer which can estimate them. Suchan observer is given in Eq. 10 [30].

{z = −L(z + Lx) − L(Ax + Bu)

dlx = z + Lx(10)

where, z represents the observer internal state, L is again matrix which can be tuned for performance anddlx is the estimate of the disturbances dlx . To demon-strate the ability of the observer estimate to trackthe disturbances, we first define an estimation error(11) between the estimate and true disturbances. Sub-stituting dlx from Eq. 10 and then expanding the z

term further from Eq. 10, the expansion of ed can bereached.

ed = ˙dlx − dlx

= z + Lx − dlx

= −LBddlx − L (Anx + Bnu) +L (Anx + Bnu + Bddlx) − dlx

ed = −LBded − dlx .

(11)

Under the assumption that the external disturbancesvary slowly, we can set dlx ≈ 0. This has two results;firstly, it is demonstrated that the error dynamics arestable if −LBd is Hurwitz. Secondly, the effect of L

can be seen more clearly. Assuming L is chosen asHurwitz and recalling that Bd = I 5×5, it shows thata larger value of L will result in a more rapid con-vergence of the error estimation. Although the errordynamics are proven stable for a steady disturbance,it has been demonstrated [31] that the observer cantrack time varying disturbances as long as the observerdynamics are faster than that of the disturbance. Thiscompletes the observer design process. It remains todesign a strategy to generate appropriate control inputsto mitigate the effect of these disturbances on thesystem.

4.2 Disturbance Compensation Gain

The disturbance observer employed in this work is ofthe “mismatched” form [30]. This condition is definedby the mismatch in dimensionality between u2×1

δ andd5×1lx in Eq. 8. More colloquially, this condition results

from not having a direct control input to address eachdisturbance channel. The result of this being that itis not possible to remove the disturbances from allthe states. It is, however, possible to remove the dis-turbances from the output channels. Based on the

disturbance estimate given from Eq. 10 and the controllaw (7), a composite control structure is produced

uδ = −kxx + Nr + kdxdlx, (12)

where kdx is the compensation gain to be designed. Asshown in [30], kdx can be found from Eq. 13

kdx = −[C(A − Bkx)

−1B]−1 × C(A − Bkx)

−1Bld .

(13)

It can be seen that the compensation gain does notrequire tuning independently from the closed loopsystem under LQR regulation. With the appropriategains calculated, the disturbance observer can now beintegrated into the system architecture. The completeLQR + DOBC system is shown in Fig 5.

4.3 Anti-Wind Up Modification

In this section, anti-windup compensation is furtherconsidered for the proposed DOBC, where the clas-sic static anti-windup structure [20] is exploited inthis paper. This approach has received much attentionin practice [18] due to its desirable properties suchas nominal control performance recovery. Considersystem (1) with saturated actuator and disturbances

x = Ax + Bsat (uδ) + Blddlx . (14)

A classic static anti-windup modification [20] for sys-tem (14) is made to the observer (10), given as follows

{z = −L(z + Lx) − L(Ax + Buδ) + kaSu

dlx = z + Lx, (15)

where kaSu is a term introduced to reduce the effectof input saturation, with ka being the anti-windup gain

Fig. 5 Control system layout for the LQR + DOBC controlscheme. The input of disturbances is denoted by d


matrix to be designed. Under the modified DOB (15),the error dynamics become

ed = −LBlded − (ka + LB)Su + d (16)

If the anti-windup gain matrix is chosen as

ka = −LB (17)

then Eq. 16 reduces to

ed = −LBlded + d

which means the effect of input saturation on dis-turbance estimation error ed and consequently distur-bance estimate disappears.

Remark 1 In this paper, the classic static wind-upcompensator is augmented to DOBC; the stabilityanalysis of the modified DOBC under input saturationis omitted for brevity. However, it can be proved thatunder the modified DOBC, the closed-loop system isasymptotically stable with a basin of attraction usingthe result in [20].

Remark 2 Under the anti-windup gain matrix inEq. 17, the modified DOB (15) can be put into anequivalent form

{z = −L(z + Lx) − L[Ax + Bsat (uδ)]dlx = z + Lx

. (18)

Although the anti-windup compensator is designedusing the classic result [20], comparing the conven-tional DOB (10) and the modified DOB (18) it can beseen that the modified DOB ends up directly using thesaturated control input sat (uδ) rather than calculatedinput uδ , which substantially eases the implementation.

5 Simulations

Results from numerical state space simulations arepresented first to compare the characteristics of thedifferent controllers in Section 5.2. For full compar-ison, both the anti-windup augmented and originalLQR + DOBC controllers are included. Beginningwith numerical simulation allows for study of perfor-mance in the presence of external disturbances only.

Then, in Section 5.3, X-Plane simulations are con-ducted. This aims to represent real world applicationof the systems as no exact model of the aircraft isavailable; an approximation was obtained through sys-tem identification. Furthermore, the simulation is non-linear entirely. This represents a difficult case for theDOBC as both internal and external disturbances willbe present, as well as unmodelled actuator dynamics.

5.1 Controller Tuning and Gain Selection

Some preliminary work was done to identify a goodbaseline LQR/LQI controller, for which the simula-tions are not included here for brevity. As the LQRcontroller is based on the LQI, there are only 2 tunableparameters; Qi and R as given in (19). More weight-ing was applied to the error in u, as there is a muchsmaller tolerance in magnitude of error for this.

Qi =

⎡⎢⎢⎣1 0 0 00 0.05 0 00 0 1 00 0 0 0.05

⎤⎥⎥⎦ R =

[1 00 1

](19)

5.2 Numerical Simulations

Conducting initial numerical simulation allows forstudy of controller performance with total controlover the disturbances. No internal modelling distur-bances will be present as the simulation model isidentical to the model used for control design. Exter-nal disturbances will only be present when explicitlyenabled.

5.2.1 Step Disturbance Performance

In this section, disturbance rejection for a rangeof disturbances are demonstrated while maintainingthe reference condition. The applied disturbances aresummarised in Table 1. For the first 2 disturbances

Table 1 Summary of disturbances applied during the statespace mixed disturbance simulation

Disturbance Magnitude Time Active (s)

wd 10 5→60

qd 2 20→60

hd −1 30→32


Fig. 6 u body velocityresponse when subject towd , qd and hd disturbances

0 5 10 15 20 25 30 35 40 45

Time (s)

14.8

14.85

14.9

14.95

15

15.05

15.1

15.15

15.2

u V

eloc

ity (

m/s

)

LQRLQILQR + DOBCLQR + DOBC (aw)Reference

(wd and qd ) the DOBC schemes show significantlyimproved performance. As no saturation is present,the anti-windup scheme does not activate. The hd dis-turbance was chosen to be of a magnitude greaterthan the system is able to reject to bring about con-trol saturation. This highlights the performance of theanti-windup scheme well as the unmodified DOBCsuffers overshoot of both reference commands due tothe windup once the disturbance is removed; the anti-windup modified observer does not suffer any such

issue and returns to the reference command easily. Inall 3 cases, the anti-windup observer controller hassignificantly improved disturbance rejection over theLQI scheme (Figs. 6, 7, 8, and 9).

5.2.2 Height Reference Tracking with Disturbance

A step change in reference height is now commanded;the step input is passed through a shaping filter tosmooth the command. A disturbance qd = −22 added

Fig. 7 h response whensubject to wd , qd and hd

disturbances

0 5 10 15 20 25 30 35 40 45

Time (s)

298

298.5

299

299.5

300

300.5

301

heig

ht (

m)



Fig. 8 Elevator deflectionwhen subject to wd , qd andhd disturbances

0 5 10 15 20 25 30 35 40 45

Time (s)

-14

-13

-12

-11

-10

-9

-8

-7

-6

Ele

vato

r D

efle

ctio

n (d

eg)

LQRLQILQR + DOBCLQR + DOBC (aw)

to the simulation at t = 20s. The results are given inFigs. 10, 11, 12, and 13. This disturbance is chosento represent a wind disturbance during a landing sce-nario. As the aircraft approaches ground level, the dis-turbance is applied. It can be seen that all controllersexcept the anti-windup DOBC undershoot both u andh reference by significant amounts. The unmodified

DOBC offers some initial disturbance rejection butquickly degrades to performance worse than the LQI;this highlights the significant and important improve-ment offered by the anti-windup modification. If thiswere a landing attempt, only the LQR + DOBC (aw)would have successfully completed the manoeuvrewith no undershoot or steady state error.

Fig. 9 Throttle settingwhen subject to wd , qd andhd disturbances

0 5 10 15 20 25 30 35 40 45

Time (s)

20

30

40

50

60

70

80

90

100

Thr

ottle

Set

ting

(%)



Fig. 10 u body velocityduring a height referencetracking manoeuvre. Adisturbance is added att = 20s

5.2.3 Varying Disturbance Rejection

The stability property for the DOBC controller givenin Section 4.1 assumed a steady disturbance. Theprevious simulations have shown good performanceunder these conditions. However, it has been demon-strated in literature [31] that the DOBC technique

can remove non-steady disturbances if the observerdynamics are sufficiently faster than that of the dis-turbance. Here, 3 different qd disturbances are appliedat 7s intervals, beginning from t = 7s. Results forthese simulations are given in Figs. 14, 15, 16, and 17.The second disturbance cannot be fully rejected andleads to saturation of the throttle; this will bring about

Fig. 11 h during a heightreference trackingmanoeuvre. A disturbanceis added at t = 20s


Fig. 12 Elevator deflectionduring a height referencetracking manoeuvre. Adisturbance is added att = 20s

0 5 10 15 20 25 30 35 40 45

Time (s)

-24

-22

-20

-18

-16

-14

-12

-10

-8

Ele

vato

r D

efle

ctio

n (d

eg)


anti-windup action for the DOBC. It can be seenthat the DOBC offers significantly improved distur-bance rejection for the varying disturbance over theother controllers, whilst not suffering any overshoot orwindup issues.

5.3 X-Plane Simulation

To verify the results obtained in the state-space sim-ulations, the controllers were further tested using X-Plane flight simulation software, which is recognised

Fig. 13 Throttle settingduring a height referencetracking manoeuvre. Adisturbance is added att = 20s

0 5 10 15 20 25 30 35 40 45

Time (s)

0

10

20

30

40

50

60

70

80

90

100

Thr

ottle

Set

ting

(%)



Fig. 14 u body velocitytracking with varying qd

disturbances

for good simulation fidelity [25]. Figure 18 shows thesystem used to obtain data. For maximum X-Planeand Simulink fidelity, the two environments were runon separate computers. A UDP data link was usedto stream the aircraft state and control commands

between the systems. The communication networkdelay was measured as < 1ms, meaning no dis-cernible delay was introduced using this method. Theintent is to demonstrate that the DOBC can still offerperformance improvement in this environment. This is

Fig. 15 h tracking withvarying qd disturbances


Fig. 16 Elevator deflectionwith varying qd

disturbances

0 5 10 15 20 25 30 35

Time (s)

-25

-20

-15

-10

-5

0

Ele

vato

r D

efle

ctio

n (d

eg)


Fig. 17 Throttle settingwith varying qd

disturbances

0 5 10 15 20 25 30 35

Time (s)

0

10

20

30

40

50

60

70

80

90

100

Thr

ottle

Set

ting

(%)


Fig. 18 Simulation environment used for X-Plane data collec-tion. Separate computers allowed X-Plane and Simulink to runat their ideal rates. Network delay was below 1ms

Table 2 Summary of disturbances applied during the non-linear mixed disturbance simulation

Disturbance Magnitude Time Active (s)

ud −1 35→75

wd 22 22→75

qd −1.5 35→75


Fig. 19 u body velocitytracking when subject to ud ,wd and qd disturbances aswell as a reference changein the X-Plane simulation

10 20 30 40 50 60 70

Time (s)

11

11.5

12

12.5

13

13.5

14

14.5

15

15.5

u V

eloc

ity (

m/s

)


representative of real world application of the systemwith the linear model, obtained by system identi-fication, is applied to a non-linear simulation. Forthese simulations, R was increased to reduce the totalgains for the controllers. This was required to main-tain stability in the simulation. Furthermore, L wasdecreased to maintain stability. The penalties were

applied equally to all controllers to retain comparabil-ity. In these simulations, 3 separate disturbances wereapplied as detailed in Table 2. Furthermore, the air-craft was given a u reference prior to the h referencechange; this is representative of actions taking dur-ing landing. Furthermore, this takes the aircraft awayfrom the condition about which the model was created,

Fig. 20 h tracking whensubject to ud , wd and qd

disturbances as well as areference change in theX-Plane simulation

10 20 30 40 50 60 70

Time (s)

280

285

290

295

300

305

heig

ht (

m)



Fig. 21 Elevator deflectionwhen subject to ud , wd andqd disturbances as well as areference change in theX-Plane simulation

10 20 30 40 50 60 70

Time (s)

-25

-20

-15

-10

-5

0

Ele

vato

r D

efle

ctio

n (d

eg)


introducing additional modelling errors. The result-ing performance is shown in Figs. 19, 20, 21, and 21.Again, the anti-windup DOBC offers significant per-formance improvements over the other controllers.The unmodified DOBC suffers from significant

undershoot and overshoot of the reference following aperiod of control saturation. As shown in the numer-ical simulations, only the anti-windup DOBC is ableto reject all the disturbances and reach the desiredlanding reference.

Fig. 22 Throttle settingwhen subject to ud , wd andqd disturbances as well as areference change in theX-Plane simulation

10 20 30 40 50 60 70

Time (s)

0

10

20

30

40

50

60

70

80

90

100

Thr

ottle

Set

ting

(%) LQR

LQILQR + DOBCLQR + DOBC (aw)


6 Conclusions and Future Work

This work has shown that both integral and distur-bance observer augmentation of a baseline LQR canimprove disturbance rejection performance. However,it has been demonstrated clearly that the disturbanceobserver augmentation provides faster and more accu-rate disturbance rejection. In situations where controlsaturation occurs, DOBC performance can becomedegraded, in some cases performing worse than theLQI. By augmenting the disturbance observer withan anti-windup scheme based on classical static anti-windup compensation, the adverse effect of controllerwindup due to actuator saturation was removed fromthe system and nominal performance restored. Insituations with no actuator saturation, the proposedanti-windup scheme had no effect on performance ofthe DOBC, which is a favourable result. It was alsodemonstrated that the linear disturbance observer wasable to replicate this performance when applied to anon-linear simulation under adverse conditions. Thenon-linear simulations demonstrated that the designedlinear observer resulted in better disturbance rejec-tion than the integral augmentation in 3 key situations:steady state at the trim condition, during a changingreference and in steady state at a condition well awayfrom the linearisation point. This demonstrates that abasic linear model is suitable for designing a baselineLQR controller which, when augmented with a dis-turbance observer, can be applied to non-linear plantwith superior performance to the traditional integralaugmentation.

The results presented here have demonstrated thatclassical integral augmentation does not provide dis-turbance rejection which can match the disturbanceobserver for response rate and therefore flight safety.This is a promising result for future application to alanding scenario to improve flight safety. Furthermore,it has been shown that the employed anti-windupscheme is able to remove the risk of controller windupdue to actuator saturation which resulted from theunmodified disturbance observer.

Open Access This article is distributed under the terms of theCreative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unre-stricted use, distribution, and reproduction in any medium,provided you give appropriate credit to the original author(s)and the source, provide a link to the Creative Commons license,and indicate if changes were made.

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Jean Smith received his M.Eng degree in 2014 from theDepartment of Aeronautical and Automotive Engineering ofLoughborough University in the United Kingdom. During hisstudy he developed an interest in autonomous aircraft and is cur-rently studying towards a Ph.D. degree in autonomous aircraftcontrol in the Centre for Autonomous Systems at Loughbor-ough University.

His research is currently focused on disturbance observerbased control and the challenges in its practical application tosmall unmanned aircraft.

Jinya Su (S’13, M’16) was born in Liaocheng, ShandongProvince, China in 1990. He received his B.Sc. degree in theSchool of Mathematics and Statistics from Shandong Uni-versity, Weihai, China in 2011. In 2016, he received a Ph.Ddegree in the Department of Aeronautical and AutomotiveEngineering, Loughborough University, Loughborough, U.K.Since 2015, he has been a research associate in the Centre forAutonomous Systems at Loughborough University.

His research interests include disturbance observer, Kalmanfilter, machine learning and their applications to autonomoussystems such as autonomous vehicle, agricultural informationsystem.

Dr Su received the Best Student Paper Award in 19th Inter-national Conference on Automation and Computing (2013), theIEEE-IES Student Paper Travel Award in 17th InternationalConference on Industrial Technology (2016), and the AnnualICI Prize from Institute of Measurement and Control in 2016. In2015, he received the prestigious Chinese Government Awardfor Outstanding Self-financed Students Abroad.

Dr. Cunjia Liu received his B.Eng. and M.Sc. degrees in guid-ance, navigation, and control from Beihang University, Beijing,China, in 2005 and 2008, respectively. In 2011, he receiveda Ph.D. degree in autonomous vehicle control from Lough-borough University, Loughborough, United Kingdom. From2011, he was a research associate with the Department ofAeronautical and Automotive Engineering at LoughboroughUniversity, where he was appointed as a lecturer in flightdynamics and control in 2013. His current research interestsinclude optimization-based control, disturbance-observer-basedcontrol, Bayesian information fusion and their applications toautonomous vehicles for flight control, path planning, decisionmaking, and situation awareness.

Prof. Wen-Hua Chen (M’00-SM’06) received the M.Sc. andPh.D. degrees from Northeast University, Shenyang China,in 1989 and 1991, respectively. From 1991 to 1996, he wasa lecturer and then associate professor with the Departmentof Automatic Control, Nanjing University of Aeronautics andAstronautics, Nanjing, China. From 1997 to 2000, he helda research position and then a lecturer in control engineer-ing with the Centre for Systems and Control, University ofGlasgow, Glasgow, United Kingdom. In 2000, he moved tothe Department of Aeronautical and Automotive Engineering,Loughborough University, Loughborough, as a lecturer, wherehe was appointed as a professor in 2012. His research inter-ests include the development of advanced control strategies(nonlinear model predictive control, disturbance observer basedcontrol, etc.) and their applications in aerospace and automotiveengineering. Currently, much of his work has also involved inthe development of unmanned autonomous intelligent systems.He is a Fellow of the Institution of Engineering and Technologyand Institution of Mechanical Engineers and a Senior Memberof IEEE.

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Disturbance Observer Based Control with Anti-Windup ... · windup and subsequent performance degradation. In this work, numerical simulations are conducted com-paring a baseline Linear