Motion Synchronous Composite Decoupling with Fewer Sensors on

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Motion Synchronous Composite Decoupling with Fewer Sensors on Multichannel Hydraulic Force Control for Aircraft Structural Loading Test System Yaoxing Shang, Ning Bai, Lingzhi Jiao, Nan Yao, Shuai Wu * and Zongxia Jiao National Key laboratory on Aircraft Fight Control, School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China; [email protected] (Y.S.); [email protected] (N.B.); [email protected] (L.J.); [email protected] (N.Y.); [email protected] (Z.J.) * Correspondence: [email protected]; Tel.: +86-10-8231-7303 Received: 6 October 2018; Accepted: 12 November 2018; Published: 20 November 2018







Abstract: The aircraft full-scale fatigue test is widely used in the modern aircraft industry for the safety of flight. Generally, the aircraft full-scale fatigue test is achieved by structural loading; multiple hydraulic actuators are used to apply load for force control. The fatigue loading test takes approximately several years. A key challenge is how to accelerate the loading frequency to shorten the total test time. Nevertheless, when pluralities of hydraulic actuator simultaneously increase the loading frequency, the mutual coupling force from the low rigidity of the aircraft structure will cause a large loading error, meaning that the test cannot be implemented. Although it is possible to reduce error by adding sensors, the force sensors need to connect several kilometers of cable. This paper proposed a novel motion synchronous composite decoupling control strategy with fewer sensors. The control method compensates the negative coupling effect of the channels by integrating the command signals and feedback signals of all channels. It can suppress coupling force and reduce errors at higher frequencies, thereby shortening the experiment time. Opposed to traditional decoupling control methods, advantages of this strategy are that it only needs force sensors and it does not need additional displacement or velocity and acceleration sensors to collect state variables for building the state space. Furthermore, it has been experimentally verified that the new motion synchronous composite decoupling control method can indeed guarantee sufficient control accuracy when the test frequency is increased. The method has great economic significance for shortening test duration. Keywords: structural test; load senor; hydraulic loading system; fatigue test; force control; aircraft strain gauges; coupling

1. Introduction The structure of an aircraft forms the basis of aircraft flight safety. In order to guarantee flight safety and predict the service life of the aircraft structure accurately, structural fatigue loading tests [1] must be carried out on the ground. According to the classic “bottom-top” approach [2,3], the aircraft full-scale fatigue test is located in the top of the “bottom-top” approach, which is the closest to the real fight situation. The FAA (Federal Aviation Administration), EASA (European Aviation Safety Administration), and CAAC (Civil Aviation Administration of China) have all clearly stated in their respective certification regulations that the full-scale fatigue test verification report must be provided. At present, the aircraft full-scale fatigue test is executed by multichannel hydraulic coordinated loading. The full-aircraft uses dozens to hundreds of hydraulic pressure control systems to apply an alternating load to simulate the huge load of an aircraft flying in the air [4]. Firstly, a hydraulic

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actuator is arranged at each test point of the aircraft structure which is equipped with a load sensor for forceisclosed-loop theaircraft aircraftstructure is covered with approximately strain actuator arranged at control. each testSecondly, point of the which is equipped with a10,000 load sensor gauges. These strain gauges monitor whether the structural deformation of the aircraft meets the for force closed-loop control. Secondly, the aircraft is covered with approximately 10,000 strain design requirements. gauges. These strain gauges monitor whether the structural deformation of the aircraft meets the The current aircraft fatigue loading test urgently needs to shorten the time: It takes 2 to design requirements. 6 years [5] to complete. Because the average life of needs modern civil aircraft is asIt high 60,000 flight The current aircraft fatigue loading test urgently to shorten the time: takesas 2 to 6 years [5] hours multiple life tests are required in the test [6,7]. The key to influencing the test time now is the to complete. Because the average life of modern civil aircraft is as high as 60,000 flight hours multiple limitation the loading frequency strong coupling between the channels life tests areofrequired in the test [6,7].and Thethe key to influencing the test time now is the[8,9]. limitation of the Due to the low rigidity of the aircraft structure and the large deformation, the current loading loading frequency and the strong coupling between the channels [8,9]. frequency only 0.1rigidity Hz. Using a aircraft typical aircraft airfoil structural strength testthe as an example, the Due toisthe low of the structure and the large deformation, current loading span of the airfoil tip and the airfoil root is as long as several tens of meters, and the airfoil tip is frequency is only 0.1 Hz. Using a typical aircraft airfoil structural strength test as an example, the deformed several meters Typical fatigue test force loadingand figure shown in span of theby airfoil tip and the[10]. airfoil root isfull-scale as long as several tens of meters, the as airfoil tip is Figure 1. Accelerating the load frequency slightly will exacerbate the load–force coupling between deformed by several meters [10]. Typical full-scale fatigue test force loading figure as shown in Figure 1. the differentthe loading channels,slightly causingwill theexacerbate loading error of the loading force control be out Accelerating load frequency the load–force coupling between theto different of tolerance [11]. causing the loading error of the loading force control to be out of tolerance [11]. loading channels,

Figure Figure 1. 1. Typical Typical full-scale full-scale fatigue fatigue test. test.

Therefore, how to overcome the coupling effect between the loading channels and achieve accurate Therefore, how to overcome the coupling effect between the loading channels and achieve and unified loading of multiple channels has become a major problem in this field. The key to overcome accurate and unified loading of multiple channels has become a major problem in this field. The key this problem is how to only use force sensors for the decoupling control [12,13] of dozens of channels. to overcome this problem is how to only use force sensors for the decoupling control [12,13] of dozens Because the size of the civil aircraft is very large, only the cable of the force sensors is several kilometers of channels. Because the size of the civil aircraft is very large, only the cable of the force sensors is in the fatigue test, and the addition of a new sensor is hardly allowed. Many decoupling methods exist several kilometers in the fatigue test, and the addition of a new sensor is hardly allowed. Many today, such as state space decoupling [14], which requires the acquisition of process variables such decoupling methods exist today, such as state space decoupling [14], which requires the acquisition as position, velocity, and even acceleration of each loading point in addition to pressure sampling. of process variables such as position, velocity, and even acceleration of each loading point in addition A large number of different types of sensors are not only unbearable for cable scale, but also exacerbate to pressure sampling. A large number of different types of sensors are not only unbearable for cable electromagnetic compatibility (EMC) problems, and the huge data computing load will limit the scale, but also exacerbate electromagnetic compatibility (EMC) problems, and the huge data real-time of the control system. computing load will limit the real-time of the control system. Therefore, this paper proposes a novel synchronous composite decoupling control method with Therefore, this paper proposes a novel synchronous composite decoupling control method with less sensors based on multichannel servo control signals. The innovation of this method is to combine less sensors based on multichannel servo control signals. The innovation of this method is to combine the control signals of all other channels with the given signal of the current channel, and use this the control signals of all other channels with the given signal of the current channel, and use this compound signal as the feed forward input signal of the current channel to compensate the servo compound signal as the feed forward input signal of the current channel to compensate the servo output of each single channel to eliminate the coupling force interference between channels. output of each single channel to eliminate the coupling force interference between channels. This method need not the complex coupling link between the simulated load force and This method need not the complex coupling link between the simulated load force and the the deformation displacement, omitting the use of state variables such as position, velocity, and deformation displacement, omitting the use of state variables such as position, velocity, and acceleration, and avoiding the signal noise caused by the numerical differentiation of the position acceleration, and avoiding the signal noise caused by the numerical differentiation of the position signal. The feed forward compensation signal used in this method has obvious advanced predictability, signal. The feed forward compensation signal used in this method has obvious advanced which can ensure the fastness and consistency of multichannel loading of digital discrete control. predictability, which can ensure the fastness and consistency of multichannel loading of digital discrete control. 2. Analysis of the Loading Coupling

2. Analysis Loading Coupling 2.1. Principleof of the Displacement Overlapping In the actual aircraft full-scale fatigue test, the loading method of various parts is also varied. 2.1. Principle of Displacement Overlapping However, the most common high-aspect-ratio airfoil is simple in shape. The high-aspect-ratio airfoil In the aircraft full-scale fatigue test, thelinear loading method of various also varied. loading can actual be approximated as a one-dimensional loading, so the loading parts pointsisare arranged However, the most common high-aspect-ratio airfoil is simple in shape. The high-aspect-ratio airfoil

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loading can be approximated as a one-dimensional linear loading, so the loading points are arranged in Byanalyzing analyzingthe therelationship relationshipbetween between the airfoil and fuselage, inaa straight straight line in space. By the airfoil and thethe fuselage, andand the the displacement of the airfoil root during loading is almost negligible. Therefore, the airfoil can displacement of the airfoil root during loading is almost negligible. Therefore, can be be regarded regardedas asaacantilever cantileverbeam. beam. Mathematical of of thethe multi-point forceforce of theofcantilever beam isbeam carried next. out Without Mathematicalmodeling modeling multi-point the cantilever is out carried next. losing the generality, the entire cantilever beam is divided into three parts which are loaded through Without losing the generality, the entire cantilever beam is divided into three parts which are loaded three channels; assuming assuming that the loading channel produces vertical upward force. The cantilever through three channels; that the loading channel aproduces a vertical upward force. The beam is also bentisinalso the bent vertical direction at direction the loading point; there point; is no bending or twisting cantilever beam in the vertical at the loading there is no bending in or other directions. the material cantileverthe beam has a small twisting in otherAccording directions.toAccording to mechanics, the materialthe mechanics, cantilever beamdeformation has a small within a certain range, the range, stress subjected to the subjected stress doestonot maximum stress. deformation within a and certain and the stress theexceed stress the does not exceed the Therefore, the deflection curve of the cantilever beam can be approximated by a linear differential maximum stress. Therefore, the deflection curve of the cantilever beam can be approximated by a equation. When three loads are simultaneously loaded on the cantilever deflection curve linear differential equation. When three loads are simultaneously loaded beam, on thethe cantilever beam, the of the cantilever be regarded ascan a linear superposition combination of different deflection deflection curvebeam of thecan cantilever beam be regarded as a linear superposition combination of curve equations generated by a single load acting on different loading points of the cantilever beam different deflection curve equations generated by a single load acting on different loading points of according to thisbeam relationship. When therelationship. linearly distributed loadlinearly force acts on the cantilever beam [15], the cantilever according to this When the distributed load force acts on the the cantilever can be by thebeam superposition principle thedeflection cantilevercurve beamequation [15], theof deflection curvebeam equation ofobtained the cantilever can be obtained by[16] the of the deflections. The model is the shown in FigureThe 2. model is shown in Figure 2. superposition principle [16] of deflections. Prototype of wing structrue

Prototype of wing structrue

ωn

Mass concentration point

ω2

ω1

L1

L2 F1

L1

Ln F2

…

Fn

(a)

L2 F1

F2

Ln …

Fn

(b)

Figure Figure2.2.Loading Loadingmodel modelof ofthe thestructural structuraltest. test.(a) (a)shows showsaasimplified simplifiedmodel modelofofthe theairfoil. airfoil.(b) (b)shows shows the thedeflection deflectionofofthe themodel modelatateach eachloading loadingpoint. point.

In InFigure Figure2a, 2a,the theloading loadingobject objectisisthe thecantilever cantileverbeam beamwhich whichisisaasimplified simplifiedmodel modelrepresenting representing the airfoil. The vertical upward arrows represent that the hydraulic cylinders apply force the airfoil. The vertical upward arrows represent that the hydraulic cylinders apply forceto todifferent different position of cantilever beam at the same time. The cantilever beam is naturally divided into position of cantilever beam at the same time. The cantilever beam is naturally divided intonnpieces pieces according position of of the theloading loadingpoint. point.The Themass massofof each section is the percentage of accordingto to the the actual actual position each section is the percentage of the the length of the section multiplied by the total mass. F is the loading force of loading channel i. iis the loading force of loading channel i. Li length of the section multiplied by the total mass. represents the distance from loading point i to the fixed represents the distance from loading point i to the fixedside sideof ofthe thecantilever cantileverbeam. beam. In In Figure Figure 2b, 2b, ωi represents representsthe thedeflection deflectionofofthe theloading loadingpoint pointi.i.Here Herewe weassume assumenn==33and andi i==1, 1,2, 2,3.3. According to the material mechanics, when only the load force F acts on the pointpoint 1, the1, According to the material mechanics, when only the load force1 acts on loading the loading deflection of point 1 is 1 is the deflection of point F1 L31 ω11 = , (1) 3EI (1) = , 3 where EI is the bending stiffness of the cantilever beam and the deflection of point 2 is where EI is the bending stiffness of the cantilever beam and the deflection of point 2 is F1 L31 (2) ω= 12 = (3 (3L (2) −2 −),L1 ), 3 3EI The the point 2 is the point 2 is Thedeflection deflectionproduced producedby byF1 atat F1(3 L31 − ), (3) (3) ω= 13 = 3 3EI (3L3 − L1 ), , and at the action points 1, 2, and 3 can be The deflections generated by , The deflections generated by F1 , F2 , and F3 at the action points 1, 2, and 3 can be calculated separately. calculated separately. According to the relevant principles of material mechanics, when only is applied on the cantilever beam, the deflection [17] of the loading point j is given as

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According to the relevant principles of material mechanics, when only Fi is applied on the cantilever beam, the deflection [17] of the loading point j is given as ωij = Fi δij ,

(4)

where δij is the relative flexibility from channel i to channel j. According to the superposition principle, when total n points are loading at the same time, ω j indicating the deflection of the loading point j is given as ωj =

n

∑i

ωij ,

(5)

Thus, the deflection vector ω can be given as ω = δij F,

(6)

where δij (i = 1, 2, . . . , j = 1, 2, . . . , n) is the flexibility matrix of the cantilever beam. F represents the vector of loading force. If i and j are all equal to 3:   ω1     ω2  =   ω3 

L31 3EI L21 (3L2 − L1 ) 6EI L21 (3L3 − L1 ) 6EI

L21 (3L2 − L1 ) 6EI L32 3EI L22 (3L3 − L2 ) 6EI

L21 (3L3 − L1 ) 6EI L22 (3L3 − L2 ) 6EI L33 3EI



 F 1    F2  .  F3

(7)

The above equation reveals the basic coupling relationship of the cantilever beam linear distributed low frequency and small amplitude loading. 2.2. Mass Concentration Method The distributed mass of the cantilever beam can be transformed into focus through mass concentration method [18]. Thus, the infinite freedom degree of the system can be transformed into multi-degree of freedom and the calculation can be simplified. According to the static equivalent principle, the concentrated gravity is equivalent to the origin. The mass strip with uniform distribution is divided into n parts in accordance with the practical loading points. The mass of part i is mi . In light of the static equivalent principle, the distributed mass of a part can be transformed into the concentrated mass of both ends. The concentrated mass of an end is mi /2. Two contiguous concentrated mass points constitute one concentrated mass in loading point, whose mass is (mi + mi + 1 )/2. After the transformation of concentrated mass, the loading model of the system with deformation is represented in Figure 2b. Here we assume n = 3, and the masses of loading points 1, 2, and 3 are 1/3, 1/3, and 1/6 of the total mass, respectively. 2.3. Analysis of the Loading Coupling When multiple channels are co-loaded, loading channels i and j are selected. While channel i is loaded, the channel j is also loaded. The coupling effect of the force necessarily causes the point i to produce additional deflection. This extra deflection is multiplied by the stiffness of the point i itself, which creates an additional force from the channel j in the channel i. It can be simply understood that the force of the channel j will be converted to point i by a certain proportional coefficient. This force is linearly added to the loading force of channel i to produce a displacement at the loading point i. The proportional parameter can be expressed as a linear coupling parameter of the cantilever beam, which is called a structural parameter. Specifically, it can be expressed as the ratio of j channel to i channel relative flexibility and i channel absolute compliance. The structure parameter Kij can be given as

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Kij = δi /δij ,

(8)

where δi is the absolute compliance, and δij is the relative flexibility of each loading point. Obviously, the force of the channel j coupling to the point i can be expressed as the structural parameters Kij multiplied by the loading force of channel j. To express more clearly, if i is equal to 1, 2, and 3, respectively, the absolute flexibility matrix of the cantilever beam is obtained as follows  3 3 3    

L1 3EI L32 3EI L33 3EI

L1 3EI L32 3EI L33 3EI

L1 3EI L32 3EI L33 3EI

 , 

(9)

Combining the δij generated by (6), the dimensionless matrix with respect to the structural parameter Kij is (i, j = 1, 2, 3) 

1

   

L21 (3L2 − L1 ) 2L32 L21 (3L3 − L1 ) 2L33

3L2 − L1 2L1

3L3 − L1 2L1 3L3 − L2 2L2

1 L22 (3L3 − L2 ) 2L33

1

   , 

(10)

Through the above analysis, the matrix can be approximated as a coefficient matrix in which the loading forces between the multiple channels. Establishing the coupling coefficient matrix has revealed the relationship between the loading points of the cantilever beam when the multichannel load force is simultaneously loaded. However, in order to further simulate the true connection relationship between the servo actuator and the loading point in the full-scale fatigue test, it is necessary to establish a dynamic model of the coupling force relationship between the loading points. It should be noted that it is different from the general static test. Actuator needs to provide bidirectional load for the loading point in the fatigue test of the airfoil structure. So, the actuator must be directly connected to the cantilever beam loading point. Since the amount of loading force must be measured, a force sensor is required between the actuator and the loading point. Then, the force coupling equation between the force sensor, the hydraulic actuator and the loading point is established. The dynamic equation can be constructed by combining the coupling forces of other channels and the output force of the own channel actuators as follows ..

.

Fi + Fo = Mi ω i + Bi ω i + Ki ,

(11)

where Fi is the force of channel i, Fo is the force of other channel, Mi is the mass of the concentrated point, Bi is the damping coefficient, and Ki is the stiffness coefficient. Subscript i indicates channel i [19–21]. Based on the above dynamic equation of single channel and deflection vector ω, the coupled equations of the loading system can be given as  .. .  K11 F1 + K12 F2 + . . . + K1n Fn = M1 ω 1 + B1 ω 1 + K1 ω1   .. .  K F +K F +...+K F = M ω 22 2 2n n 2 2 + B2 ω 2 + K2 ω2 21 1 .  ......   .. .  Kn1 F1 + Kn2 F2 + . . . + Knn Fn = Mn ω n + Bn ω n + Kn ωn

(12)

The above equations of motion reveal the coupling relationship between the actuator and loading point. The coupling force dynamics equations of the linear multi-loading point coupling coefficient are constructed by exploring the force coupling relationship between different loading points and the

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model of the control object in the control system. It is the basis for building a mathematical model of dynamic relationship between the actuator and the loading point. It establishes the mathematical the entire control system. model of the control object in the control system. It is the basis for building a mathematical model of the entire control system. 3. Modeling of the Loading System 3. Modeling of the Loading System 3.1. Single Channel Loading System 3.1. Single LoadingofSystem After Channel the modeling the control object is completed, the modeling of the system execution objectAfter wasthe performed the object formation of the entire control system. In the full-size modelingtooffacilitate the control is completed, the modeling of the system executionfatigue object loading test, it will be limited by space. Therefore, the actuator is required to have small volume, was performed to facilitate the formation of the entire control system. In the full-size fatigue loading large fast response speed. So, hydraulic valve-controlled are used as test, itoutput will be force, limitedand by space. Therefore, the actuator is required to have smallcylinders volume, large output actuating force, and actuators. fast response speed. So, hydraulic valve-controlled cylinders are used as actuating actuators. The schematic diagram of the valve-controlled cylinder [22] is shown in Figure Figure 3. 3. Po Q2

Ps Q1

Xv Pf = P1 - P2 P1

X1 X2 P2

Force load sensor

Figure Figure 3. Schematic Schematic diagram diagram of of the the valve-controlled cylinder.

For a control system, the actuator acts as one of several key subsystems. The actuator has many characteristics, which determines thethe performance of the system. The mathematical model characteristics, whichdirectly directly determines performance of entire the entire system. The mathematical of the single-channel hydraulic actuator of the motion of decoupling control system is constructed [23]. is model of the single-channel hydraulic actuator the motion decoupling control system The linear constructed [23].flow equation of actuator system valve is described by The linear flow equation of actuator system valve is described by Q L = Kq xv − Kc p f , (13) = − , (13) The Hydraulic Hydraulic cylinder cylinder flow flow continuity The continuity equation equation is is subjected subjected to to V dp f dxd + + C,s p f , Q= + L = A +4 dt 4E dt

(14) (14)

The is expressed expressed by by The equation equation of of forces forces is (15) = d2 x+ dx+ ( − ),
p f A = Ma 2d + Ba d + Ka xd − xd0 , (15) dt dt According to the analysis of Section 2.3, the piston rod of the hydraulic cylinder is not rigidly According to the analysis of Section 2.3, the by piston rodsensor of thewith hydraulic cylinder is notInrigidly connected with the loading point. It is connected a force a certain flexibility. order connected withthe themodeling loading point. is connected a forceaccurate, sensor with a certain flexibility. In order to ensure that of the It loading systemby is more the load is taken as the research to ensure the modeling of the loading system object. Thethat load equation of the channel is given asis more accurate, the load is taken as the research object. The load equation of the channel is given as (16) ( − )= + + .
d2 xd0 dxd0 0 0 K a xd − xd = M L 2 + BL (16) + K L xd . On the basis of the hydraulic servo valve flow continuity equation of the dt the flow dt equation, hydraulic cylinder, the force balance equation of the hydraulic cylinder piston rod, and the loading On the basis of the hydraulic servo valve flow equation, the flow continuity equation of the equation of the loading point, it is easy to construct a single-channel closed-loop hydraulic servo hydraulic cylinder, the force balance equation of the hydraulic cylinder piston rod, and the loading control system with the PID (Proportion-Integral-Derivative) controller [24,25].

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equation of the loading point, it is easy to construct a single-channel closed-loop hydraulic servo Sensors 2018, 18, xwith FOR PEER REVIEW 7 of 18 control system the PID (Proportion-Integral-Derivative) controller [24,25]. 3.2. 3.2.Multichannel MultichannelLoading LoadingSystem System InInorder to to further improve the mathematical modeling of the of multichannel force coupled control order further improve the mathematical modeling the multichannel force coupled system, a mathematical model of the force-coupled equations is added based on the multi-servo control system, a mathematical model of the force-coupled equations is added based on the control channel. multi-servo control channel. InInthe themultichannel multichannelstructure structureloading loadingsystem system[26] [26]the theoutput outputforce forceofofeach eachchannel channelcontains containsthe the coupling couplingforce forcetransmitted transmittedby byother otherchannels. channels.Based Basedon onthis, this,aadistributed distributed3-channel 3-channelcoupled coupledloading loading model modelisisestablished establishedand andshown shownininFigure Figure4.4.

-⊗

PID

Kvi Kq Ti s + 1

⊗

-

A V S + Kcs 4E

-

⊗

1 Ma s + Ba

Controller1

⊗

Controller2

⊗

Controller3

F2

F3

-

U1

U2

U3

Ka F1''=Function(F1',F2',F3') F2''=Function(F1',F2',F3') F3''=Function(F1',F2',F3')

2

Servo Valve

Cylinder

Servo Valve

Cylinder

Servo Valve

Cylinder

F1''

F1 '

F2 '

Coupling

⊗

⊗

-

1 ML s +BL s+KL

A

F1

1 s

F3'

F2''

F3''

Figure Figure4.4.The Thecoupled coupledmodel modelofof3-channel 3-channelloading. loading.

The three-channel coupling force control system is based on three single-channel valve-controlled The three-channel coupling force control system is based on three single-channel cylinder systems. The input signal of the couple model F 0 is the force output signal of each single valve-controlled cylinder systems. The input signal of the couple model is the force output signal loading channel. The output of the couple model F00 can be connected to the load equation and of each single loading channel. The output of the couple model can be connected to the load feedback channel of each individual channel. The couple model is the multichannel coupling force equation and feedback channel of each individual channel. The couple model is the multichannel dynamics equations deduced from Section 2.3. The above system is the coupling force loading of coupling force dynamics equations deduced from Section 2.3. The above system is the coupling force multichannel. A summary table of all symbols and acronyms is given in Table 1 in the next section. loading of multichannel. A summary table of all symbols and acronyms is given in Table 1 in the next section.of Loading Performance 3.3. Analysis MATLAB (MathWorks, R2016b) simulation can be performed on the mathematical model 3.3. The Analysis of Loading Performance of the multichannel force-coupled servo control system constructed in Section 3.2. It can verify the The MATLAB (MathWorks, R2016b) simulation can be performed on the mathematical model coupling force interference phenomenon in the multichannel loading process of the airfoil during the of the multichannel force-coupled servo control system constructed in Section 3.2. It can verify the aircraft full-scale fatigue test. coupling force interference phenomenon in the multichannel loading process of the airfoil during the The symbol definitions and main parameters of the simulation model are given in Table 1. aircraft full-scale fatigue test. The symbol definitions and main parameters of the simulation model are given in Table 1. Table 1. Symbol definitions and main parameters.

Symbol

A V E

Definition total flow from servo valve flow gain of servo valve servo valve spool displacement flow pressure coefficient of the servo valve load pressure of system effective area of the piston displacements of the piston rod total volume of the hydraulic cylinder elastic modulus

Value and Unit / 3 m / / / 14.6 × 10 m / 4 × 10 m 7 × 10 pa

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Table 1. Symbol definitions and main parameters. Symbol

Definition

QL total flow from servo valve Kq flow gain of servo valve xv servo valve spool displacement Kc flow pressure coefficient of the servo valve pf load pressure of system Sensors 2018, 18, x FOR PEER REVIEW A effective area of the piston Sensors 2018, 18, x FOR PEER REVIEW xd displacements of the piston rod comprehensive coefficient V total volume ofleakage the hydraulic cylinder comprehensive leakage coefficient E elastic modulus mass of the piston rod mass of the piston rod Cs comprehensive leakage coefficient viscous damping coefficient viscousmass damping Ma of the coefficient piston rod stiffness coefficient of the coefficient force sensors Ba viscous damping stiffness coefficient of the force sensors displacement of the sensor’s lower surface Ka stiffness coefficient of the force displacement of the sensor’s lower sensors surface the mass of the concentrated mass ofsurface load xd0 displacement of the sensor’s lower the mass of the mass ofofload ML the damping mass of concentrated thecoefficient concentrated mass load load damping coefficient load BL damping coefficient load stiffness coefficient of load KL stiffness coefficient load stiffness coefficient of of load

Value and Unit / 3 m2 / / / 14.6 × 10−4 m2 / −6 m 3 ∙ s) /(N 4.7 × 10 4 × 10 m 4.7 × 10 m8 /(N ∙ s) 7 × 10 pa / / m5 / ( N · s ) 4.7 × 10−13 / // / // / // 10 /kg 10 kg 1 N10∙ kg s/m 1 1NN∙·s/m s/m 10 6 N/m 10 N/m N/m 10

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To verify the influence of the coupling disturbance, the contrast tests when single channel loading Toverify verifythe theinfluence influenceof of thecoupling couplingdisturbance, disturbance,the thecontrast contrasttests tests when whensingle singlechannel channel loading and To multichannel loading are the conducted. The dynamic characteristics are shown in Figure 5. loading and multichannel multichannel loading loading are and are conducted. conducted. The Thedynamic dynamiccharacteristics characteristicsare areshown shownininFigure Figure5.5.

(a) (a)

(b) (b)

Figure 5. The tracking performances of time domain. Figure5. 5. The The tracking tracking performances performances of of time time domain. domain. Figure

In theabove above twocharts charts thereference reference signalrepresents represents thecommand command input.The The samplesignal signal In In the the above two two charts the the referencesignal signal representsthe the commandinput. input. The sample sample signal stands for the system output signal. Figure 5a gives the sinusoidal tracking performance of single stands stands for for the the system system output output signal. signal. Figure Figure 5a 5a gives gives the the sinusoidal sinusoidal tracking tracking performance performance of of single single loading Channel11in in thetime time domain. Figure Figure 5billustrates illustrates thesystem system characteristicsof of Channel11in in loading loadingChannel Channel 1 in the the time domain. domain. Figure 5b 5b illustrates the the system characteristics characteristics of Channel Channel 1 in the case of sinusoidal multichannel loading. By comparing these two figures the tracking accuracy of the the case case of of sinusoidal sinusoidal multichannel multichannelloading. loading. By By comparing comparing these these two two figures figures the the tracking tracking accuracy accuracy of of multi-loading system is seriously reduced. multi-loading multi-loading system systemisisseriously seriouslyreduced. reduced. Figure 6 describes the system error error of Channel Channel 1 with single single loading and and multi-loading, Figure Figure 66 describes describes the the system system error of of Channel 11 with with single loading loading and multi-loading, multi-loading, respectively, distinguished with solid line and dotted line. respectively, distinguished with solid line and dotted line. respectively, distinguished with solid line and dotted line.

Figure Figure6. 6. The The system system error errorof ofloading loadingChannel Channel11for forboth bothsingle singleloading loadingand andmulti-loading. multi-loading. Figure 6. The system error of loading Channel 1 for both single loading and multi-loading.

Figure 6 clearly shows that the tracking performance of the multi-loading system deteriorates Figure 6 clearly shows that the tracking performance of the multi-loading system deteriorates 6 clearly shows that the tracking performance of the multi-loading system deteriorates whenFigure considering a single loading situation. when considering a single loading situation. when considering a single loading situation. The frequency analysis of the coupled force loading system is shown in Figure 7. The frequency analysis of the coupled force loading system is shown in Figure 7. In the diagram, the loading point of Channel 1 which is indicated by solid line is close to the “airfoil In the diagram, the loading point of Channel 1 which is indicated by solid line is close to the “airfoil tip”, the loading point of Channel 2 which is indicated by a dash line is in the middle of the “airfoil” tip”, the loading point of Channel 2 which is indicated by a dash line is in the middle of the “airfoil” and the loading point of Channel 3 which is indicated by dash-dot line is close to the and the loading point of Channel 3 which is indicated by dash-dot line is close to the

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The frequency analysis of the coupled force loading system is shown in Figure 7. In the diagram, the loading point of Channel 1 which is indicated by solid line is close to the “airfoil tip”, the loading point of Channel 2 which is indicated by a dash line is in the middle of the “airfoil” and the loading point of Channel 3 which is indicated by dash-dot line is close to the “airfoil root”. When loaded separately, the loading of Channel 3, Channel 2, and Channel 1 is gradually reduced due to the coupling force, which is consistent with the previous stiffness analysis results. That is the closer to the airfoil tip, the lower the stiffness. The phase is more likely to produce hysteresis during loading, and the amplitude is more likely to cause attenuation; for single loading channel, the loading performance also decreases as the loading frequency becomes higher. Sensors 2018, 18, x FOR PEER REVIEW 9 of 18

Figure 7. Bode diagram thecoupled coupled force force loading Figure 7. Bode diagram ofofthe loadingsystem. system.

By performing domain and frequencyanalysis analysis on on the through simulation, By performing timetime domain and frequency the coupled coupledsystem system through simulation, the following conclusions can be obtained. The coupling force between the channels will affect the the the following conclusions can be obtained. The coupling force between the channels will affect tracking accuracy of the force loading system. The frequency of the loading system increases and the tracking accuracy of the force loading system. The frequency of the loading system increases and the coupling effect between the loading points is intensified. In linear loading, the lower the stiffness is, coupling effect between the loading points is intensified. In linear loading, the lower the stiffness the stronger the coupling effect becomes. It requires a stronger control algorithm. Thus in order to is, theimprove strongerthe thedynamic coupling effect becomes. It requires asystem stronger algorithm. characteristics of multi-loading andcontrol reduce the tracking Thus error, in it order is to improve the to dynamic of multi-loading system and reduce the tracking error, it is necessary design a characteristics reasonable decoupling control method. necessary to design a reasonable decoupling control method. 4. The Motion Synchronous Composite Control Method

4. The Motion Synchronous Composite Control Method 4.1. The Principle of Motion Synchronous Composite Control Method

4.1. The Principle of Motion Synchronous Composite Control Method

The foundation of the motion synchronous composite decoupling control method is that when excessive force exists between the active load and the passive load [27] it will be eliminated when The foundation of the motion synchronous composite decoupling control method is thatthe when two objects are consistent. When choosing a channel as passive loading, the other active channels excessive force exists between the active load and the passive load [27] it will be eliminated when the offer motion signals toWhen passive loadingachannel the motion passive loading goingoffer two objects are consistent. choosing channeltoasguarantee passive loading, theofother active channels along with the others. motion signals to passive loading channel to guarantee the motion of passive loading going along with In the multi-loading system, which is a typical force control system [28,29], the excessive force the others. is caused by desynchronization among loading channels. This decoupling method is designed from Inthe theterm multi-loading system, which is a typical force control system [28,29], the excessive force of ensuring consistent motion among channels. The motion of every loading channel is is caused by desynchronization among loading This signal. decoupling method is designed controlled by the pressure difference providedchannels. from the servo Because the servo signals andfrom the term of ensuring consistent motion among channels. The motion of every loading force signals have advanced predictive effect, the motion synchronous composite decouple channel control is controlled by fetches the pressure difference the servo signal. Because the servo method these two signals asprovided the currentfrom channel’s compensation variable [30]. In this signals method,and some mathematical operations wereeffect, undertaken to dealsynchronous with the control signals decouple and the force force signals have advanced predictive the motion composite control command in order to realize prediction.compensation variable [30]. In this method, method fetches signals these two signals as theadvanced current channel’s From Figure 4 and the correlation equations determined in the first two sections, the output force of a given channel is deduced: (

− )

(

)(

)

−

∑

= ,

(17)

represents the coupling where F is hydraulic cylinder output force, u is the control signal, ∑ force derived from the other channels, and is the sum of and . Reorganize above equation

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some mathematical operations were undertaken to deal with the control signals and the force command signals in order to realize advanced prediction. From Figure 4 and the correlation equations determined in the first two sections, the output force of a given channel is deduced: " Ka

V F + ∑ Kij Fi 1 K A 4E s + Kcs (u vi Kq V − F) − V 1 + Ts 4E s + Kcs Ml s2 + Bl s + Kl ( Ma s + Ba )( 4E s + Kcs ) + A2 s

#

= F,

(17)

where F is hydraulic cylinder output force, u is the control signal, ∑ Kij Fi represents the coupling force derived from the other channels, and Kcs is the sum of Kc and Cs . Reorganize above equation and the expression of the output force is solved as follows

F=

Kvi Kq A( Ml s2 + Bl s+Kl ) Ma 2 2 a u − [ V4E s + (Kcs Ma + VB 1+ Ts 4E ) s + Kcs Ba + A ] s ∑ Kij Fi Ka , V V ( Ml s2 + Bl s + Kl + Ka )[( Ma s2 + Ba s + Ka )( 4E s + Kcs ) + A2 s] − ( 4E s + Kcs )Ka2

then, F=

G1 u − G2 s ∑ Kij Fi , G3

(18)

(19)

where G1 , G2 and G3 are polynomials related to Laplacian operator s. It is apparent that the coupling force has negative effect on the output of current loading channel. In the light of theory, it is reliable to eliminate the excessive force by putting a compensation variable uc into the control signal according to following formula. G1 (uo + uc ) − G2 s ∑ Kij Fi G uo = 1 , (20) G3 G3 where uo is original control signal and uc is the compensation control signal. To make the above formula, we can get G2 s K F, (21) uc = G1 ∑ ij i It can be known from calculation that the coefficients of many high-order terms about s are relatively small compared to the constant terms. So, we directly ignore some of the high-order items, the compensation link can be directly reduced to uc = Gn ∑ Kij Fi ,

(22)

where Gn is equal to G2 /G1 . The equation of the control signal with respect to the force output signal is compensated by the above single channel, which is extended to n channels. A transfer matrix function of the compensation control signal vector uc with respect to the output force vector F can be obtained. uc = GF, F = G−1 uc ,

(23)

where G is the transfer matrix of the Laplace. The expanded form of the above equation is given as   uc1 = ( a11 + a12 s + . . .) F1 + (b11 + b12 s + . . .) F2 + . . . + (k11 + k12 s + . . .) Fn    u = ( a + a s + . . .) F + (b + b s + . . .) F + . . . + (k + k s + . . .) F n c2 22 22 2 22 21 1 21 21 ,  . . . . . .    ucn = ( an1 + an2 s + . . .) F1 + (bn1 + bn2 s + . . .) F2 + . . . + (k n1 + k n2 s + . . .) Fn

(24)

where uci is the control signal of channel i, Fi is the output force of channel i, and the preceding coefficient is a polynomial about s. (i = 1, 2, 3, . . . , n)

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In the motion synchronous composite control method, the square term and higher terms of s are neglected. Thus, the following function can be given as   a12 sF1 + b12 sF2 + . . . + k12 sFn = uc1 − a11 F1 − b11 F2 − . . . − k11 Fn    a sF + b sF + . . . + k sF = u − a F − b F − . . . − k F 22 2 22 n c2 22 1 21 1 21 2 21 n ,  . . . . . .    an2 sF1 + bn2 sF2 + . . . + k32 sFn = ucn − an1 F1 − bn1 F2 − . . . − k n1 Fn

(25)

Sensors 2018, 18,took x FORas PEER 11 and of 18 where sFi is theREVIEW new variables of the equation set. The above equations can be solved sFi can be expressed as the linear combination of Fi and uci . Then once again referring to the previous formula for uc : = = G , (26) G2 2 s ∑ Kij Fi = Kij sFi , (26) uc = ∑ G1 G1 After is plugged into the function of compensation control signal, the compensation control After can sFi is signal beplugged given asinto the function of compensation control signal, the compensation control signal uc can be given as G2 G2 u=c = s ∑ Kij F=i = [ C[,uc]., F]. (27) G1 G1

C is is aa constant constant vector vector about about Kij . . This realizes the derivation of the decoupling decoupling control where C compensation signal by linear linear combination combination of of the the channel channel control control signal signal and and the the output output force forcesignal. signal. From the above function, the decoupling control compensation signal can be expressed as the linear combination combination [31] of control signals and force command signals. The multi-loading system with motion synchronous composite composite decoupling decoupling unit unit is is shown shown in in Figure Figure 8. 8. K1 U1'

Linear compenation

U2'

U3'

U2

K2

F1

K3

U3

K4

U1

K5

F2

K6

F3

K7 K8 K9

F1

Controller1

⊗

Controller2

⊗

Controller3

F2

F3

-

U1

U2

U3

+

⊗

U1''

+

⊗

U2''

+

U3''

⊗

Servo Valve

Cylinder

Servo Valve

Cylinder

Servo Valve

Cylinder

U1'

+ ⊗+

U2'

+ ⊗ +

U3'

F1''

Coupling

⊗

+ ⊗ +

F2''

F3''

Figure 8. Schematic diagram of motion synchronous composite decoupling control method. Figure 8. Schematic diagram of motion synchronous composite decoupling control method.

Due to the control signals and the command signals of each loading channel are selected as the Due to the control signals and the command signals of each loading channel are selected as the input of the decoupling module, the decoupling signal retains higher order differential information, input of the decoupling module, the decoupling signal retains higher order differential information, which is beneficial to improve the decoupling control precision. Moreover, the control signals and which is beneficial to improve the decoupling control precision. Moreover, the control signals and command signals have predictive effect and this decoupling method avoids differential processing command signals have predictive effect and this decoupling method avoids differential processing which is easy to implement on engineering. which is easy to implement on engineering. 4.2. The Simulation of Motion Synchronous Composite Control Method 4.2. The Simulation of Motion Synchronous Composite Control Method In order to verify the compensation controller proposed in this paper, the corresponding In order to verify isthe compensation proposed in isthis the corresponding simulation verification given in Figure 9.controller The reference signal thepaper, force command input of simulation verification is given in Figure 9. The reference signal is the force command input of channel 1. The sample signal shows the system output of Channel 1. channel 1. The sample signal shows the system output of Channel 1.

which is easy to implement on engineering. 4.2. The Simulation of Motion Synchronous Composite Control Method In order to verify the compensation controller proposed in this paper, the corresponding verification is given in Figure 9. The reference signal is the force command input of Sensorssimulation 2018, 18, 4050 12 of 18 channel 1. The sample signal shows the system output of Channel 1.

(a)

(b)

Figure Thetracking trackingperformances performances ofofChannel 1. 1. Figure 9. 9. The Channel Sensors 2018, 18, x FOR PEER REVIEW

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Figure 9a gives the sinusoidal tracking performance of Channel 1 when multi-loading without Figure 9a18, gives sinusoidal tracking performance of Channel 1 when multi-loading without Sensors 2018, x in FORthe PEER REVIEW 12 of 18 decoupling module the time domain. Figure 9b gives the sinusoidal tracking performance of decoupling module in the time domain. Figure 9b gives the sinusoidal tracking performance of Channel 1 when multi-loading with decoupling module in the time domain. Compared above two gives the sinusoidal tracking performance Channel 1 when multi-loading without Channel Figure 1 when9amulti-loading with decoupling module inofthe time domain. Compared above two pictures,decoupling it is apparent that the system errorFigure after 9b adding the decoupling module shrinks.ofThus a module in the time domain. gives the sinusoidal tracking performance pictures, it is apparent that the system error after adding the decoupling module shrinks. Thus a conclusion could be be obtained that the motion synchronous composite decoupling control method Channel 1 when multi-loading module in the time domain. Compared above two conclusion could obtained thatwith the decoupling motion synchronous composite decoupling control method decreases the system error exiting inin multi-loading system and improve dynamic characteristics. pictures, is apparent that the system error aftersystem addingand theimprove decoupling module shrinks. Thus a decreases theitsystem error exiting multi-loading thethe dynamic characteristics. conclusion could be obtained that the motion synchronous composite decoupling control method The system error is shown in Figure 10. The system error is shown in Figure 10. decreases the system error exiting in multi-loading system and improve the dynamic characteristics. The system error is shown in Figure 10.

Figure 10. The system error ofofChannel multi-loadingwith with and without decoupling module. Figure 10. The system error Channel11when when multi-loading and without decoupling module. Figure 10. The system error of Channel 1 when multi-loading with and without decoupling module.

In Figure 10, the line and line respectively indicates the system errorerror of channel 1 In Figure 10,dotted the dotted line the andsolid the solid line respectively indicates the system of Figure 10, the dotted line decoupling. and solid line respectively the domain system error 1Inwhen multi-loading andthe with decoupling. theindicates abovedomain time analysis, whenchannel multi-loading without andwithout with From theFrom above time analysis, itofcan be channel 1decoupling when multi-loading and algorithm with decoupling. From the above time domain analysis, it can bethe proved that the decoupling control an important in the multichannel proved that controlwithout algorithm plays anplays important role inrole the multichannel coupled it canloading be proved that the decoupling controlcomposite algorithm decoupling plays an important role in the multichannel coupled system. Motion synchronous method can effectively improve loading system. Motion synchronous composite decoupling method can effectively improve the coupled loading system. synchronous the tracking accuracy of theMotion forcereduce and reduce thecomposite error. decoupling method can effectively improve tracking accuracy ofaccuracy the force and the error. the tracking of the force and reduce the error.control method. The system’s Bode diagram We perform frequency analysis on the decoupling We perform frequency analysis on the decoupling method. The system’s Bode diagram We perform frequency analysis on the decoupling control control method. system’s for decoupling and without decoupling in the control system is shown inThe Figure 11. Bode diagram for decoupling and without decoupling in the control shown Figure for decoupling and without decoupling in the controlsystem system isisshown in in Figure 11. 11.

Figure 11. The system error of channel 1 when multi-loading with and without decoupling module.

Figure 11.system The contrast diagram decouplingwith andand coupling system. Figure 11. The error of Bode channel 1 when of multi-loading withoutloading decoupling module. The diagram above is a comparison of the frequency response of the Channel 2. The figure The diagram above is a comparison of the frequency response of the Channel 2. The figure consists of two parts, which represent the amplitude-frequency characteristics and the consists of two parts, which represent the amplitude-frequency and the phase-frequency characteristics. In the simulation of the coupling forcecharacteristics system, the frequency phase-frequency characteristics. Inline. the After simulation of is the coupling force system, thealgorithm, frequency response is indicated by the solid the system added to the decoupling control response is indicated by the solidofline. After the2 system is added theWith decoupling control algorithm, the frequency response curve the Channel is indicated by dottoline. the increase of frequency,

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The diagram above is a comparison of the frequency response of the Channel 2. The figure consists of two parts, which represent the amplitude-frequency characteristics and the phase-frequency characteristics. In the simulation of the coupling force system, the frequency response is indicated by the solid line. After the system is added to the decoupling control algorithm, the frequency response curve of the Channel 2 is indicated by dot line. With the increase of frequency, the control characteristics of the decoupling control algorithm have achieved obvious effects in both the amplitude-frequency characteristic phase-frequency characteristic. Sensors 2018, 18, xand FORthe PEER REVIEW 13 of 18 5. Experiment Experiment 5. In the the full-scale full-scale fatigue fatigue test, test, the the test test agency agency usually usually perform perform multi-point multi-point linear linear loading loading on on the the In airfoil. Therefore, the test bench is designed in the same way. According to the determined loading airfoil. Therefore, the test bench is designed in the same way. According to the determined loading method, the the test test bench bench consists consists of of aa simplified simplified design design of of the the loading loading cantilever cantilever beam, beam, aa supporting supporting method, rigid frame, a valve-controlled hydraulic cylinder, and a centralized hydraulic source. rigid frame, a valve-controlled hydraulic cylinder, and a centralized hydraulic source. In order order to to make make the the test test bench bench meeting meeting the the extensive extensive test test requirements requirements and and economic economic In considerations of of experimental experimental materials, materials, aa segmented segmented cantilever cantilever beam beam structure structure is is designed; designed; the the considerations material is processed by 40 Cr. We used ANSYS (ANSYS, 18.2) to simulate the loading of the test bench. material is processed by 40 Cr. We used ANSYS (ANSYS, 18.2) to simulate the loading of the ASNSYS simulation for cantilever and test bench shown inisFigure test bench. ASNSYS simulation forbeam cantilever beam andistest bench shown12a,b. in Figure 12a,b.

(a)

(b)

Figure Figure 12. ANSYS ANSYS simulation simulation for for cantilever cantilever beam beam and and test test bench. bench. (a) (a) shows shows ANSYS ANSYS simulation simulation for for cantilever cantilever beam. beam. (b) (b) shows shows ANSYS ANSYS simulation simulation for for test test bench. bench.

In order order to to simulate simulate the the force force of of the the real real airfoil, airfoil, we we applied applied four four forces—20 forces—20 kN, 10 kN, kN, 88 kN, kN, and and In kN—to the the four four action action points, points, respectively; respectively; the shape variables were 7.2 mm, 14.4 mm, 43 mm, mm, and and 33 kN—to 129 mm. To prove designed support frame conforms to thetoconstraint form ofform the separate analysis To provethat thatthe the designed support frame conforms the constraint of the separate of the loaded weparts, designed a segmented cantilever beam and frame toframe be integrated through analysis of theparts, loaded we designed a segmented cantilever beam and to be integrated the earring connection. Through Through ANSYS analysis, we applied kN, 1020 kN, 8 kN, and83kN, kN through thestructure earring structure connection. ANSYS analysis, we20 applied kN, 10 kN, loading force again at the corresponding position. The deformation amounts are approximately the and 3 kN loading force again at the corresponding position. The deformation amounts are same as that of the the same test piece: 6.8ofmm, 13.9piece: mm, 42 approximately as that the test 6.8mm, mm,and 13.9125.1 mm,mm. 42 mm, and 125.1 mm. Then, the the modal modal analysis analysis was was carried carried out out on on the test bench. Through Through the the results, results, it it was was found found Then, that the the first first mode mode of of the the test test bench bench was was 9.167 9.167 Hz. Hz. Test Test frequency is much lower lower than 9.7 9.7 Hz, which which that excludes the danger designed in in thisthis way is aisgood simulation of the excludes dangerof ofresonance. resonance.The Thetest testbench bench designed way a good simulation ofload the condition of the aircraft airfoil and meets the purpose of requirements. load condition of the aircraft airfoil and meets the purpose of requirements. The hardware hardware of of experiment experiment contains contains valve valve control control cylinders, cylinders, force force tensors, tensors, etc., etc., illustrated illustrated in in The Figure 13. Figure

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bench. Figure13. 13.Distributed Distributedstructure structureloading loadingtest testbench. bench. Figure

Figure 13 shows the channels loading system. From thetip tipofofthe airfoil, Figure13 13shows showsthe the33channels channelsloading loadingsystem. system.From Fromthe theairfoil airfoiltotothe theroot rootofofthe theairfoil, airfoil, Figure the three channels are Channel 1, Channel 2, and Channel 3, respectively. The maximum bearing channelsare areChannel Channel1,1,Channel Channel2,2,and andChannel Channel3,3,respectively. respectively.The Themaximum maximumbearing bearing the three channels capacities [32] of the three channels are correspondingly 8000 N, 10,000 N, and 20,000 N. of the three channels are correspondingly 8000 N, 10,000 N, and 20,000 N. capacities [32] of the three channels are correspondingly 8000 N, 10,000 N, and 20,000 N. Thesignal signalflow flow multi-loading system expressed in Figure 14. flowofof ofmulti-loading multi-loadingsystem systemisis isexpressed expressedin inFigure Figure14. 14. The

Figure14. 14.The Thecomplete completesystem systemdiagram diagramofofthe themultichannel multichannelloading loading system. loadingsystem. system. Figure

The software mainly responsible for collecting relevant electrical signals and bus signals, and Thesoftware softwareisis ismainly mainlyresponsible responsiblefor forcollecting collectingrelevant relevantelectrical electricalsignals signalsand andbus bussignals, signals,and and The transmitting the signals collected in real time to the control system of host computer through TCP; at transmitting the signals collected in real time to the control system of host computer through TCP; transmitting the signals collected in real time to the control system of host computer through TCP; atat the same time, the host computer receives the instructions for multichannel and multi-modes switching thesame sametime, time,the thehost hostcomputer computerreceives receivesthe theinstructions instructionsfor formultichannel multichanneland andmulti-modes multi-modes the signals, bussignals, signals,bus andsignals, hardware analog outputs. In this experiment, itexperiment, is feasible toitdetermine switching and hardware analog outputs. In this is feasiblethe switching signals, bus signals, and hardware analog outputs. In this experiment, it is feasible toto optimal value of each compensation parameter by experimental trial. determine the optimal value of each compensation parameter by experimental trial. determine the optimal value of each compensation parameter by experimental trial. The real force tracking ofofall 200 Nm loading at 0.5 HzHz before andand afterafter adding the Thereal realforce forcetracking trackingof allchannels channelsunder under 200 Nm loading 0.5 before adding The all channels under 200 Nm loading atat0.5 Hz before and after adding decoupling module are shown in Figures 15–17. thedecoupling decouplingmodule moduleare areshown shownininFigures Figures15–17. 15–17. the

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(a) (a) (a)

15 of of 18 18 15 15 of 18 15 of 18

(b) (b) (b)

Figure 15. The force tracking experiment of Channel 1 in the time domain. Figure 15. The force tracking experiment of Channel 1 in the time domain. Figure 15. 15. The force force tracking tracking experiment experiment of of Channel Channel 11 in in the the time time domain. domain. Figure

(a) (a) (a)

(b) (b) (b)

(a) (a) (a)

(b) (b) (b)

Figure 16. The force tracking experiment of Channel 2 in the time domain. Figure Figure 16. 16. The The force force tracking tracking experiment experiment of Channel 2 in the time domain. Figure 16. The force tracking experiment of Channel 2 in the time domain.

Figure 17. 17. The The force force tracking tracking experiment experiment of of Channel Channel 33 in in the thetime timedomain. domain. Figure Figure 17. The force tracking experiment of Channel 3 in the time domain. Figure 17. The force tracking experiment of Channel 3 in the time domain.

In thethe reference signal is theiscommand input,input, SampleSample 1 is the1output without In these theseFigures Figuresa, a, reference signal the command is the force output force In these Figures a, the reference signal is the command input, Sample 1 is the output force decoupling when all three channels loading, Sample 2 means the output signal with in without decoupling when allreference threeare channels loading, Sample 2 means the output signal force with In these Figures a, the signal isare the command input, Sample 1 is thedecoupling output without decoupling when all In three channels loading, Sample 2system meanserror the without output signal with the situation of multi-loading. these Figures are b, 1 implies the decoupling decoupling in the situation multi-loading. InError these Figures b, Error 1 implies the system without decoupling when allofthree channels are loading, Sample 2 means the output signal error with decoupling in the the situation of multi-loading. In these Figures load. b, Error 1 implies the system error and Errordecoupling 2 senses error with decoupling when all decoupling channels without and Error senses the error load. decoupling in the situation of2multi-loading. Inwith these Figures b,when Errorall 1 channels implies the system error without decoupling and Error 2 sensesfigures, the error with decoupling when all channels load.decoupling As be from the the motion synchronization composition As can can be seen seenand from the above thewith motion synchronization composition without decoupling Error 2above sensesfigures, the error decoupling when all channels load.decoupling As can be seen from the above figures,characteristics the motion synchronization composition decoupling method amplitude and of system. method has improved amplitude andphase phase characteristics ofdistribute distributeloading loading system. decoupling As has canimproved be seen from the above figures, the motion synchronization composition method has improved amplitude and phase characteristics of distribute loading system. method has improved amplitude and phase characteristics of distribute loading system. 6. 6. Discussion Discussion 6. Discussion 6. Discussion This thethe coupling forceforce problem in the aircraft test.fatigue This decoupling Thispaper papersolved solved coupling problem in the full-scale aircraft fatigue full-scale test. This This paper solved the coupling force problem loading in the of aircraft full-scale fatigue test. This control algorithm is especially suitable for multichannel the airfoil. The idea of this paper is decoupling control algorithm is especially suitable for multichannel loading of the airfoil. The idea This paper solved the coupling force problem in the aircraft full-scale fatigue test. This decoupling control algorithm is especially suitable for multichannel loading of the system airfoil. The idea derived from the use of the steering angular velocity command in the load simulator to obtain of this papercontrol is derived from the use of the steering angular velocity command theairfoil. load simulator decoupling algorithm is especially suitable for multichannel loading ofinthe The idea of this paper is derived fromsothe of the steering angular velocity command in the load simulator the synchronization as use to eliminate theasredundant force. system to obtain thesignal, synchronization signal, so toangular eliminate the redundant force. of this paper is derived from the use of the steering velocity command in the load simulator system to obtain the synchronization signal, so as to eliminate the redundant force.interference of the In load system, system subject to active motion In the theobtain loadsimulator simulator system,the theloading loading system is subject toredundant the active motion interference of system to the synchronization signal, so as to is eliminate thethe force. In the load simulator system, the loading system is subject to the active motion interference of loaded object (such as the steering gear) during the tracking load spectrum process. The first problem the loaded object (such assystem, the steering gear) during tracking spectrum process. The first In the load simulator the loading systemthe is subject to load the active motion interference of the loaded object (such as the steering gear) during the tracking loadfrom spectrum process. Thewhich first in improving the loading accuracy is accuracy to eliminate theeliminate motion disturbance the loaded object, problem in object improving to the motion from the loaded the loaded (suchthe as loading the steering gear)isduring the tracking loaddisturbance spectrum process. The first problem inthe improving loading accuracy is to eliminate thespeed motion disturbance from themethod loaded belongs to categorythe ofthe synchronous control The synchronization control object, which belongs to category of synchronous control The speed from synchronization problem in improving the loading accuracy is question. to eliminate thequestion. motion disturbance the loaded object, which belongs to the category of synchronous control question. The speed synchronization introduces valve control forcontrol speed compensation, avoiding dependence on the displacement controlwhich method introduces signals for speed compensation, avoiding dependence on object, belongs tosignals thevalve category of synchronous control question. The speed synchronization control methodThis introduces valve control signals for speed compensation, avoidingunder dependence on sensor signal. method could improve the ability to eliminate the interference large and the displacement sensor signal. method could the ability to eliminate interference control method introduces valveThis control signals forimprove speed compensation, avoiding the dependence on the displacement sensor signal.control This method could improve the ability to eliminate theapplied interference medium loads. a derivative algorithm of speed synchronization, this idea is toidea the under large andAs medium loads. As a derivative control algorithm of speed synchronization, this the displacement sensor signal. This method could improve the ability to eliminate the interference under large and medium loads. AsThe a derivative control algorithm of speed synchronization, this idea multichannel loading system [33]. difference is that asdifference the number of loading increases, is applied themedium multichannel loading system [33]. Thealgorithm that as the channels number of loading under largetoand loads. As a derivative control of is speed synchronization, this idea is applied to the multichannel loading system [33]. The difference is that as the number of loading is applied to the multichannel loading system [33]. The difference is that as the number of loading

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the influence of coupling force becomes more and more prominent, severely reducing the loading accuracy, especially when increasing the loading frequency. This also puts higher demands on the decoupling control method. In this paper, a new less sensors motion synchronous composite control method is proposed. On the basis of using the valve control signals and force commands to ensure passive motion coordination, the dynamic tracking characteristics of multi-loading system are improved. It can be found from the comparison of the experiment results that the control scheme can effectively eliminate the coupling disturbance of each channel and has a good compensation control effect. In the three-channels loading test, the negative coupling force of Channel 3 is largest. The phase lag of Channel 3 is very severe because Channel 3 is affected by the forces of all channels. After the compensation of valve control signals and force command signals, the error caused by the coupling force is significantly reduced. 7. Conclusions From above statement, the following conclusions can be obtained within the decoupling strategy on multichannel loading system. 1.

2.

The novel motion synchronous composite decoupling control method can realize decoupling in the case of linear loading with fewer sensors. Yet the traditional decoupling control method requires the addition of displacement, velocity, and acceleration sensors or high-order differentiation, which will increase the complexity of measurement system. The composite control method uses only the command signal and control signal to achieve multichannel decoupling under the condition of increasing the loading frequency. It is able to improve the dynamic tracking accuracy of the multichannel loading system. It is of great significance that this decouple method could guarantee control accuracy in the case where the test frequency is increased. The method is able to maintain accurate loading of the force at increasing frequency, so that the loading time can be shortened.

Author Contributions: Conceptualization, Y.S. and Z.J.; Methodology, Y.S. and Z.J.; Software, L.J. and S.W.; Validation, L.J., N.B., and S.W.; Formal Analysis, N.Y.; Investigation, N.B.; Resources, Y.S.; Data Curation, N.Y.; Writing—original draft preparation, L.J.; Writing—review and editing, N.Y., Y.S., and N.B.; Visualization, Z.J.; Supervision, Y.S.; Project Administration, Y.S. Funding: This article was funded by the National Natural Science Foundation of China (Project Number: 51475020). Conflicts of Interest: The authors declare no conflicts of interest.

References 1. 2. 3. 4. 5. 6. 7. 8.

Molent, L. History of Structural Fatigue Testing at Fishermans Bend Australia. Hist. Struct. Fatigue Test. Fishermans Bend Aust. 2005, 891–892, 106–114. [CrossRef] Qiang, B. Evaluation of full scale Aircraft Structure Strength Test Technology. Aeronaut. Sci. Technol. 2012, 6, 10–13. Scarselli, G.; Castorini, E.; Panella, F.W.; Nobile, R.; Maffezzoli, A. Structural behaviour modelling of bolted joints in composite laminates subjected to cyclic loading. Aerosp. Sci. Technol. 2015, 43, 89–95. [CrossRef] Shang, Y.; Liu, X.; Jiao, Z. An integrated load sensing valve-controlled actuator based on power-by-wire for aircraft structural test. Aerosp. Sci. Technol. 2018, 77, 117–128. [CrossRef] Si, E. Full-scale Fatigue Test of Commercial Airplane Structure. Civ. Aircr. Des. Res. 2012, 104, 47–52. Forrest, C.; Forrest, C.; Wiser, D. Landing Gear Structural Health Monitoring (SHM). Procedia Struct. Integr. 2017, 5, 1153–1159. [CrossRef] Serioznov, A.N.; Metyolkin, N.G. Integrated automatization and instrumentation system for static and life testing of full-scale modern maneuverable aircraft. Aerosp. Tech. Shipbuild. 1999, 15–19. [CrossRef] Karel, G. Fast fatigue testing and fast setup. In Proceedings of the Aerospace Test Expo 2006, Hamburg, Germany, 4–6 April 2006.

Sensors 2018, 18, 4050

9. 10. 11.

12. 13. 14. 15. 16. 17. 18. 19.

20. 21. 22. 23.

24. 25. 26. 27. 28.

29. 30. 31.

17 of 18

Jafari, A. Coupling between the Output Force and Stiffness in Different Variable Stiffness Actuators. Actuators 2014, 3, 270. [CrossRef] Hammerton, J.R.; Su, W.; Zhu, G. Optimum distributed wing shaping and control loads for highly flexible aircraft. Aerosp. Sci. Technol. 2018, 79, 255–265. [CrossRef] Soumya, D.; Kapil, G.; Stanley, R.J. A Comprehensive Structural Analysis Process for Failure Assessment in Aircraft Lap-Joint Mimics Using Intramodal Fusion of Eddy Current Data. Res. Nondestruct. Eval. 2012, 23, 146–170. Sachs, G. Path-attitude decoupling and flying qualities implications in hypersonic flight. Aerosp. Sci. Technol. 1998, 2, 49–59. [CrossRef] Albostan, O.; Göka¸san, M. Mode decoupling robust eigenstructure assignment applied to the lateral-directional dynamics of the F-16 aircraft. Aerosp. Sci. Technol. 2018, 77, 677–687. [CrossRef] Zhang, R.; Gao, F. State Space Model Predictive Control Using Partial Decoupling and Output Weighting for Improved Model/Plant Mismatch Performance. Ind. Eng. Chem. Res. 2013, 52, 817–829. [CrossRef] Vepa, R. Aeroelastic Analysis of Wing Structures Using Equivalent Plate Models. AIAA J. 2015, 46, 1216–1225. [CrossRef] Li, G.; Zayontz, S.; Most, E. In situ forces of the anterior and posterior cruciate ligaments in high knee flexion: An in vitro investigation. J. Orthop. Res. 2004, 22, 293–297. [CrossRef] Promis, G.; Gabor, A.; Hamelin, P. Effect of post-tensioning on the bending behaviour of mineral matrix composite beams. Construct. Build. Mater. 2012, 34, 442–450. [CrossRef] Eldred, L.B.; Kapania, R.K.; Barthelemy, J.F.M. Sensitivity analysis of aeroelastic response of a wing using piecewise pressure representation. J. Aircr. 1996, 33, 2974–2984. [CrossRef] Naeli, K.; Brand, O. Coupling High Force Sensitivity and High Stiffness in Piezoresistive Cantilevers with Embedded Si-Nanowires. In Proceedings of the 2007 IEEE Sensors, Atlanta, GA, USA, 28–31 October 2007; pp. 1065–1068. Wang, C.; Khodaparast, H.H.; Friswell, M.I. Conceptual study of a morphing winglet based on unsymmetrical stiffness. Aerosp. Sci. Technol. 2016, 58, 546–558. [CrossRef] Feraboli, P. Composite Materials Strength Determination within the Current Certification Methodology for Aircraft Structures. J. Aircr. 2015, 46, 1365–1374. [CrossRef] Kilic, E.; Dolen, M.; Koku, A.B. Accurate pressure prediction of a servo-valve controlled hydraulic system. Mechatronics 2012, 22, 997–1014. [CrossRef] Pace, M.D.L.; Dalla Vedova, P.; Maggiore, L. Proposal of Prognostic Parametric Method Applied to an Electrohydraulic Servomechanism Affected by Multiple Failures. WSEAS Trans. Environ. Dev. 2014, 10, 278–490. Nam, Y.; Lee, J.; Hong, S.K. Force control system design for aerodynamic load simulator. In Proceedings of the 2000 IEEE American Control Conference, Chicago, IL, USA, 28–30 June 2002; Volume 5, pp. 3043–3047. Nam, Y. QFT force loop design for the aerodynamic load simulator. IEEE Trans. Aerosp. Electron. Syst. 2001, 37, 1384–1392. Pannala, A.S.; Dransfield, P.; Palaniswami, M. Controller Design for a Multichannel Electrohydraulic System. J. Dyn. Syst. Meas. Control 1989, 111, 299–306. [CrossRef] Igarashi, Y.; Hatanaka, T.; Fujita, M. Passivity-Based Attitude Synchronization in SE (3). IEEE Trans. Control Syst. Technol. 2009, 17, 1119–1134. [CrossRef] Suresh, P.S.; Radhakrishnan, G.; Shankar, K. Optimal trends in Manoeuvre Load Control at subsonic and supersonic flight points for tailless delta wing aircraft. Dialogues Cardiovasc. Med. DCM 2013, 24, 128–135. [CrossRef] Shamisa, A.; Kiani, Z. Robust fault-tolerant controller design for aerodynamic load simulator. Aerosp. Sci. Technol. 2018, 78, 332–341. [CrossRef] Wang, C.; Jiao, Z.; Quan, L. Adaptive velocity synchronization compound control of electro-hydraulic load simulator. Aerosp. Sci. Technol. 2015, 42, 309–321. [CrossRef] Sinapius, J.M. Experimental dynamic load simulation by means of modal force combination. Aerosp. Sci. Technol. 1997, 1, 267–275. [CrossRef]

Sensors 2018, 18, 4050

32.

33.

18 of 18

Santos, P.D.R.; Sousa, D.B.; Gamboa, P.V.; Zhao, Y. Effect of design parameters on the mass of a variable-span morphing wing based on finite element structural analysis and optimization. Aerosp. Sci. Technol. 2018, 80, 587–603. [CrossRef] Tsay, T.S. Decoupling the flight control system of a supersonic vehicle. Aerosp. Sci. Technol. 2007, 11, 553–562. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).