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College of Automation Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 211106，P.R.China

Abstract: In order to improve the frequency response and anti-interference characteristics of the smart electromechanical actuator（EMA）system，and aiming at the force fighting problem when multiple actuators work synchronously，a multi input multi output（MIMO）position difference cross coupling control coordinated strategy based on double?closed-loop load feedforward control is proposed and designed.In this strategy，the singular value method of return difference matrix is used to design the parameter range that meets the requirements of system stability margin，and the sensitivity function and the H∞norm theory are used to design and determine the optimal solution in the obtained parameter stability region，so that the multi actuator system has excellent synchronization，stability and anti-interference.At the same time，the mathematical model of the integrated smart EMA system is established.According to the requirements of point-to-point control，the controller of double-loop control and load feedforward compensation is determined and designed to improve the frequency response and anti-interference ability of single actuator.Finally，the 270 V high-voltage smart EMA system experimental platform is built，and the frequency response，load feedforward compensation and coordinated control experiments are carried out to verify the correctness of the position difference cross coupling control strategy and the rationality of the parameter design，so that the system can reach the servo control indexes of bandwidth 6 Hz，the maximum output force 20 000 N and the synchronization error ≤0.1 mm，which effectively solves the problem of force fighting.

Key words：smart electromechanical actuator（EMA）；force fighting；coordinated control strategy；cross coupling control；singular value method of return difference matrix；sensitivity H∞norm control

0 Introduction

Under the background of aircraft electrifica?tion，the wide use of electric actuator system has be?come a trend［1］.Smart electromechanical actuator（EMA）is a relatively new actuator concept in more electric and all electric aircraft.It has great develop?ment potential and is expected to be applied to key electric transmission systems such as aircraft brak?ing，rudder surface control and oil pump in the fu?ture［2-3］.Smart EMA integrates the motor，control?ler and transmission unit，and is connected with the aircraft controller through the data line，which im?proves the reliability，maintainability and servo tracking characteristics of the whole flight control system［4］.

Since the 1970s，the first development in the field of space applications has stimulated the devel?opment of EMAs.Smart EMAs with high power density and high control performance are one of the key equipments of airborne electromechanical sys?tems，and have been applied in the flight control sys?tems of aviation F-18，F(xiàn)-35，C-130，space shuttle，crew return aircraft X-38 and unmanned aerial vehi?cle［5-6］.The Chinese Academy of Aerospace has al?so carried out in-depth research on the actuation technology of smart EMAs.However，it is still in the initial stage of development compared with for?eign technologies［7-8］，especially in the development of high-voltage smart EMA system with high reli?ability，high frequency response，high integration and high thrust.The reliability，stability and control characteristics of actuator products need to be im?proved.

Compared with ordinary EMAs，smart EMAs have more excellent servo tracking characteristics and anti-interference ability，and their performance requirements such as high frequency response and low tracking error put forward higher requirements for control algorithms［3］.On the basis that the con?trol strategy meets the servo performance require?ments，the smart EMA system also needs to have the ability to output large load thrust，at the same time have high reliability and strong fault tolerance.Therefore，multiple smart EMAs are often used to drive the load surface together.However，due to component errors and installation deviations，the drive of multiple smart EMAs cannot be completely synchronized，which inevitably leads to force fight?ing among multiple actuators［9-10］.

At present，researchers in various countries have carried out some studies on the issue of force fighting.Ref.［11］points out that whether it is an ac?tuator system with similar redundancy configuration or a hybrid actuator system with dissimilar redun?dancy，the force equalization control strategy is the best choice to reduce the force fighting.Refs.［11-12］list several typical force equalization algo?rithms，the main idea of which is to reduce the force fighting by reducing the displacement deviation or force deviation of the two?channel output by means of compensation.Refs.［13-15］carried out model?ling for the hybrid actuation system，and used the in?tegral controller of position feedback and force feed?back to deal with the force fighting.It was conclud?ed that position feedback can restrain the force fight?ing more effectively than force feedback.Therefore，in order to obtain a balanced actuating output force，it is necessary and critical to study a high-perfor?mance multi motor position coordinated control strategy and realize its application in engineering.

Take dual motor control as an example，the co?ordinated control mainly includes parallel control，master-slave control，and cross coupling control［16］.Both the parallel control and the master-slave con?trol belong to the non-coupling control，and are only suitable for occasions with low requirements for syn?chronization.The cross coupling control strategy of dual motor was proposed by Koren in 1980［17］，add?ing error feedback on the basis of parallel control to improve the system synchronization and anti-inter?ference ability.However，since the purpose of coor?dinated control is to make the position or rotational speed of the two motors exactly the same or to main?tain a certain proportion，the system only contains one input and does not belong to a multiple input multiple output（MIMO）system.There are difficul?ties and limitations in the design of synchronization parameters，which is not conducive to the practical application of engineering.

Firstly，aiming at the high-frequency response and“point-to-point”control requirements of the smart EMA system，this paper adopts the positioncurrent loop double-loop control method for a single actuator，and designs the PID parameters of the loop regulators.In addition，a load feedforward con?trol strategy is introduced to reduce the negative im?pact of random load disturbance of the system.Sec?ondly，in order to realize the large thrust output re?quirements，an innovative position difference cross coupling control strategy is proposed and designed through an MIMO system analysis method.The sin?gular value method of return difference matrix is used to determine the parameter range of the regula?tor of position loop and position difference loop un?der the desired stability margin，and the optimal val?ue of the parameters is selected in combination with the sensitivityH∞norm control theory，so as to en?sure the dynamic，steady-state performance and an?ti-interference performance of the dual smart EMA system.Finally，experiments are carried out on the smart EMA experimental platform to verify the fea?sibility of the proposed control strategy and the ratio?nality of parameter tuning.The experimental results show that the system achieves the specified servo performance index，and effectively solves the force fighting problem caused by the parallel driving of multiple smart EMAs.

1 Model and Control Strategy of Smart EMA System

In order to meet the requirements of high reli?ability，high safety and miniaturized actuation sys?tem of future aircraft，a highly integrated smart EMA system is designed to drive the rudder surface load，integrating the drive controller，motor，reduc?er and transmission mechanism，as shown in Fig.1.Among them，the permanent magnet synchronous motor（PMSM），reducer and ball screw are in se?ries structure forming an electric actuator.The mid?dle part is the mechanical transmission unit of the electric actuator，and two drive controllers are ar?ranged on both sides.The two drive controllers adopt high thermal conductivity and high strength materials to connect with the housing where the ac?tuating motors are located.

Fig.1 Integrated smart EMA system

As the power source of the system，the PMSM drives the reducer to rotate，and the shaft end of the reducer is connected to the ball screw，so as to drive the screw to extend or retract to realize the recipro?cating linear operation of the load，thereby pushing the rudder surface to the specified angle or position.

1.1 Establishment of mathematical model

This section establishes the models of relevant components of the designed smart EMA system re?spectively.The single actuator is reasonably simpli?fied，and the structure shown in Fig.2 is obtained.In Fig.2，Tem，θq，JqandBqare the output electro?magnetic torque，rotation angle，moment of inertia and viscosity coefficient of the PMSM，respective?ly.Jg1andJg2are the moments of inertia of the front and rear gears，andNis the reduction ratio.JhandBhare the moment of inertia and viscous coefficient on the ball screw side.θhandyare the output angle and linear displacement of the actuator，F(xiàn)ais the axial thrust of the screw，andTehis the equivalent torque.

Fig.2 Simplified structure diagram of electric actuator

1.1.1 Model of ball screw

Assuming that the force of the ball screw on the rudder surface isFa，the equivalent torqueTehand moment of inertiaJg3on the ball screw shaft are as follows

where Ph is the lead of the ball screw，that is，the displacement of the linear motion of the ball screw corresponding to each revolution of the reducer.ηis the efficiency of the ball screw traveling process，which is taken as 1 here.

The relationship between the actuator output angleθhand the linear displacementyis

1.1.2 Model of reducer

The differential equations on both sides of the reducer are as follows

whereTeqis the gear torques on the primary side，withTeq=Teh/N.Let

Then，the mathematical model of the mechanical part of the actuator is obtained as follows［18］

1.1.3 Model of PMSM

Considering that the practical PMSM model is relatively complex nonlinear and strongly coupled，in order to facilitate the design and analysis of the system，a PMSM mathematical model is estab?lished through thedqcoordinate transformation［18-19］.Using the vector control method withid=0，the stator voltage equation is obtained，shown as

whereRsis the armature phase resistance of the mo?tor，ωethe electrical angular velocity of the rotor，andψmthe rotor flux linkage.uq，iq，Lqare the quadrature axis（q-axis）components of the stator voltage，current，and phase inductance，respectively.

The electromagnetic torque equation of PMSM is

wherepnis the number of pole pairs of the motor.

1.2 Determination of control strategy

1.2.1 High frequency response servo control strategy

In PMSM servo control system，the positionspeed-current three?loop control strategy is usually adopted.Smart EMA servo system belongs to fixed-point position tracking control，which has low requirements for speed accuracy control.In order to pursue better position dynamic response perfor?mance，realize the requirements of“point-to-point”position tracking and high frequency response，the speed loop of traditional three?loop control is re?moved and the double?closed-loop control strategy of position outer loop and current inner loop is adopt?ed［18］.

While improving the response speed of the smart EMA system，the amount of overshoot will also increase.In addition，when the load force in?creases，the negative impact of random load distur?bance on the system control will gradually become prominent.Therefore，on the basis of double?loop control，a load torque observer is designed，and load feedforward control is used to optimize the control of the smart EMA，which can suppress overshoot and enhance the anti-interference abili?ty［20］.The control strategy block diagram is shown in Fig.3，wherer*is the reference position，rthe output position，APR the automatic position regula?tor，ACR the automatic current regulator，dqthe synchronous rotation coordinate system，abcthe natural coordinate system，andαβthe static coordi?nate system.

Fig.3 Structural block diagram of double?loop control system with load torque feedforward

1.2.2 Limitations of traditional synchronous loop control

After ensuring that the dynamic and steady state of a single smart EMA meets the performance index requirements，the coordinated control strate?gy of double?actuator drive motor is studied to adapt to the practical application scenario of large load thrust.

Parallel control is very easy to lose synchroniza?tion after being disturbed，resulting in serious force fighting［21］.Therefore，a position synchronous loop is usually added to the control loop，and the output displacement of the two actuators is synchronized through the coordinated control of the synchronous loop，thereby reducing or even eliminating force fighting.The transfer function block diagram of the traditional synchronous loop control strategy is drawn，as shown in Fig.4.

Fig.4 Transfer function block diagram of traditional syn?chronous loop control

In Fig.4，Φi（s）is the current loop closed-loop transfer function，andKppandKpare the proportion?al coefficients of the position loop and the position synchronous loop regulator.

In order to control the same output displace?ment，the two actuators are given the same position command，that is，r1*=r2*.However，in the actual system，the motor and gear structure of the two ac?tuators are asymmetrical，so even if the position is given the same，the actual position output must be different，and there is a position difference between the actuators.Through the introduction of the posi?tion synchronous loop，the position difference of the two actuators is amplified by the synchronous loop regulator and then output to the position loop to ad?just the position control signal，thereby realizing the purpose of reducing the position difference.

According to the coordinated control principle of the synchronous loop，the traditional synchro?nous loop control strategy is essentially a single in?put multiple output（SIMO）system.If the transfer function model of the control system is established，the obtained transfer function matrix is a non-square matrix with unequal number of rows and columns，and the stability and robustness analysis theories of general MIMO systems are not applicable to such systems.Therefore，although the traditional syn?chronous loop coordinated control strategy can re?duce the position difference to a certain extent，it is very difficult to quantitatively design the synchro?nous loop parameters，which has limitations.

1.2.3 Position difference cross coupling control strategy

Since the synchronous loop coefficient will greatly affect the synchronization of the position out?put，it is necessary to break through the limitations of the traditional synchronous loop coordinated con?trol in the design of loop parameters.The core idea of synchronous loop coordinated control is to control the output position difference of two motors to be 0.In order to accurately control the position differ?ence，the closed-loop control loop of position differ?ence is introduced，and a new coordinated control method is obtained，that is，position difference cross coupling control strategy.Fig.5 is the control block diagram of the strategy，obviously it is a MI?MO control system.

Fig.5 Transfer function block diagram of position differ?ence cross coupling control

In Fig.5，H1（s）is the position loop regulator，andH2（s）the position difference loop regulator.The position difference cross coupling control strate?gy includes two inputs and outputs，and the parame?ter tuning of the loop regulator can be realized by ap?plying the correlation analysis method of the MIMO system.The next section will carry out the specific design of the proposed control strategy.

2 Design of Control Strategy for Smart EMA System

The design focuses on the selected high-fre?quency response control strategy and the proposed position difference cross coupling control strategy.Table 1 lists the PMSM parameters of smart EMA system to guide the design of controller parameters.

Table 1 Parameters of PMSM

2.1 Parameter design of current inner loop

The servo performance of the smart EMA sys?tem is mainly determined by the performance of the current loop［22］，so the design of the current loop is very important.The equivalent control structure of the current loop is shown in Fig.6，and the switch?ing frequencyfPWMis taken as 10 kHz.

Fig.6 Equivalent control structure of current loop

In Fig.6，T∑i=2TPWM，Te=Ls/Rsis the elec?tromagnetic time constant of the motor.The current loop regulator ACR adopts PI control，Kcpis the proportional coefficient，andτciis the integral time constant.Applying the zero-pole cancellation design method to eliminate the uncorrected dominant pole of the system is beneficial to improve the current loop frequency response.Letτci=Te，the closedloop transfer function is obtained as

whereKI=Kcp/（τciRs）=Kcp/Ls.

For the typical second-order system of Eq.（11），takeξ=0.707 to design the current loop parameters，and the obtained current loop regulator parameters are as follows

2.2 Design of load feedforward compensation strategy

The control system of the smart EMA is weak in dealing with random load disturbance.In order to improve the anti-interference of the system，load feedforward is used to compensate the current loop control.The addition of load feedforward will not af?fect the characteristics of current loop feedback con?trol，which can greatly eliminate steady-state errors，improve the dynamic performance of the system，and reduce load disturbances，including low-frequen?cy strong disturbances［22］.The schematic diagram of load feedforward compensation is shown in Fig.7.

Fig.7 Schematic diagram of load torque feedforward

In order to observe the load situation synchro?nously，Luenberger load torque state observer is used for observation.SelectωmandTLas the state quantities，the closed-loop state space expression of the state observer is

whereK=［k1k2］Tis the state feedback gain ma?trix，and the variable with superscript“”the state variable corresponding to the system variable in the observer.Further derivation obtains the observer system matrix

Combining with the knowledge of modern con?trol principles［23］，it can be known that the torque load observer is fully observable only when all the eigenvalues of the observer system matrixFhave negative real parts.Set the desired poles asαandβ，and obtain the expression of the state feedback gain matrixKaboutαandβ，shown as

If the observation results of the designed load observer are feedforward compensated to the cur?rent loop，the impact of external load disturbance on the system can be effectively reduced［20］.

2.3 Loop design of position difference cross coupling control strategy

After completing the design of the current loop with load torque feedforward compensation，accord?ing to the proposed position difference cross cou?pling control strategy，the system position loop and position difference loop controller parameters are tuned by using the stability margin and robustness analysis method of the MIMO system.

2.3.1 Stability margin of MIMO system

For multi-variable linear steady-state systems，the margin value of a single channel is generally used as an index to test the relative stability of the system in engineering，but it is not suitable to mea?sure the situation when the gain and phase of each channel of the system change at the same time.The singular value method of system return difference matrix provides an idea to solve this problem［24］.The stability margin of the system is determined by calculating the minimum singular value of the return difference matrix，which has the advantage of small amount of calculation.

The stability margin represents the“distance”between the system and the critical stability.There?fore，the stability margin of the system can be evalu?ated by introducing a disturbance into the original system to make the system just reach the critical sta?ble state［25］.For the general feedback system，as shown in Fig.8，whereG（s）is the system openloop transfer function matrix，the measurement ma?trixL（s）is introduced at the input and taken as the following diagonal form.

Fig.8 Unit negative feedback control system model

When the system reaches critical stability，the maximum allowable value of the simultaneous change of gainkiand phase?iin all loops is defined as the gain margin and phase margin of the system.

If the system remains stable after introducing the measurement matrixL（s），the system return difference matrix should meet the following requirements

The sufficient condition to make Eq.（18）hold is

According to the properties of singular value

Considering the simultaneous change of gainkiand phase?iin each loop of the system，combined with Eq.（16），the sufficient conditions to ensure the stability of the system can be obtained as follows

Since the actual system is known，can be calculated directly at any frequency.Taking the minimum singular valueof the return difference matrix as the parameter，and assuming≥x，according to Eq.（23），set gainki=1 and phase?i=0 of each loop respectively，the gain margin（GM）and phase margin（PM）of the MI?MO system can be obtained as

2.3.2 Loop parameter tuning based on stability margin

Based on the derived GM and PM above，the minimum singular value parameter range of the re?turn difference matrix that meets the requirements of stability margin can be obtained.If the minimum singular value of the return difference matrix of the smart EMA system can be obtained and the relation?ship between the loop parameters and the minimum singular value can be established，the regulator pa?rameters can be calculated reversely，so as to great?ly simplify the tuning process of the regulator［26］.

For the actuator system，considering the dy?namic and steady-state performance of the system，its stability margin is usually taken as［23］

According to the singular value method of the return difference matrix，the minimum singular val?ue range of the return difference matrix of the corre?sponding control system is directly calculated as

Ideally，it is assumed that the parameters and structures of the electrical and mechanical compo?nents of the two smart EMAs are the same，and the load torque and disturbance are ignored.Pure pro?portional control is adopted for the position loop and position difference loop regulator，takingH1（s）=H2（s）=Kp，andΦi（s）=1 to simplify the calculation.Taker1andr2as the open-loop output of the sys?tem，then write the open-loop transfer function ma?trixG（s）of the smart EMA system under the posi?tion difference cross coupling control（Fig.5）as fol?lows

Calculate the return difference matrixT（s）as follows

T（s）meets

Therefore，T（s）is a normal matrix whose singular value is equal to the modulus of the eigenvalue.The minimum singular value of the system return differ?ence matrix under the position difference cross cou?pling control strategy is

According to Eq.（30），the curve relationship between the minimum singular value of the system return difference matrixand the parameterKpto be designed is shown in Fig.9.

Fig.9 Relation between Kp and minimum singular value

As can be seen from Fig.9，the proportional regulator parameters of the position loop and the po?sition difference loop are inversely proportional to the square of the minimum singular value.From the minimum singular value range of the system return difference matrix in Eq.（26），the range of the pro?portional coefficientKpcan be calculated inversely that

2.4 Analysis of anti?interference ability

When the smart EMA system works in prac?tice，it will be subject to different types of external random disturbances，which will affect the stability of the system.Therefore，considering the anti-inter?ference ability of the system，the parameter stability region is optimized based on the sensitivityH∞con?trol theory to design a parameter that can not only obtain the desired stability margin，but also have ex?cellent anti-interference ability.

The sensitivity function matrixS（s）of MIMO system is the closed-loop transfer function matrix from interferenceTLto control errore.Suppose theH∞norm ofSis defined as

According to the concept of operator induced norm［27］，the norm ofSis defined

WhenS∈H∞，x∈L2（-∞，+∞），there are the conclusions

That is，theH∞norm is the induced norm of the sec?ond norm of the system inH∞space，which reflects the maximum gain of the signal from interference to control error.Therefore，the smaller theH∞norm of the system sensitivity function matrixS（s），the smaller the influence of external interference on the system control error.

According to the block diagram of position dif?ference cross coupling control（Fig.5），the transfer function from interferenceTLto control errorecan be obtained，and the sensitivity function matrix of twodimensional smart EMA system can be established as

whereb=Ph/2πN，Φi（s）=1/（2T∑is+1）.The closed-loop transfer function of the current loop is regarded as a first-order inertial link.TheH∞norm of the sensitivity function of the smart EMA control system is calculated as

It can be seen from the above formula that the regulator parameterKp，as one of the denominator terms，determines the value of theH∞norm of the system sensitivity function，and the two are nega?tively correlated.WhenKpincreases，theoretically‖S（s）‖∞decreases.DrawH∞norm curves of sys?tem sensitivity function under differentKpparame?ters in MATLAB，as shown in Fig.10.

Fig.10 H∞norm curves of system sensitivity function under different Kp parameters

In Fig.10，the direction of the black arrow indi?cates the change trend of ||S（s）||∞as the proportional coefficientKpincreases.It can be seen that with the increase ofKp，theH∞norm of the system sensitivi?ty function decreases，which is consistent with the theoretical analysis.

When theH∞norm of the system sensitivity function is less than 1，it is considered that the sys?tem can maintain its stability under disturbance，and the smaller the value，the stronger the anti-interfer?ence ability.As can be seen from Fig.10，whenKptakes any value in the range of 6.43—27，the system can have excellent stability and anti-interference per?formance.WhenKp=27，theH∞norm of sensitivity functionS（s）is the smallest，that is，the gain from interference to error is the smallest，and the anti-in?terference of the system is the strongest.Therefore，the optimal values of position difference and position difference loop regulator are obtained atKp=27.

3 Experimental Verification

3.1 Experimental platform

In order to verify the outstanding performance of the control strategy of the smart EMA system de?signed above，the system experimental platform is built and the corresponding experimental verification is carried out.

Fig.11 shows the physical picture of the experi?mental test platform.The test platform consists of two smart EMAs with symmetrical structures，a simulated load platform and a rudder surface simula?tor.Among them，a single smart EMA integrates key components such as PMSM，controller，reduc?er and ball screw.

Fig.11 Experimental test platform

Fig.12 shows the hardware control structure of the smart EMA system，where SCI is the serial communication interface and CAN the controller ar?ea network.Smart EMA 1#and Smart EMA 2#have the same hardware structure and are both con?trolled by the host computer through SCI communi?cation.Smart EMA 1#also acts as the main control?ler to deal with the coordination problem between the two actuators，and sends coordination com?mands to EMA 2#through CAN communication.

Fig.12 Structure diagram of system hardware control

Table 2 lists the performance requirements of the smart EMA system，and the corresponding per?formance indicators will be experimentally verified below.

Table 2 Performance index of smart EMA system

3.2 Frequency response experiment

It is generally believed that the amplitude atten?uation is less than 0.707 times and the phase lag is less than 90°，the frequency response is good，and the output signal can track the input sinusoidal given signal well.Under no-load condition，the positioncurrent double?loop control strategy is adopted，the given position signal amplitude is 2.5 mm，and the frequencies are 2，4 and 6 Hz，respectively.The po?sition frequency response waveform andiqcurrent waveform are observed，as shown in Fig.13.

Fig.13 Experimental waveform of system frequency re?sponse under double-loop control

Table 3 quantitatively analyzes the frequency response of the smart EMA system under different frequency given conditions.It can be seen from Ta?ble 3 that with the increase of the given frequency，the amplitude attenuation and phase lag of the actua?tor both increase.When the frequency is given as 6 Hz，the actuator can still maintain a better fre?quency response，meeting the requirement of 20%travel bandwidth ≥6 Hz.It can be known from the experimental results that the smart EMA has the servo response characteristics of high frequency re?sponse.

Table 3 Frequency response experimental data of smart EMA

3.3 Load feedforward compensation experi?ment

Considering that the actuator disturbance will increase under heavy load，the application of load feedforward compensation based on double?loop control can effectively eliminate the load disturbance under heavy or full load.

When the load force is 20 000 N，the frequen?cy response experimental results without and with load feedforward compensation are compared，as shown in Fig.14.

Fig.14 Frequency response experimental waveform com?parison of load feedforward compensation

When the given position frequency reaches 1.4 Hz，the position waveform without load feedfor?ward compensation has obvious phase lag，the lag angle exceeds 90°，and the signal tracking perfor?mance is poor.After the introduction of load feedfor?ward compensation，the phase can still follow under the given frequency of 1.5 Hz，the position differ?ence between the given and output is almost 0，and the frequency response is good.The experimental results show that the designed load feedforward compensation controller can effectively improve the position response bandwidth of the smart EMA sys?tem，make the system more suitable for heavy load conditions and enhance the anti-interference ability.

3.4 Coordinated control experiment of dual ac?tuators

On the basis of ensuring that a single smart EMA has good dynamic and steady-state perfor?mance，the position difference cross coupling con?trol strategy studied above is used to control the two actuators，and the comparative experiments of paral?lel control and cross coupling control of dual actua?tors are carried out.

When the load force is 5 000 N，the given posi?tion signal amplitude is 10 mm and the given fre?quency is 1.5 Hz，observe the position waveform and position difference waveform of dual actuators under the coordinated control of parallel control and position difference cross coupling，as shown in Fig.15.

Fig.15 Frequency response experimental waveform of dual actuators under two different control strategies

It can be seen from Fig.15 that when the paral?lel control strategy is adopted，there is a large phase difference between the two actuators at the frequen?cy of 1.5 Hz，which is about 60°.By contrast，the position difference cross coupling control strategy can maintain good coordination and consistency at the same given frequency，and the maximum posi?tion difference fluctuation is within 0.1 mm，which meets the requirement of the synchronization error of the smart EMA system ≤0.1 mm.Through the comparison of experimental results，it is concluded that compared with the parallel control，the pro?posed position difference cross coupling control strategy can effectively solve the problem of output position incoordination and force fighting of dual ac?tuators，thereby improving the overall performance of the system.

4 Conclusions

According to the requirements of high frequen?cy response，large load thrust and strong robustness of smart EMA system，this paper studies the posi?tion-current double?closed-loop control and load feedforward control strategy，and puts forward a po?sition difference cross coupling control strategy based on MIMO system.The loop parameters are specifically designed to improve the motor servo characteristics and position output synchronization.The main work and conclusions of this paper in?clude：

（1）The integrated smart EMA system is de?vised，and the mathematical models of ball screw，reducer and PMSM are established in turn.For a single smart EMA system，the strategy of positioncurrent double?loop control combined with load feed?forward compensation is adopted，and the loop con?trol parameters are designed to ensure its dynamic，steady-state characteristics and anti-interference abil?ity，so that the maximum output force and band?width meet the technical index requirements.

（2）The limitations of traditional synchronous loop control strategy in theoretical design are ana?lyzed，and a coordinated control strategy based on position difference cross coupling is proposed.For the cross coupled position loop and position differ?ence loop，the singular value method of MIMO sys?tem return difference matrix is utilized to determine the parameter stability range that meets the require?ments of gain and phase margin，and then the opti?mization is carried out in the parameter stability re?gion based on the sensitivity function.The parame?ter that make the system have excellent synchroniza?tion and robustness is finally determined.

（3）The experimental results show that the use of the position difference cross coupling control strategy can make the dual actuators maintain better coordination and consistency under the given signal of higher frequency，and alleviate the force fighting between the actuators.Compared with the parallel control strategy，the coordinated control strategy proposed in this paper has certain advantages and can ensure that the smart EMA system meets the re?quirements of the synchronization error index.In conclusion，the designed control strategy of the smart EMA system has practical value for engineer?ing application.