Automatic carrier landing control for unmanned aerial vehicles based on preview control and particle filtering

Aerospace Science and Technology 81 (2018) 99–107

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Aerospace Science and Technology www.elsevier.com/locate/aescte

Automatic carrier landing control for unmanned aerial vehicles based on preview control and particle filtering ✩ Ziyang Zhen a,b,∗ , Shuoying Jiang a,b , Kun Ma a,b a b

Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China No.29, Jiangjun Road, Nanjing, China

a r t i c l e

i n f o

Article history: Received 15 October 2016 Received in revised form 17 July 2018 Accepted 21 July 2018 Available online 31 July 2018 Keywords: Unmanned aerial vehicle Automatic carrier landing Preview control Particle filtering Flight control

a b s t r a c t For the carrier-based unmanned aerial vehicles (UAVs), one of the important problems is the design of an automatic carrier landing system (ACLS) that would enable autonomous landing of the UAVs on a moving aircraft carrier. However, the safe autolanding on a moving aircraft is a complex task, mainly because of the deck motion and airwake disturbances, and dimension limitation. In this paper, an innovative ACLS system for carrier-based UAVs is developed, which is composed of the flight deck motion prediction, reference glide slope generation and integrated guidance and control (IGC) modules. The particle filtering method is used to online predict the magnitudes and frequencies of the deck motion, which are used to correct the reference glide slope to achieve minimum dispersion around the ideal touchdown point. An optimal preview control (OPC) scheme is presented for the IGC subsystem design, which fuses the preview information of the reference glide slope, equality constraint of UAV dynamics and performance index function, and predicted information of the carrier deck motion. Simulation results of a nonlinear UAV model show the effectiveness of the ACLS system in carrier autolanding under the deck motion and airwake disturbances. © 2018 Elsevier Masson SAS. All rights reserved.

1. Introduction With the successful carrier landing of the U.S. Navy’s X-47B by an arresting cable in 2013, the era of carrier-based unmanned aerial vehicle (UAV) is coming. However, carrier autolanding presents one of the most critical problems faced by the carrierbased aircraft. The small space of the carrier deck along with the terrible marine environmental disturbances such as the deck motion and airwake impose severe limitations on the landing performance. To overcome these difficulties, a reliable automatic carrier landing system (ACLS) is indispensible to improve the automatic landing safety of UAV. To maintain the predetermined flight speed, stabilize the flight attitude and track the reference glide slope, the flight control plays an important role in the autolanding of UAVs. Several control methods have been used in the design of the ACLS of the UAVs. Wadley et al. [1] designed an inner loop comprised of a desired dynamics regulator, a control allocation and optimization algorithm, and also designed a PID based outer-loop guidance law. The U.S.

✩

Fully documented templates are available in the elsarticle package on CTAN. Corresponding author at: Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China. E-mail address: [email protected] (Z. Zhen).

*

https://doi.org/10.1016/j.ast.2018.07.039 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.

Navy Research Laboratory developed an attitude and path angle control system based on the PID control method for a close-in covert autonomous disposable aircraft [2]. Actually, the above traditional engineering control methods may achieve satisfied landing performance in normal situations [3]. However, it is difficult for them to track the randomly changed reference glide path under the deck motion disturbances. Therefore, some advanced control methods for the ACLSs have been investigated in recent years. The dynamic inversion control theory was applied to design an ACLS for the unmanned combat aerial vehicle, which relied on the exact system model [4,5]. After adding wind and sea state turbulence, the control performance was degraded. Zheng et al. [6,7] presented some improved back-stepping methods for carrierbased UAVs, which were able to provide accurate tracking under some unknown aerodynamic parameters and actuator faults. However, the complexity of controller design makes them difficult to implement in engineering. An adaptive controller based on the approximate dynamic inversion and neural network was developed as the attitude-command-attitude-hold portion of the vehicle’s autopilot, which showed benefits over traditional controllers in robustness and tracking performance [8]. Moreover, some intelligent control methods have also sprung up, such as intelligent optimization control [9], neural network based adaptive control [10] and fuzzy integrated slide mode control [11]. They were fused with

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other methods to improve the control performance of the UAVs. However, they were difficult to be realized in real applications, and little literature considers the flight deck motion compensation and airwake rejection problems. Preview control aims to solve the trajectory tracking and disturbance rejection problems where the signals to be tracked or rejected are available a priori by a certain amount of time. It has attracted many researchers for its applications in autonomous vehicles, robotics and process control. The applications of preview control for active vehicle suspension system [12,13], motor servo system [14], biped walking robot [15] and rotorcraft [16] have been presented. It is suitable for systems that have reference signals known a priori. For the carrier autolanding control problem, the glide path is previewable and the carrier deck motion is predictable. Therefore, this paper presents an optimal preview control (OPC) method for the carrier autolanding of the UAVs. Different from the results in the literature, the main contributions of this paper are as follows: 1) The proposed OPC scheme utilizes the preview information of the reference glide slope, equality constraints of UAV dynamics and performance index function, to improve the landing path tracking precision of the carrier-based UAVs, which has not been reported in the literature. The OPC scheme is composed of a state feedback controller and a previewable reference signals feedforward controller. The nonlinear UAV model simulations verify the high landing precision of the OPC based ACLS system. 2) The deck motion prediction information is used to compensate the disturbance of the flight deck motion on the autolanding, which has not been studied in [1,2,6–9]. A particle filter is designed to predict the future information of deck motion, and the OPC based ACLS utilizes it to generate the feedforward compensation signal for disturbance rejection. The nonlinear UAV model’s simulations verify the effectiveness in disturbance rejection of the ACLS. 3) The OPC based ACLS is characterized by integrated guidance and control (IGC), which is different from the carrier landing control methods in [1–4,6–8,10]. The IGC system is blended without separation of the inner-loop and outer-loop controllers design, which simplifies the design process of the ACLS. The rest of this paper is organized as follows. In Section 2, the carrier autolanding problem is described. In Section 3, an ACLS framework for the carrier-based UAVs is developed. In Section 4, an OPC based IGC scheme is designed. In Section 5, the simulation results verify the desired system performance. In Section 6, we summarize our findings with conclusions. 2. Carrier autolanding problem of UAVs In this section, the nonlinear UAV model, deck motion model and airwake model are formulated, and the carrier autolanding guidance and control problem of the carrier-based UAVs is described.

⎧ ⎨ X˙ = V cos μ cos ϕ Y˙ = V cos μ sin ϕ ⎩ ˙ H = V sin μ ⎧ ⎨ φ˙ = p + (r cos φ + q sin φ) tan θ ψ˙ = cos1 θ (r cos φ + q sin φ) ⎩˙ θ = q cos φ − r sin φ ⎧ ˙ u u˙ + v v˙ + w w ˙ ⎪ V ⎨V = ˙ − w u˙ uw α˙ = u2 + w 2 ⎪ ⎩ β˙ = v V˙ − V v˙ 2

(3)

(4)

(5)

V cos β

Thus, the nonlinear UAV model can be expressed by

x˙ = f (x, u )

(6)

where x = [ V , α , β, θ, φ, ψ, p , q, r , H , Y ] , denoting the airspeed, angle of attack, sideslip angle, roll, pitch and yaw angles and angular rates, height and lateral deviation, respectively. u = [δe , δT , δa , δr ] T , denoting the elevator, throttle, aileron and rudder deflections, respectively. Deck motion model. The sea wave motion is generally considered as a stable random process with a narrow bandwidth. Durand presented a power spectrum based deck motion model [19]. The power spectral density function curves can be obtained by the experiments or simulations, which are used to find the optimal coefficients, and then a shaping filter can be constructed. The time domain information of the deck motion is obtained by filtering the white noise through the shaping filter. A general model for the translational deck motions (surge, sway, heave) is given by [19] T

G (s) =

a1 s2 + a2 s + a3 s4 + b 1 s3 + b 2 s2 + b 3 s + b 4

(7)

and a general model for the angular deck motions (pitch, roll, yaw) is given by

G (s) =

a1 s + a2 s4

+ b1

s3

+ b 2 s2 + b 3 s + b 4

(8)

where a1 ∼ a3 , b1 ∼ b4 are the constant coefficients. Airwake model. A general carrier airwake disturbance model is composed of free air turbulence component (u 1 , v 1 , w 1 ), steady component (u 2 , w 2 ), periodic component (u 3 , w 3 ), and random component (u 4 , v 4 , w 4 ), given by [20]

⎧ ⎨ u g = u1 + u2 + u3 + u4 v g = v1 + v4 ⎩ w g = w1 + w2 + w3 + w4

(9)

where u g denotes the axial airwake, v g denotes the side airwake, w g denotes the normal airwake. The specific mathematical equations of the four components of airwake can be found in [20]. 2.2. Autolanding problem of UAV

2.1. Modeling of UAV, deck motion and airwake Nonlinear UAV model. The equation of motion (EOM) set of the fixed-wing UAV is a fully-coupled nonlinear differential equations in a non-rotating Earth inertial reference frame, given by [17,18]

⎧ F ⎪ ⎨ u˙ = vr − wq − g sin θ + mx F v˙ = −ur − wp + g cos θ sin φ + my ⎪ ⎩w Fz ˙ = uq − vp + g cos θ cos φ + m ⎧ ⎨ p˙ = (c 1 r + c 2 p )q + c 3 L¯ + c 4 N q˙ = c 5 pr − c 6 ( p 2 − r 2 ) + c 7 M ⎩ r˙ = (c 8 p + c 2 r )q + c 4 L¯ + c 9 N

(1)

(2)

Difficulties of the carrier autolanding. There are several reasons why the carrier autolanding of the UAVs is a very difficult task. First, the landing must be performed in the presence of carrier deck motion, air wake and normal air turbulence. Especially, the carrier deck motion is the main factor which can greatly complicate this process. Second, the UAVs usually have unstable dynamics at low approach speeds, because they are usually operating on the backside (unstable) region in the landing phase. Therefore, to achieve a carrier autolanding, an automatic power compensation is necessary for the landing speed keeping control through adjusting the throttle opening. Third, the UAVs must be high enough to clear the carrier ramp, but low enough to catch the number 4 wire

Z. Zhen et al. / Aerospace Science and Technology 81 (2018) 99–107

101

Fig. 1. Framework of ACLS system.

with a hook attached to the aircraft. Therefore, the UAVs are required to track a reference glide slope with high precision. The reference glide slope is directing to an ideal touchdown point on a moving aircraft carrier. Guidance and control problems. Therefore, the UAVs carrier autolanding problem can be separated into the following two parts: 1) Guidance problem: Generally the UAVs complete the carrier autolanding by tracking a reference glide slope. Once the UAVs fly off the glide slope, the guidance system will generate the tracking error. For the UAVs, either horizontally or vertically, they must fly within a certain glide slope error or they need to be waved off. Furthermore, deck motion can change the position of the ideal touchdown point, especially the longitudinal deck motion can change the ideal landing height, which may cause the UAVs unable to land safely. Normally, at about final ten seconds, the reference glide path is a randomly changed curve for the purpose of compensating the deck motion, which is difficult to be tracked. Therefore, the deck motion compensation is very important for carrier autolanding. 2) Flight control problem: The controlled plant is the UAV system with dynamics of nonlinearity, multivariable coupling and unstable in low dynamic pressure. Generally, the glide path error is eliminated by controlling the attitudes of the UAV. To guarantee that the UAV can track the landing command precisely, a flight control system with fast response time and high accuracy is required. The UAV should fly at the correct airspeed and land at the right point on the flight deck, since the carrier autolanding should be cooperative with the moving aircraft carrier. Moreover, the carrier autolanding must occur with wings level, the proper lineup, and an acceptable sink rate to prevent damage from a hard landing. 3. Framework of ACLS system With the development of modern control theories, the design of guidance and control can be integrated based on the multivariable design strategy, replacing the traditional ACLS with separated guidance and control structure [1,3–7]. Therefore, a novel ACLS for the UAVs carrier autolanding is developed, which is composed of the carrier deck motion prediction module, landing command and reference glide slope generation module and IGC subsystem, shown in Fig. 1. The carrier deck motion prediction module is designed based on a particle filtering algorithm, to predict the deck motion information and send them to the landing command and reference

glide slope generation module. The landing command and reference glide slope generation module determines the landing speed and glide path according to the relative motion between the aircraft carrier and the UAV. The IGC system is blended without separated design of the inner-loop control laws and outer-loop guidance laws.

3.1. Carrier deck motion prediction

The deck motion predictor is designed based on the particle filter theory which need the discrete time model of deck motion. According to the linear constant system transfer functions (7)–(8), discretizing the deck motion equation, we get



:

xk = k,k−1 xk−1 + k,k−1 w k−1

(10)

zk = H k xk + υk

where k,k−1 is the state transition matrix; k,k−1 is the noise coefficient matrix; H k is the observation coefficient matrix; w k−1 is the system dynamic noise, whose variance matrix is Q k−1 ; υk is the observation noise, whose variance matrix is R k . The calculation procedure of the predictor is as follows [21]. Step I: Calculate the optimal state estimation xˆ k|k of system (10). 1) Initialize k = 0, take samples by the prior probability P (x0 ) and obtain the initial particle swarm {x0i }iN=1 , set the particles’ weights {ω0i }iN=1 = N −1 , N is the number of the particles; 2) Pre-

dict the particles {xki }iN=1 of tk based on (10) with {xki −1 }iN=1 of tk−1 ; 3) Update the particles’ weights by using ωki = ωki −1 · P ( zk |ˆxki ), and

ki = ωki / normalize the weights by using ω

N 

i =1

ωki ; 4) Resample data

according to the weights { ωki }iN=1 and obtain the particle swarm

{xki }iN=1 , reset the weights {ωki }iN=1 as N −1 ; 5) Estimate the state by N  xˆ k|k = ωki · xki , and k = k + 1. If k is less than the set threshold, i =1

go back to 2), else exit. Step II: Predict the deck motion information after the time τ , according to xˆ k+m|k = (k + m, k)ˆxk|k , in which m = τ / T s , (k + m, k) = e A τ =

∞ 

i =0

1 i!

· Ai τ i .

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3.2. Landing command and glide path generation

where X (k) =



In the final landing phase, the flight deck motion disturbance compensation is one of the key techniques. The landing command should be determined in advance, including the initial approach height H c0 , velocity V c , and reference glide slope path angle γc . A corrected reference glide slope { X c (t ), Y c (t ), − H c (t )} whose origin is in the ideal touchdown point on the flight deck is generated by [21]

⎧ ⎨ X c (t ) = V c (t − t c ) cos γc cos(ψ S + λac ) +  X S1 +  X S2 Y c (t ) = V c (t − t c ) cos γc sin(ψ S + λac ) + Y S1 + Y S2 ⎩ H c (t ) = V c (t − t c ) sin γc −  Z S1 −  Z S2

(11)

c

displacement vector of the ideal touchdown point caused by the translational motion of the flight deck, while { X S2 , Y S2 ,  Z S2 } is the displacement vector of the ideal touchdown point caused by the angular motion of the flight deck, which are transformed from the translational motion vector { X su , Y sw ,  Z he } and the angular motion vector {θ S , φ S , ψ S } of the flight deck. 3.3. Integrated guidance and control system

4. Optimal preview control scheme based IGC system Preview control is a linearization-based control scheme. The linearization-based strategy has been widely used in the real flight control system design. Therefore, in this section, we will deduce an optimal preview control algorithm and use it to design the IGC system in ACLS. 4.1. Optimal preview control algorithm

:

x(k + 1) = Ax(k) + Bu (k) y (k) = C x(k)

−C B B

 T ∞ e (k) Q e e (k) + u T (k) Q u u (k) ∞k=− Mr +1 T = k=− Mr +1 X (k) Q X X (k) + u T (k) Q u u (k)

, Gr =

(14)



Qe 0 is a positive semidefinite matrix, Q u is a 0 0 positive definite matrix. where Q X =

Assumption 1. ( A , B ) is controllable and ( A , C ) is observable. Assumption 2. r (k) is previewable, and the preview step is M r , which means that values r (k) ∼ r (k + M r ) are available. Theorem 1. For the closed-loop system with the plant (12), by minimizing the performance index function (14), the optimal preview control law Mr

K r ( j )r (k + j )

(15)

j =1

guarantees the optimality and the asymptotic stability of the control system. Here, the state feedback gain matrix K X and the idea output feedforward gain matrices K r ( j ), j = 1, 2, ..., M r are respectively calculated by

K X = −( Q u + G uT O G u )−1 G uT O G X K r ( j ) = −( Q u +

G uT

−1

O Gu)

G uT (G X

(16)

+ Gu K X )

j −1

O Gr

(17)

with a Riccati equation

O = Q X + G TX O G X − G TX O G u ( Q u + G uT O G u )−1 G uT O G X

(18)

Proof. First, due to Assumption 2, we construct an extended error system

X¯ (k + 1) = G¯ X X¯ (k) + G¯ U u (k) (19)



X (k) GX GR Gu where X¯ (k) = , G¯ X = , G¯ U = , GR = R (k) 0 IR 0 ⎡ ⎤ ⎡ ⎤ 0 I ··· 0 r (k + 1) ⎢ ⎥ .. ⎢ r (k + 2) ⎥ ⎢ ⎥ . 0 ⎥ ⎥, R (k) = ⎢ [G r 0 · · · 0], I R = ⎢ ⎢. ⎥. ⎢ ⎥ . . ⎣ ⎦ .. I ⎦ ⎣ .  r ( k + M ) r 0 0

J=



∞

k=− M r +1

(12)

where x ∈ R n is the state vector, u ∈ R r is the control input vector, y ∈ R m is the output vector. Suppose that the desired output vector is r (k), define error vector e (k) = r (k) − y (k), introduce the difference operator ( w (k) = w (k + 1) − w (k)), and construct the following error system:

X (k + 1) = G X X (k) + G u u (k) + G r r (k + 1)



Now the performance index function (14) is transformed into

Consider a generalized discrete plant :





I −C A , Gu = 0 A

J=

u ∗ (k) = K X X (k) +

During the carrier landing process, the glide path and landing commands of the UAV are known in advance, which are useful to improve the landing precision. Therefore, the preview control scheme is applied in the IGC subsystem, due to the following reasons. The OPC method uses future preview knowledge of the reference signal or disturbance in order to improve the tracking quality or reject the disturbance. The preview control problems can be categorized into two types depending on the previewed signal: either the desired trajectory in a tracking problem, or the external disturbance signal in a regulating problem. For the UAVs, the carrier autolanding problem can be regarded as a tracking problem with previewed information. Here, the previewed information includes the landing command, reference glide slope, equality constraint of the system dynamics and performance index function. Design process of the OPC based IGC system will be given in next section.



I . 0 Therefore, the optimal preview controller is defined to be u ∗ (k) that minimizes the following infinite-time performance index function:



H c0 where the landing time t c = V −sin γ . { X S1 , Y S1 ,  Z S1 } is the c



e (k) , GX = x(k)

(13)





X¯ (k) T Q¯ X X¯ (k) + u T (k) Q u u (k)

(20)



QX 0 . The problem (20) with the extended error 0 0 system (19) is exactly an optimal state regulator problem. Hence, based on the Pontryagin’s minimum principle, we get the optimal preview controller: where Q¯ X =

u ∗ (k) = −[ Q u + G¯ UT P G¯ U ]−1 G¯ UT P G¯ X X¯ (k)

(21)

with a Riccati equation T T P = Q X + G¯ TX P G¯ X − G¯ TX P G¯ U [ Q u + G¯ U P G¯ U ]−1 G¯ U P G¯ X

(22)

Z. Zhen et al. / Aerospace Science and Technology 81 (2018) 99–107

Now we partition P =



O ST

S , and substitute it to (21) and (22), T

we get











O S G u −1 ) 0 u + T 0

S T



 T O S GX GR X (k) Gu 0 0 IR R (k) ST T = −( Q u + G uT O G u )−1 G uT O G X X (k) −( Q u + G uT O G u )−1 G uT ( O G R + S I R ) R (k) = K X X (k) + K r R (k)

u ∗ (k) = −( Q

G uT

(23)

where

(25)

with a Riccati equation



O S ST T

T





O S QX 0 GX 0 GX GR = + T T T 0 IR 0 T 0 G R I R S T O  T O S GX 0 Gu − ( Q + G 0 u T T u 0 S T T ST G R I R



 O S G u −1 GX GR ) G uT 0 0 0 IR ST T

S T



(26) then we get

O = Q X + G TX O G X − G TX O G u ( Q u + G uT O G u )−1 G uT O G X

(27)

S = G TX [ O G R + S I R ] − G TX O G u ( Q u + G uT O G u )−1 G uT [ O G R + S I R ]

(28)

If we partition

S = [ S (1)

···

K r (2) S (2)

···

K r ( M r )]

(29)

S ( M r )]

(30)

and substitute them into (25), we get

K r = [ K r (1) K r (2) · · · K r ( M r )] = −( Q u + G uT O G u )−1 G uT ( O [G r 0 · · · +[0 S (1) · · · S ( M r − 1)])

0]

(31)

we substitute (30) to (28) then get

S = [ S (1) S (2) · · · S ( M r )] = G TX [ O [G r 0 · · · 0] + [0 S (1) · · · S ( M r − 1)]] (32) −G TX O G u ( Q u + G uT O G u )−1 G uT [ O [G r 0 · · · 0] +[0 S (1) · · · S ( M r − 1)]] According to (31) and (32), we can get

⎧ K r (1) = −( Q u + G uT O G u )−1 G uT O G r ⎪ ⎪ ⎪ ⎨ K (2) = −( Q + G T O G )−1 G T ξ T O G r

u

u

u

u

The longitudinal controller of the UAV automatically adjusts the elevator angle and the throttle opening to control the pitch attitude and airspeed, and to make UAV track the reference glide slope. By linearization of the nonlinear UAV model (1), a linear model can be obtained, which can be further decoupled into a longitudinal model and a lateral model. Linear longitudinal UAV model. The longitudinal model is given by

(24)

K r = −( Q u + G uT O G u )−1 G uT ( O G R + S I R )

K r = [ K r (1)

4.2. OPC based longitudinal controller design



K X = −( Q u + G uT O G u )−1 G uT O G X



103

r

.. ⎪ ⎪ . ⎪ ⎩ K r ( M r ) = −( Q u + G uT O G u )−1 G uT (ξ T ) M r −1 O G r

(33)

where ξ T = G X + G u K X . Hence

K r ( j ) = −( Q u + G uT O G u )−1 G uT (G X + G u K X ) j −1 O G r

(34)

here, Assumption 1 guarantees that there exists a symmetric positive definite matrix O , then Theorem 1 can be proven. Viewing from Theorem 1, it is found that the OPC scheme can fuse the future desired output information, system dynamic equation constraint information (12) and performance index function constraint information (14).

x˙ lon = A lon xlon + B lon ulon ylon (k) = C lon xlon (k)

(35)

where xlon = [ V , α , q, θ,  H ] T , ulon = [δe , δ T ] T , ylon = [ V ,  H ] T , here  denotes the deviation from the balanced flight state, and variables with a subscript lon denote the longitudinal variables. Longitudinal controller. According to Theorem 1, the optimal preview controller for the longitudinal channel is designed as

Mr ⎧ ∗ ulon (k) = K Xlon Xlon (k) + K ( j )rlon (k + j ) ⎪ j =1 rlon ⎪ ⎪ T −1 G T O G ⎪ ⎪ K = −( Q + G O G ) ulon ⎪ ulon lon ulon ulon lon Xlon ⎪ Xlon T T ⎪ ⎨ K rlon ( j ) = −( Q ulon + G ulon O lon G ulon )−1 G ulon j −1 × (G Xlon + G ulon K Xlon ) O lon G rlon ⎪ ⎪ ⎪ O lon = Q Xlon + G TXlon O lon G Xlon ⎪ ⎪ ⎪ T ⎪ − G TXlon O lon G ulon ( Q ulon + G ulon O lon G ulon )−1 ⎪ ⎩

(36)

T G ulon O lon G Xlon

4.3. OPC based lateral controller design In order to make the carrier based UAVs fly along the center line of the flight deck, the lateral control system must also be implemented. Once the UAV veered off the center line, the lateral controller will correct the flight path by adjusting the aileron and rudder deflections. Linear lateral UAV model. The lateral model of the carrier-based UAV is given by



x˙ lat = A lat xlat + B lat ulat ylat (k) = C lat xlat (k)

(37)

where xlat = [β, p , r , φ, Y ] T , ulat = [δa , δr ] T , ylat = Y . And variables with a subscript lat denote the lateral variables. Lateral controller. According to Theorem 1, the optimal preview controller for the lateral channel is designed as

Mr ⎧ ∗ ⎪ ⎪ ulat (k) = K Xlat Xlat (k) + j =1 K rlat ( j )rlat (k + j ) ⎪ T −1 T ⎪ ⎪ ⎪ K Xlat = −( Q ulat + G ulat O lat G ulat ) G ulat O lat G Xlat ⎪ T T ⎪ ⎨ K rlat ( j ) = −( Q ulat + G ulat O lat G ulat )−1 G ulat j −1 × (G Xlat + G ulat K Xlat ) O lat G rlat ⎪ ⎪ ⎪ O lat = Q Xlat + G TXlat O lat G Xlat − G TXlat O lat G ulat ⎪ ⎪ ⎪ T ⎪ × ( Q ulat + G ulat O lat G ulat )−1 ⎪ ⎩

(38)

T G ulat O lat G Xlat

5. Simulation study In this section, we will apply the OPC based ACLS system to the nonlinear UAV model and verify the carrier autolanding performance. The effectiveness of the OPC method is verified by comparing with the traditional PID control method and linear quadratic (LQ) control method.

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Fig. 2. Deck motion under smooth sea condition and its prediction values.

Fig. 3. Deck motion under moderate sea condition and its prediction values.

Fig. 4. Deck motion under severe sea condition and its prediction values.

5.1. Simulation conditions

Nonlinear UAV model and its linearization. A nonlinear model of an UAV with six degrees-of-freedom is established in MATLAB/Simulink programming environment. The “Silver Fox” UAV [22] is chosen as a prototype for this work, which parameters and aerodynamics data are given in [23]. The equilibrium flight state values of the UAV are: V = 20 m/s, α = 3.959◦ , θ = 0.4584◦ , δe = −0.3994◦ , δT = 0.4407, H = 19 m. The numerical linear models are obtained by linearization of the nonlinear model in this equilibrium flight state. ACLS system based on OPC. The framework of ACLS system is given in Fig. 1. The landing command and reference glide slope are generated according to (11). The OPC based IGC laws are expressed by (36) and (38). In the simulation, the inclination angle of the reference glide slope is −3.5◦ , the initial altitude deviation is 3 m,

and the initial lateral deviation is 1m. The sampling time is T s = 0.1 s and the preview time of the preview controller is τ = 2 s. Deck motion model and its prediction. For the carrier deck motion model, the simulation conditions of the white noise are set as: noise power is 1.0, sample time is 0.1 s, seed is 14444. The predictive time is 2 s. The particle filter based deck motion predictor is adopted and the effect of the predictor under smooth sea condition, moderate sea condition and severe sea condition are shown in Figs. 2–4. It is found that the deck motion predictive errors are small enough which will contribute to the satisfied compensation. Airwake model. In the process of carrier autolanding, the airwake disturbance has a great influence on the safety of the carrier landing. To simulate the real carrier landing environment, the airwake disturbance is considered for verifying the robustness of the proposed ACLS scheme. According to [20], the simulation results of the total air disturbance components u g , w g , v g can be shown in Fig. 5.

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Table 1 Parameters of PID control system. Kθ p KH p KY

p

0.65 0.07 0.1

Kφ

p

2

Kβ

p

1

KV

p

1

K θi i KH p Kψ K φi K βi

K Vi

0.65 0.05 3.5

K θd K dH Kp

0.09 0 0.3

1.8

K φd

0.05

0.5

Kr

0.3

1.5

Fig. 6. Glide path tracking errors of OPC method with deck motion under different sea conditions.

LQ control scheme. The LQ controllers for the longitudinal channel and lateral channel are respectively designed as Fig. 5. Airwake disturbance components u g , w g , v g .

5.2. Parameters of controllers PID control scheme. The PID control system consists of three channels: height deviation control channel, lateral deviation control channel and autothrottle channel. The height deviation guidance and control laws are designed by p

θc = ( K H + p

δe = ( K θ +

i KH

s

+ K dH s)( H c −  H )

(39)

+ K θd s)(θc − θ)

(40)

i

Kθ s

The lateral deviation guidance and control laws are designed by p

φc = ( K Y + p

δa = ( K φ +

K Yi s K φi s

+ K Yd s)(Y c − Y ) + K ψ (ψc − ψ) d

+ K φ s)(φc − φ) − K p  p p

δr = − K r r − ( K β +

K βi s

)(βc − β)

p

K Vi s

)( V c −  V )

The PID control parameters are given in the Table 1.

(45)

(46)

B lat O lat A lat

where Q ulon = [1 0; 0 2] and Q ulat = [2.5 0; 0 2]. Preview control scheme. The preview step M r of longitudinal OPC is 20, and the adjustable parameters Q elon = [0.5 0; 0 15], Q ulon = [1 0; 0 2]. The preview step M r of lateral OPC is 20, and the adjustable parameters Q elat = 1, Q ulat = [2.5 0; 0 2].

(41) 5.3. Simulation results and analysis

(42) (43)

The autothrottle control law is designed by

δ T = ( K V +

⎧ ∗ ⎪ ⎪ ulon (k) = K xlon xlon (k)T ⎪ T ⎪ O lon A lon ⎨ K xlon = −( Q ulon + B lon O lon B lon )−1 B lon T T O lon = C lon Q xlon C lon + Alon O lon A lon ⎪ T T ⎪ − Alon O lon B lon ( Q ulon + B lon O lon B lon )−1 ⎪ ⎪ ⎩ T B O lon A lon ⎧ ∗ lon ulat (k) = K xlat xlat (k) ⎪ ⎪ ⎪ T T ⎪ O lat B lat )−1 B lat O lat A lat ⎨ K xlat = −( Q ulat + B lat T T O lat = C lat Q xlat C lat + Alat O lat A lat ⎪ T T ⎪ − Alat O lat B lat ( Q ulat + B lat O lat B lat )−1 ⎪ ⎪ ⎩ T

(44)

Fig. 6 shows the longitudinal and lateral path tracking errors of OPC method with three different deck motion states (including smooth, mederate and severe sea conditions). It is found that the OPC method can achieve satisfied glide path tracking performance even under the large deck motion disturbance. Fig. 7 and Fig. 8 show the comparison of longitudinal and lateral glide path tracking errors of the OPC, LQ and PID control methods with different deck motion disturbances. It is found that three schemes can effectively control the UAV to track the reference glide slope under the smooth deck motion disturbance. How-

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Z. Zhen et al. / Aerospace Science and Technology 81 (2018) 99–107

Fig. 7. Comparison of glide path tracking response of OPC, LQ and PID controllers with deck motion under smooth sea condition.

Fig. 8. Comparison of glide path tracking response of OPC, LQ and PID controllers with deck motion under moderate sea condition.

Fig. 9. Comparison of glide path tracking response of OPC, LQ and PID controllers with both deck motion and airwake disturbances under smooth sea condition.

Fig. 10. Comparison of glide path tracking response of OPC, LQ and PID controllers with both deck motion and airwake disturbances under moderate sea condition.

6. Conclusion ever, the landing performance of PID control scheme deteriorates rapidly when there are large deck motion disturbances, while the OPC scheme still maintains the highest landing performance. The OPC method achieves the higher tracking precision and fastest setting time among the three different control methods, under the disturbance of deck motion. Therefore, the OPC scheme has the best deck motion compensation effect and the highest carrier landing performance. Figs. 9–10 show the comparison of longitudinal and lateral glide path tracking errors of OPC, LQ and PID control schemes with both the deck motion and airwake disturbances under different sea conditions. We get that the PID control method is difficult to reject the airwake disturbance, and the OPC method achieves the best robustness under the airwake disturbance.

This work aims to solve the carrier autolanding problem of UAVs. In order to make the UAV track the reference glide slope, especially considering the carrier deck motion and airwake disturbances at the final stage of the carrier landing phase, an ACLS system based on an OPC scheme with a particle filter is developed. Different from the literature on carrier landing control problem, the proposed ACLS system can effectively utilize the information of the previewable reference glide slope, predictable carrier deck motion, UAV dynamical equation and performance index function constraints, to improve the landing precision. Simulation results of a nonlinear UAV model show that the optimal preview control scheme has faster response time and higher accuracy than the traditional PID control scheme and the LQ scheme.

Z. Zhen et al. / Aerospace Science and Technology 81 (2018) 99–107

The developed ACLS system improves the carrier landing performance of UAVs, which contributes to increasing the success rate of the automatic carrier landing for the UAVs. The OPC based flight controllers are linear time-invariant controllers, which can be easily realized in the practical applications. However, the OPC scheme is a model based control strategy, thus an accurate numerical dynamic model of the UAV is necessary for the control design. Therefore, the preview control methods independent of the system models will be more attractive. Moreover, many improved particle filtering methods or other optimization algorithms have been presented recently, therefore, it is necessary to apply these improved methods in the deck motion prediction. These problems are expected to be studied in the future work. Conflict of interest statement There is no conflict of interest. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 61741313, 61673209, 61533008), the Aeronautical Science Foundation (NO. 2016ZA52009), the Fundamental Research Funds for the Central Universities (No. NS2017015), and the Jiangsu Six Peak of Talents Program (NO. KTHY-027). References [1] J. Wadley, G. Tallant, R. Ruszkowski, Adaptive flight control of a carrier based unmanned air vehicle, in: AIAA Guidance, Navigation, and Control Conference and Exhibit, 11–14 August 2003, Austin, Texas, 2003. [2] A. Kahn, D. Edwards, Navigation, guidance and control for the CICADA expendable micro air vehicle, in: Proceedings of AIAA Guidance, Navigation and Control Conference, 2012. [3] J.M. Urnes, R.K. Hess, Development of the F/A-18A automatic carrier landing system, J. Guid. Control Dyn. 8 (395) (1985) 289–295. [4] N.A. Denison, Automated carrier landing of an unmanned combat aerial vehicle using dynamic inversion, in: Air Force Institute of Technology, 2007. [5] J.D. Boskovic, J. Redding, An autonomous carrier landing system for unmanned aerial vehicles, in: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, 2009.

107

[6] F.Y. Zheng, H.J. Gong, Z.Y. Zhen, Adaptive constraint backstepping fault tolerant control for small carrier UAV with uncertain parameters, Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 230 (2016) 407–425. [7] F.Y. Zheng, Z.Y. Zhen, H.J. Gong, Observer-based backstepping longitudinal control for carrier-based UAV with actuator faults, J. Syst. Eng. Electron. 28 (2) (2017) 322–337. [8] A. Kahn, Adaptive control for small fixed-wing unmanned air vehicles, in: Proceedings of AIAA Guidance, Navigation, and Control Conference, 2010, pp. 2010–8413. [9] A. Bourmistrova, S. Khantsis, Control System Design Optimisation via Genetic Programming, in: Proceedings of IEEE Congress on Evolutionary Computation, 2007, pp. 1993–2000. [10] L. Sonneveldt, E.R.V. Oort, Q.P. Chu, et al., Nonlinear adaptive trajectory control applied to an F-16 model, J. Guid. Control Dyn. 32 (1) (2015) 25–39. [11] F.Y. Zheng, H.J. Gong, Z.Y. Zhen, Integral sliding mode control based UAV automatic landing system, System Eng. Electron. Technol. 37 (7) (2015) 1621–1628. [12] R.S. Prabakar, C. Sujatha, S. Narayanan, Optimal semi-active preview control response of a half car vehicle model with magnetorheological damper, J. Sound Vib. 326 (3–5) (2009) 400–420. [13] P.S. Li, L. James, C.C. Kie, Multi-objective control for active vehicle suspension with wheelbase preview, J. Sound Vib. 333 (2014) 5269–5282. [14] M.M.M. Negm, J.M. Bakhashwain, M.H. Shwehdi, Speed control of a three-phase induction motor based on robust optimal preview control theory, IEEE Trans. Energy Convers. 21 (1) (2006) 77–84. [15] S. Shimmyo, T. Sato, K. Ohnishi, Biped walking pattern generation by using preview control based on three-mass model, IEEE Trans. Ind. Electron. 60 (11) (2013) 5137–5147. [16] N. Paulino, C. Silvestre, R. Cunha, Affine parameter-dependent preview control for rotorcraft terrain following flight, J. Guid. Control Dyn. 29 (6) (2006) 1350–1359. [17] Z.Y. Zhen, J. Jiang, X.H. Wang, C. Gao, Information fusion based optimal attitude control for large civil aircraft in landing phase, ISA Trans. 55 (2015) 81–91. [18] B.L. Stevens, F.L. Lewis, Aircraft Control and Simulation, Wiley, Hoboken, NJ, 2003, pp. 254–500. [19] T.S. Durand, G.L. Teper, An Analysis of Terminal Flight Path Control in Carrier Landing, USA: AD19641964, 1964. [20] Anon. Military Specifications-Flying Qualities of Piloted Airplanes. MIL-F-8785C, Department of Defence, USA, Notice 2, 28th August, 1996. [21] Z.Y. Zhen, S.Y. Jiang, J. Jiang, Preview control and particle filtering for automatic carrier landing, IEEE Trans. Aerosp. Electron. Syst. (2018), Early Access. [22] M.C.L. Patterson, A. Brescia, Requirements Driven UAV Development, USA: ADA504039, 2007. [23] A. Archontakis, Assessing the flight quality of a large UAV for sensors/ground robots aerial delivery, in: Thesis of Naval Postgraduate School, 2010.