A Adaptive Control Scheme for UAV Carrier Landing Using...

Research ArticleA L1 Adaptive Control Scheme for UAV Carrier Landing UsingNonlinear Dynamic Inversion

Ke Lu 1,2 and Chunsheng Liu1

1College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China2Science & Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jingdezhen,Jiangxi, 333001, China

Correspondence should be addressed to Ke Lu; [email protected]

Received 31 October 2018; Revised 20 January 2019; Accepted 25 February 2019; Published 2 May 2019

Academic Editor: André Cavalieri

Copyright © 2019 Ke Lu and Chunsheng Liu. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in anymedium, provided the original work is properly cited.

This paper presents a L1 adaptive controller augmenting a dynamic inversion controller for UAV (unmanned aerial vehicle) carrierlanding. A three axis and a power compensator NDI (nonlinear dynamic inversion) controller serves as the baseline controller forthis architecture. The inner-loop command inputs are roll-rate, pitch-rate, yaw-rate, and thrust commands. The outer-loopcommand inputs come from the guidance law to correct the glide slope. However, imperfect model inversion and nonaccurateaerodynamic data may cause degradation of performance and may lead to the failure of the carrier landing. The L1 adaptivecontroller is designed as augmentation controller to account for matched and unmatched system uncertainties. Theperformance of the controller is examined through a Monte Carlo simulation which shows the effectiveness of the developed L1adaptive control scheme based on nonlinear dynamic inversion.

1. Introduction

Aircraft carrier landings have been regarded as one of themost challenging phases of flight due to the extremely tightspace available for touchdown on the flight deck of an aircraftcarrier. The pilot must aim for a single spot on the flight deckwith a very small margin for error [1]. The area used to landon the deck is very small, which is only about 55 feet wide and40 feet long. A small deviation from the desired landing boxmay lead to crashing into other aircraft on the flight deck.The problem of autonomous carrier landing of UAV ishighly challenging due to wind gust disturbances and shipmotion under high sea states [2]. However, carrier flightoperations are necessary for the support of combat opera-tions and must take place whenever they are needed. Withconsideration of all of the effects, developing a system whichautomates the carrier landing process is extremely importantand will increase the design difficulty of controller [3].

While the topic of automated carrier landing has beenstudied for several decades, most researchers have focusedon linear control methods. H-dot and glide-slope feedback

are used as their bases which are found in Ref. [4–6]. How-ever, with air turbulence added, the landing performancesof these controllers were degraded [5]. As carrier landing sys-tems are inherently nonlinear, nonlinear control schemesshould be the next logical step with the development of com-puter capability. In Ref. [7], Steinberg expanded his investi-gation to the application of a fuzzy logic carrier landingsystem. What he cared about was the ability of the controllerto adapt to changing conditions, and the initial results werepromising. In Ref. [8], Steinberg and Page compared thebaseline performances of several different nonlinear controlschemes applied to automated carrier landing. It showed thatthe nonlinear control may be a very good choice for futurecarrier landing system. In Ref. [9], a fuzzy-logic-basedapproach was used to design an autonomous landing systemfor unmanned aerial vehicles. In Ref. [10], preview controlfor unmanned aerial vehicle carrier landing was presented.In Ref. [11], active disturbance rejection control was usedfor unmanned aerial vehicle carrier landing. These nonlinearcontrol methods proved useful in this application. Denisonapplied nonlinear dynamic inversion to design a carrier

HindawiInternational Journal of Aerospace EngineeringVolume 2019, Article ID 6917393, 8 pageshttps://doi.org/10.1155/2019/6917393

http://orcid.org/0000-0002-4208-405X

https://creativecommons.org/licenses/by/4.0/




https://doi.org/10.1155/2019/6917393

landing system for unmanned combat aerial vehicles consid-ering turbulence [12]. The performance of the system wasevaluated using Monte-Carlo simulations. However, afteradding wind and sea state turbulence, the controller perfor-mance was degraded. Although nonlinear dynamic inversioncould eliminate the need for extensive gain scheduling, how-ever, since the system parameters are not exactly known andthe plant inversion is not accurate, dynamic inversion con-troller may possess performance degradation. In order tosolve this problem, in Ref. [13], online neural networks wereused to compensate plant inversion error. Sliding mode var-iable structure control could be used to enhance the systemrobustness, but the chatter problem is not very acceptable[14]. Another widely used method is the linear robust con-troller [15, 16]. However, a high-order robust controller isrequired, such as a fourteen-order controller to ensure theflying control system robustness for X-38 [17].

L1 adaptive control algorithm is a recently developedadaptive control methodology. The key feature of L1 adaptivecontrol architecture is its fast and robust adaptation, whichdoes not interact with the trade-off between performanceand robustness [18]. It was developed with aerospace controlin mind and has been found to be suitable for flying applica-tions [19, 20].

In this paper, nonlinear dynamic inversion based con-troller is designed for carrier landing flight control system.Then L1 adaptive control algorithm is used to augment thebaseline controller. The effects of the adaptive element onthe flight control system are demonstrated with Monte Carlosimulations.

2. UAV Flight Dynamics Model and CarrierLanding Environment

In this section, a nonlinear UAV flight dynamicsmodel is developed. Then, the carrier landing environ-ment is described.

2.1. UAV Flight Dynamics Model. The aircraft which was usedfor this study was the Joint Unmanned Combat Air System(J-UCAS) Equivalent Model (EQ model) developed by theAir Force Research Laboratory (AFRL) [21]. The EQ modelhas three sets of control surfaces: flaps for pitch control, ele-vons for roll control, and clamshells for yaw control. Thephysical parameters for the aircraft are summarized in Table 1.

The simulation uses the standard equations of motionand kinematic relations found in a variety of standard refer-ences on flight dynamics.

X = F X,U, σ , 1

where F ∈ R12×1 denotes a vector of nonlinear algebraicequations involving X, U, and σ. The state variables are givenin the form of a vector X ∈ R12×1; U = δe, δf , δc, δt denotes avector constituting the control inputs; σ is unmodeled non-linearity dynamics.

2.2. Aircraft Carrier Model and Wind Turbulence Model. TheNimitz-class carrier is employed in this paper. There are 4

wires spaced 40 feet apart for aircraft landing. The detailedparameters can be found in Ref. [12]. The aircraft carriermotion is composed of a forward motion with constantvelocity and perturbations caused by sea states. The pertur-bations are composed of rotational degrees and translationaldegrees of freedom. The rotational degrees of freedom aretermed roll and pitch. In the translational degrees of freedom,up and down motion is called heave, forward to aft motion iscalled surge, and port to starboard motion is called sway [12].The perturbations are modeled as sinusoidal waves using theinformation provided in Table 2 [12, 22]. Sea state 0 refers tocalm seas and the values are all zero, and sea state 6 isextremely heavy seas.

A large source of touchdown error is the turbulent airenvironment found in the approach path [4]. The wind tur-bulence model is composed of the free atmospheric turbu-lence and ship burble. The burble is the wind pattern foundimmediately behind the carrier fantail, which consists of asteady component, an unsteady component, and a periodiccomponent [22].

Table 1: Summary of EQ model physical parameters.

Parameter Value

Weight 1 20 × 104 kgWing area 75.12m2

Mean aerodynamic chord 5.68m

Wing span 16.67m

Aspect ratio 3.70

Ixx 6 52 × 104 kg·m2

Iyy 4 29 × 104 kg·m2

Izz 1 33 × 105 kg·m2

Ixz Ixy Izy 0.00 kg·m2

Table 2: Summary of sea state perturbations.

Sea state Perturbation Amplitude Frequency

4

Roll 0.6223 deg 0.2856 rad/sec

Pitch 0.5162 deg 0.5236 rad/sec

Surge 0.9546 ft 0.3307 rad/sec

Sway 1.4142 ft 0.3307 rad/sec

Heave 2.2274 ft 0.3491 rad/sec

5






6






2 International Journal of Aerospace Engineering

The wind turbulence model is given by

Ug =U1 +U2 +U3 +U4,

Vg =V1 + V4,

Wg =W1 +W2 +W3 +W4,

2

where U1, V1, and W1 represent free atmospheric turbu-lence; U2 and W2 represent the steady component of burbleturbulence; U3 and W3 represent the periodic component ofburble turbulence; U4, V4, and W4 represent random com-ponent of burble turbulence. The periodic component couldbe ignored, as it is due to the slow pitch periodic motion ofcarrier. The random component of burble and free atmo-spheric turbulence are modeled using Dryden turbulence[12]. In this study, the Dryden wind turbulence model usesthe Dryden spectral representation by passing band-limitedwhite noise through appropriate forming filters to meetthe MIL-HDBK-1797B, while the steady component isessentially a shift in all components of the turbulence,which causes a 6 ft drop below the glide slope and conse-quent touchdown 125 ft short of the ideal touchdownpoint [4].

3. The Controller Design

In this section, a L1 adaptive augmented dynamic inver-sion controller for UAV carrier landing is designed. In thisstudy, the command inputs for the controller are providedby the guidance system. The guidance system generate theyaw angle and pitch angle commands which can be foundin Ref. [12]. The side-slip angle command is always zero,and the angle of attack command depends on ApproachPower Compensation System. The Approach Power Com-pensation System automatically controls thrust to maintaina reference angle of attack during the carrier approach,thus effectively controlling the flight path angle throughpitch angle [5, 23]. The baseline controller is a full nonlin-ear dynamic inversion controller based on large part ofRef. [24] and Ref. [12]. An inner-loop controller, designedby dynamic inversion, is used to linearize the UAVdynamics. This inner-loop controller lacks guaranteedrobustness to uncertainties in the flight dynamics model.This would cause degradation of NDI controller perfor-mance and even lead to the failure of the carrier landing.To address robustness to model uncertainties, a L1 adap-tive controller is designed as augmentation controller.The complete architecture is presented in Figure 1.

UAV flightdynamics

Approach powercompensation system

NDI controller

L1 adaptivecontroller

Linearcontroller

Linearcontroller

L1 adaptivecontroller

Outerloop NDIcontroller

X

X = [xa ya ha u v w ϕ θ ψ p q r]T

Carriermotions

Guidancelaws

Wind turbulencemodel

𝜔 = [p q r] T

Linearcontroller

𝜔

ωd

uad

�rustinversion

Td

𝜃cmd𝛽cmd

𝛿ecmd𝛿acmd𝛿rcmd

𝛿tcmd

𝛹cmd

𝛹cmd

𝜃cmd

𝛽cmd = 0°𝛼cmd = 8°

𝛼cmd

𝛼

αd

𝛼

𝜔c

𝜔

Inner loopNDI controller

𝛹

𝛹

𝜃

𝜃

𝛽

𝛽

Figure 1: Flight control system block diagram.

UAV flightdynamics

qDynamicinversion

Linearcontroller

q

XqcmdLinearcontroller

𝜃cmd𝜃cmd

𝜃 −

Kg xqˆ ˆ ˆxq = Amxq + Bmu + B𝜎

𝜎 = −B−1 (Am−1 (eAmTs−I))−1 eAmTsx(iTs)

uad

L1 adaptive controller ofpiecewise constant adaptive law

[𝜃 q]T

𝜃Dynamicinversion

C(s)

ˆ ˆ𝜎1 + Hm−1 (s) Hum (s) H𝜎2

𝛿ecmdqcmd

Figure 2: Block diagram of L1 adaptive controller of piecewise constant adaptive law for pitch channel.

3International Journal of Aerospace Engineering

3.1. Baseline Controller: Nonlinear Dynamic Inversion. Non-linear dynamic inversion is a technique in which feedbackis used to linearize the system to be controlled and to providedesired dynamic [15, 24]. The inner loop controller is used tocontrol the angular accelerations and thrust of the aircraft.Thus, a simple first-order equation was added for thrustcontrol [12].

T =1τ

δtTmax − T , 3

where τ is the engine time constant and Tmax is the max-imum at the given flight condition.

The inner-loop dynamics are presented below:

Xin = Fin X Xin +Gin X Uin, 4

whereXin = p q r T T; Fin ∈ R4×1 andGin ∈ R4×1 are vec-tors of nonlinear algebraic equations.

With the pseudocontrol signalXind, the general nonlineardynamic inversion control law is given by

Uin = G−1in Xind − Fin X Xin , 5

where the over-hats have been used to denote that parame-ters are estimated, which are provided through look-up tablesin a real-time operation.

Inserting equation (5) into equation (4) leads to the fol-lowing equation:

Xin = Fin X Xin −Gin X G−1in Fin X Xin +Gin X G−1

in Xind

6

Equation (6) is the actual closed-loop input/output rela-tion after applying feedback linearization. Moreover, if theestimates in equation (6) are exact, then equation (6) yieldsan exact linear relation:

Xin =Xind 7

The out-loop dynamics inversion controller is designedin much the same way as the interloop controller. The out-loop dynamics are presented below:

Xout = Fout Xout +Gout Xout Xin, 8

where Xout = θ ψ β α T; Fout ∈ R4×1 and Gout ∈R4×1 are vectors of nonlinear algebraic equations.

With the pseudocontrol signal Xoutd, the general nonlin-ear dynamic inversion control law is given by

Xinc = G−1out Xoutd − Fout Xout 9

Inserting equation (9) into equation (8) leads to the fol-lowing equation:

Xout = Fout Xout +Gout Xout G−1out Xoutd − Fout Xout

10

If the estimates in equation (10) are exact, then equation(10) yields an exact linear relation:

Xout =Xoutd 11

3.2. L1 Adaptive Controller. The NDI-based controllerdescribed assumes exact knowledge of the system. How-ever, this is not the case. To address robustness to modeluncertainties, a L1 adaptive controller is designed as augmen-tation controller to compensate for unmodeled dynamics.

The pitch channel under baseline controller can be writ-ten in the form of

xq = −Amxq + Bmuq t + f t, xq t , z t ,

xq 0 = xq0,

xz t = g t, xz t , q ,

xz 0 = xz0,

z t = g0 t, xz t ,

y t = cTxq t ,

12

where xq = θ, q T ;Am ∈ R2×2 is a known real number definingthe desired dynamics for the closed-loop system; Bm, c areknown constant vectors; f t, xq t , z t represents all non-linearities and further uncertainties of the system. Theunmodeled dynamics of the states Z contribute to theseuncertainties; y t is the system output.

The system (12) can be written in the form

xq = −Amxq + Bm uq t + f 1 t, xq t , z t + Bumf 2 t, xq t , z t ,

xq 0 = xq0,

xz t = g t, xz t , xq ,

xz 0 = xz0,

z t = g0 t, xz t ,

y t = cTxq t ,

13


where Bum is created as the null space of BTm while keeping the

square matrix Bm Bum of full rank. f1 ⋅ represents thematched component of the uncertainties, whereas Bumf2 ⋅represents the unmatched component.

The system above verifies the following assumptions [25].

Assumption 1 (Boundedness of f i t, 0 ). There exists Bi > 0,such that f i t, 0 ∞ ≤ Bi holds for t ≥ 0 and for i = 1, 2.

Assumption 2 (Semiglobal Lipschitz condition). For arbitraryδ > 0, there exist positive K1δ, K2δ, such that

f i t, x1 − f i t, x2 ∞ ≤ Kiδ x1 − x2 ∞, i = 1, 2, 14

for all xj ∞≤ δ, j = 1, 2, uniformly in t.

Assumption 3 (Stability of unmodeled dynamics). The xz-dynamics are BIBO stable with respect to both initialconditions xz0 and input x t .

In this study, the uncertainties are mainly causedby aerodynamic parameters and the wind disturbance.They are always uniformly bounded and limited inhow fast they can change. Thus, these assumptions arereasonable.

3.2.1. Piecewise Constant L1 Adaptive Controller Design. Thestructure of the L1 adaptive augmentation is depicted inFigure 2. In this application a piecewise constant type of L1adaptive controller is used as descried in Ref. [25] Section 3.3.

A piecewise constant L1 adaptive controller is composedof a state predictor, an adaptive law, and a control law.

(1) State predictor

xq = Amxq t + Bm u t + σ1 t + Bumσ2 t 15

(2) Adaptive law

σ1 t

σ2 t= −B−1Φ−1 Ts e

AmTs xq iTs − xq iTs ,

16

where B = Bm Bum , Φ Ts = A−1m eAmTs − I , and

Ts is adaptation sampling time

(3) Control law

uad s = C s kgr s − σ1 s −H−1m s Hum s σ2 s ,

17

where Hm s = cT sI − Am−1Bm, Hum s = cT

sI − Am−1Bum, and C s is low-pass filter with C

0 = 1

Hm s is the reference transfer function from thematched input. Hum s is the reference transfer functionfrom unmatched input. kg is set to the steady gain kg = −1/cTA−1

m Bm .

3.2.2. Closed-Loop Reference System and PerformanceBounds. We define the closed-loop reference systemas [25]

xqref = −Amxqref + Bm uqref t + f1 t, xqref t , z t

+ Bumf2 t, xqref t , z t ,

xqref 0 = xq0,

uqref = −C s η1ref s +H−1m s Hum s η2ref s − kgr s

yref t = cTxqref t ,18

where η1ref s and η2ref s are the Laplace transformsof the signals ηiref t ≜ f i t, xqref t , z t , i = 1, 2.

Theorem 1 [25]. Given the adaptive closed-loop systemwith the L1 adaptive controller defined via (15), (16),and (17), subject to the L1-norm condition, the controlledsystem (13) will follow the reference system within thefollowing limits:

xq − xqref L∞≤ γx Ts ,

uq − uqref L∞≤ γu Ts ,

19

where γx and γu are dependent on f i t, x bounds and L1controller design parameters, Am, C s , and Ts.

Remark 1. As the sampling period Ts goes to zero, the sys-tem (13) will follow the reference system (18) arbitrarily

Time (s)109876543210

Pitc

h an

gle (

deg)

−2

0

2

4

6

8

10

12

14

16

Pitch commandPitch without L1 adaptive controlPitch with L1 adaptive control

Figure 3: Pitch angle capture task without parameter perturbations.


closely. It implies that the performance limitations areconsistent with the hardware limitations.

limTs→0

γx = 0,

limTs→0

γu = 0,20

Remark 2. the low-pass filter C s defines the trade-offbetween performance and robustness. Reducing the band-width of the filter, the time-delay margin of the systemcan be increased, while the performance reduced. On thecontrary, increasing the bandwidth of the filter leads toimproved performance with reduced robustness.

3.2.3. Implementation Details. The desired dynamics forpitch channel is set by a parameter ωθ = 5 rad/s, which corre-sponds to closed-loop reference response bandwidth. Thedamping parameter is set to 0.9 in this design.

The low-pass filter guarantees that the control signalstays in the low-frequency range even in the presence of fastadaptation. In Ref. [25], the authors suggest that the band-width of the filter is not frequencies beyond the control chan-nel bandwidth through to the control signal. On the otherhand, the filter bandwidths are related to the correspondingreference system bandwidth. So the filter bandwidths shouldbe higher than the desired system [26].

As presented before, the sampling time Ts has a signifi-cant influence on the L1 adaptive controller with piecewise-constant adaptation law. In Ref. [25], the authors suggest thatthe sampling time Ts is to choose as low as possible, consid-ering available computing power [25, 27]. After a series ofsimulations, the following parameters of the L1 controllerwere obtained:

C s =30

s + 30, Ts = 0 005s 21

4. Simulations

In order to examine the performance of L1 augmenteddynamic inversion controller for UAV carrier landing, threesimulation scenarios are considered.

Scenario 1. Pitch angle capture simulation.In this case, aerodynamic parameters are varied by 20%.

Mass and mass inertia properties are varied by 5%. The con-trol effectiveness are varied by 50%. Figure 3 shows the pitchangle tracking performance of the dynamic inversion con-troller with linear compensation versus its performance withL1 adaptive controller without parameter perturbations.Without parameter perturbations, performances of bothcontrol laws are very similar. However, as the parameter per-turbations are added (Figure 4), the performance of the linearcontroller degrades while the L1 controller manages to reduceeffects of parameter changes to controlled states better.

Scenario 2. UAV carrier landing simple simulation.In this case, turbulence and sea state effects are not

included. The forward speed of UAV is Va = 65 m/s, and

the aircraft carrier speed is Vb = 5 m/s. Figure 5 depicts theheight change during the carrier landing task. Figure 6depicts the top-down view of the trajectory of both theUAV and the carrier. When the simulation began, the UAVimmediately began to turn to intercept the glide path. As itapproached the prescribed glide path, it came out approxi-mately on the glide path at the landing heading with littleovershoot. It then maintained the prescribed glide path allthe way to touchdown. These results show that the controllerperforms well when turbulence and sea state effects are notincluded.

Scenario 3. UAV carrier landing Monte Carlo simulation.In this case, the performance of the controller is evaluated

through a Monte Carlo simulation. In order to compare withRef [12], the same simulation conditions are set. Accordingto Ref. [22], the simulation results of the total wind distur-bance components Ug, Vg, and Wg are shown in Figure 7,and the deck motion under sea state 4 is shown in Figure 8.

Time (s)109876543210

Pitc

h an

gle (

deg)

–2

0

2

4

6

8

10

12

14

16

Pitch command Pitch without L1 adaptive controlPitch with L1 adaptive control

Figure 4: Pitch angle capture task with parameter perturbations.

x/m−1000 −500 0 500

h/m

−50

0

50

100

150

200

UAVCarrier

Figure 5: UAV landing trajectory in the vertical plane.


The number of 500 Monte Carlo simulation experimentsare carried out. In this case, wind turbulence and sea stateeffects are included. The landing dispersions under NDIbaseline controller with linear compensation can be foundin Ref [12], while the landing dispersions with L1 adaptivecontrol augmentation under the same simulation conditionsis shown in Figure 9. It can be derived from Ref [12] that theincrease in wind turbulence greatly degraded the perfor-mance of the controller, as 13 (2.6%) caught the 1 wire, 123(24.6%) caught the 2 wire, 250 (50.0%) caught the 3 wire,and 114 (22.8%) caught the 4 wire [12]. However, when theL1 adaptive augmentation was added to the control loop, all500 simulation runs resulted in a successful trap. Of these,473 (95%) landed in the desired landing area.

5. Conclusions

In this paper, the design of a nonlinear inversion controllerfor UAV carrier landing has been developed. Furthermore,it has been explained how to augment this baseline controllerwith a L1 adaptive controller. The nonlinear simulationresults demonstrate that the baseline controller performs wellwhen the system model is accurate and without wind turbu-lence. However, when turbulence and sea state effects areincluded, the landing dispersion under L1 adaptive augmen-tation provides significant improvement.

Data Availability

This publication is supported by multiple datasets, which areopenly available at locations cited in References.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper.

Acknowledgments

This work was supported by the Aeronautical Science Foun-dation of China (Grant No. 20175752045; 2016ZA02001).

Times (s)1050 15 20 25 30 35 40

Carr

ier h

eave

per

turb

atio

n (m

)

–1.5

–1

–0.5

0

0.5

1

Figure 8: Deck motion under sea state 4.

Right of centerline Left of centerline−100 −80 −60 −40 −20 0 20 40 60 80 100

−100

−80

−60

−40

−20

0

20

40

60

80

3 wire

4 wire

2 wire

1 wire

<-- Runway edge

<--Safe landing edge

<--Desired landing area

Shor

t of a

impo

int

Long

of a

impo

int

(ft)

(ft)

Figure 9: Landing dispersion under NDI controller with L1adaptive control augmentation.

Distance a� carrier (m)0100200300400500

Win

d tu

rbul

ence

(m/s

)

–5

0

5

UgVgWg

Figure 7: Wind turbulence components.

x/m−1000 −500 0 500 1000

y/m

−1000

−500

0

500

CarrierUAV

Figure 6: UAV Landing trajectory in the horizontal plane.


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