energies

Article A Power System for Electric Tracked during High-Speed with Optimization-Based Distribution Control

Hong Huang 1,2, Li Zhai 1,2,* ID and Zeda Wang 1,2 1 National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China; [email protected] (H.H.); [email protected] (Z.W.) 2 Co-Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, Beijing 100081, China * Correspondence: [email protected]; Tel.: +86-010-6891-5202

 Received: 19 April 2018; Accepted: 11 June 2018; Published: 13 June 2018  Abstract: It is significant to improve the steering maneuverability of dual-motor drive tracked vehicles (2MDTVs), which have wide applications in the tracked industry. In this paper, we focus on the problem of insufficient propulsion motor power during high-speed steering. Some correction formulas are introduced to improve the accuracy of the mathematical model. A steering coupling system and an optimization-based torque distribution control strategy is adopted to improve the lateral stability of the vehicle. The 2MDTV model and the proposed control strategy are built in the multi-body software RecurDyn and the control software Matlab/Simulink, respectively. According to the real-time steering simulation by the hardware-in-the-loop (HIL) method, the 2MDTV with the coupling device outputs more power during high-speed steering. The results show the speed during steering is quite high though, the stability of the vehicle can be achieved due to using the torque distribution strategy, and the steering maneuverability of the vehicle is also improved.

Keywords: tracked vehicle; dual-motor; high-speed steering; power coupling; torque control

1. Introduction With the development of modern electronic technology, traditional mechanical transmissions may possibly be replaced by electric drive systems due to the application of advanced electrical equipment like high power density motors and power inverters. Electric drive systems are used not only in wheeled vehicles, but also in tracked vehicles. Electric tracked vehicles (ETVs) can operate at any steering radius and achieve continuously variable speed regulation, which avoids the mechanical vibration caused by the shift. Moreover the layout of the electric drive system is more flexible and it’s easy to achieve modular management in ETVs. It can be predicted that the electric drive technology is a major trend in the development of ETV power transmission systems for military, agriculture, construction and mining applications [1]. Dual-motor independent drives are generally used in the electric drive systems of ETVs [2]. By controlling the speed or torque of the traction motor on both sides to achieve the coordinated control of the longitudinal and lateral forces, respectively, the ETV can drive straight or turn with different radii [3]. As a result of the dual-motor independent drive structure, the steering and transmission mechanism found in traditional tracked vehicles is unnecessary. By real-time control of the speed or torque of the traction motor on both sides, the vehicle can achieve continuously variable steering, which is called electronic control differential steering (ECDS). This comprehensive electronic differential steering control can significantly improve the steering stability and trajectory tracking [4]. Different from wheeled vehicles, skid steering is widely used in tracked vehicles. Therefore, due to the contact between the track and the ground, there is a steering resistance moment under the

Energies 2018, 11, 1538; doi:10.3390/en11061538 www.mdpi.com/journal/energies Energies 2018, 11, 1538 2 of 17 steering situation. In particular, when the 2MDTV turns at low speed with small radius, the vehicle will be subjected to a large steering resistance moment, so the motor torque required is higher than the vehicle’s demand estimated based on straight running condition [5]. In addition, when the vehicle turns at high speed, the motor power required for the outer side track is higher, which results in the need for a high power motor with high overload capacity, leading to larger size of the motor and power electronic device. It is worth noting that in the dynamic steering, the requirements of motor torque and power are also much higher than that in the steady state steering [4]. Thus, based on the above challenges, many power coupling devices have been proposed to reduce the power requirements for a single track have been designed and added between two traction motors to couple the power of the two motors [6–8]. However, the motors cannot be controlled well enough to realize infinitely variable steering because of the constraint of a shaft between the two motors. Gai et al. [9] also proposed a coupling transmission arrangement to achieve power coupling, so that the power regenerated from the in low-speed side can flow to the sprocket in the high-speed side. However, due to the use of four planetary units in the coupling transmission arrangement, this system is very complicated and bulky. Moreover it is difficult to obtain better steering radius following electronic differential steering. A half shaft differential control structure [10] was proposed to allow simple coupling of power from the two half shafts and control of the relative speed between the two half shafts. However it increases the size of the assembly system. The power-split-based transmission scheme and coupling characteristics of the planet coupled device were analyzed [11]. The electro-mechanical transmission is composed of an engine, two motors, a planet coupling device and a planetary transmission. The power from the engine and the motor can be coupled by the planet coupling device, thereby increasing the output power of the vehicle. However planet couple devices are used in wheeled vehicles and are not suitable for tracked vehicles. A power coupling assembly based on fixed shaft coupling is proposed to couple the torque from a main motor and an auxiliary motor [12]. The output torque of the outside sprocket increases with the coupling assembly, but the scheme with two main motors and two auxiliary motors does not reduce the total power requirements for motors in 2MDTVs. A steering coupling system composed of a steering motor, two planetary gear couplers and two propulsion motors is designed to improve the output power [13]. However the mechanical characteristics of the coupler and the steering performance during high speed were not fully considered. The steering control of tracked vehicles can be divided into two categories generally: adjusting speed difference between two based on speed or torque control [14,15]. A coordinated hierarchy control strategy of driving torque is proposed for distributed electric drive tracked vehicles [16]. The quadratic programming method is used to design the torque optimization distribution law of the in- motors. A steering control strategy has been proposed for tracked vehicles propelled by electric transmissions [17]. The self-adaptive control strategy is designed on the basis of Model Reference Adaptive Control Theory. This strategy could be used to effectively adjust the motors’ driving and ensure great steering stability. Some research focus on the energy management strategies of the hybrid electric powertrain to improve the fuel economy [18]. Algorithms such as Stochastic Dynamic Programming, Radau Pseudospectral Method and Reinforcement Learning are implemented for optimizing the energy management strategy [19–21]. However, few studies have focused on the maneuverability and stability of the 2MDTV during high speed steering [22]. Most of the existing analyses investigate the tracked vehicles without coupling devices during low-speed steering, so the proposed theory and control strategies are only adapted to low-speed steering, and have some limitations for high-speed steering. Due to the absence of the stability control and the shortage of propulsion motor power, the problem of torque allocation for 2MDTVs during steering is still unsolved. In addition, tracks is prone to slip considering the high speed of the vehicle and the adhesion coefficient of the road. At the same time the vehicle is more sensitive to the outside interference caused by the surroundings and pavements, so the vehicle may be out of speed or even roll over if the control system cannot meet the requirements. Energies 2018, 11, 1538 3 of 17

In this paper, the impact of efficiency decline is taken into consideration and an electromechanical coupling device is proposed to solve the problem of insufficient power during high-speed steering in curves of different radii. An optimal torque distribution strategy based on torque control considering the slip between track and pavement is proposed to achieve better torque and power utilization. The steering co-simulation model is built by the multi-body software Recurdyn and the control software Matlab/Simulink. A real-time electronic steering control simulation by the Hardware-in-the-Loop (HIL) method verifies the effectiveness of the coupling device and the proposed strategy.

2. Mathematical Model for Steering The steering of tracked vehicled is achieved by adjusting the speed difference between the two tracks. The electric drive structures of the electric tracked vehicle includes dual-motor independent drive, single motor drive, and hybrid electromechanical complex drive. Dual-motor independent drive structures have been widely used due to their simple structure, high transmission efficiency, flexible layout and other advantages. In this paper, a dual-motor independent drive electric tracked vehicle (2MIETV) is selected, and the vehicle’s configuration is as shown in Table1.

Table 1. Vehicle Parameters.

Parameters Value Parameters Value

Vehicle tread, B (m) 1.3 Drive ratio, ig 6.35 Ground contact length, L (m) 1.7 Mass of vehicle, m (kg) 2800 Rolling resistance coefficient, f 0.04 Mass gain coefficient, δ 1.5 Transmission efficiency, η 0.9 Moment of inertia, J (kg/m2) 3000

The vehicle dynamics performance indicators during straight running are listed as follows:

(1) Maximum speed should be 72 km/h. (2) Maximum climbing degree should be 32◦ and the climbing speed is 18 km/h. (3) Acceleration capability: 0 to 32 km/h in less than 8 s.

The parameters of the propulsion motor can be determined by the above indicators in general [23], where the transmission efficiency is assumed as a constant value of 0.9. However, the transmission efficiency will decrease while the vehicle speed increases due to the friction loss of crawler mechanism consisting of tracks, sprockets, road , inducers, etc. Then the efficiency of transmission system during the high-speed running can be defined as follows [24]:

ηt = 0.95 − 0.0017v (v > 30 km/h) (1) where ηt is the transmission efficiency, v is vehicle speed. In addition, the loss due to internal resistance in crawler mechanism of tracked vehicle cannot be ignored during high-speed driving, and the power consumed by internal resistance in electric tracked vehicles is defined as follows [25]:

0.46mgv v P = (30 + 0.9 ) (2) ir 7200000 1.6 where Pir is the power consumed by internal resistance in crawler mechanism. The above power loss described in Equation (2) was not considered in a previous study [23], and since the output power of propulsion motor cannot satisfy the requirements for high-speed running, the parameters of the drive motor should be determined by consideration of Pir at high running, as shown in Table2. Energies 2018, 11, x FOR PEER REVIEW 4 of 16 Energies 2018, 11, 1538 4 of 17

Table 2. Motor Parameters Comparison. Table 2. Motor Parameters Comparison. Parameters Rated/Maximum Power Rated/Maximum Torque Rated/Maximum Speed Loss considered 32/50 kW 122/215 N·m 2500/9000 rpm Parameters Rated/Maximum Power Rated/Maximum Torque Rated/Maximum Speed Loss ignored 20/40 kW 64/150 N·m 3000/9000 rpm Loss considered 32/50 kW 122/215 N·m 2500/9000 rpm Loss ignored 20/40 kW 64/150 N·m 3000/9000 rpm We took right steering as an example, FL is the traction force on the outer track, FR is the tractionforce on the inner track, RL is the rolling resistance force on the outer track, RR is the rolling resistanceWe took on the right inner steering track, asMμ an is example,the steeringFL resistanceis the traction moment, force vL onis the the track outer speed track, onF theR is outer the tractionforceside, vR is the on track the speed inner track,on theR innerL is the side rolling and ω resistance is the yaw force rate. on Steering the outer maneuvers track, RR withis the different rolling resistanceradii can be on shown the inner in Figure track, M 1.µ Misμ theis defined steering as resistance follows [26]: moment, vL is the track speed on the outer side, v is the track speed on the inner side and ω is the yaw rate. Steering maneuvers with different R μ radii can be shown in Figure1. M is defined11 as follows [26max]: Mµμ ==μmgL mgL R (3) 440.925+⋅ 0.15 1 1 µ M = µmgL = max BmgL (3) µ 4 4 R 0.925 + 0.15 · B where μ is the coefficient of roll resistance, μmax is the maximum rolling resistance coefficient, R is the wheresteeringµ is radius the coefficient of the vehicle. of roll The resistance, rolling µresistancemax is the maximumof the two rollingtracks is resistance the same coefficient, in magnitudeR is thebut steeringopposite radius in direction of the vehicle.when vR Theand rolling vL are resistanceopposite in of sign. the twoIf vR tracks and v isL are the same same in in sign, magnitude the rolling but oppositeresistance in of direction the two when tracksvR willand vbeL arethe oppositesame in indirection. sign. If v TheR and rollingvL are resistance same in sign, RL and the rollingRR are resistanceexpressed of as the follows: two tracks will be the same in direction. The rolling resistance RL and RR are expressed as follows: ==1 RRLR= RRfmg= f mg (4)(4) L R 2

(a) (b)

Figure 1. Forces analysis (a) R ≤ 0.5B steering; (b) R > 0.5B steering. Figure 1. Forces analysis (a) R ≤ 0.5B steering; (b) R > 0.5B steering.

2.1. Small Radius Steering (R ≤ 0.5B) 2.1. Small Radius Steering (R ≤ 0.5B) This situation can be further divided into three categories: R = 0, 0 < R < 0.5B, R = 0.5B. The This situation can be further divided into three categories: R = 0, 0 < R < 0.5B, R = 0.5B. equilibrium relationship between the force and moment of the vehicle when turning from resting, as The equilibrium relationship between the force and moment of the vehicle when turning from resting, shown in Figure 1a, can be expressed as: as shown in Figure1a, can be expressed as: dv (  −+−=δ FFRRLRRL mdv FL − FR + RR − RL = δmdtdt  B B dω (5)(5) (FL + FR) · − (RL + RR) · − Mµ = J ω  2B Bd2 dt ()FF+⋅−+⋅−=() RR Mμ J  LR22 LR dt where FL and FR are tractive force but opposite in direction. whereIt’ F worthL and mentioningFR are tractive that force when butR opposite= 0, FL =inF direction.R, VL = V R, lateral acceleration is zero, dv/dt = 0, and whenIt’ worthR = 0.5mentioningB, VR = 0, thatRR = when 0. R = 0, FL = FR, VL = VR, lateral acceleration is zero, dv/dt = 0, and whenThe R = motor 0.5B, speedVR = 0, onRR both= 0. sides can be expressed as: The motor speed on both sides can be expressed as:  1000ig B  nL = 120πr · 3.6 · ω · ( 2 − R) z (6) 1000i  n = g · 3.6 · ω · ( B + R) R 120πrz 2

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where rz is the radius of the sprocket, rz = 150 mm From (1)–(6), the motor torque and power can be obtained as follows:

 FL,R  TL,R = i η · rz g t (7)  TL,R·nL,R PL,R = 9549

T is tractive torque but opposite in direction. P is consumed power used to drive the track. Subscript “L” or “R” means the left or right side of the vehicle.

2.2. Big Radius Steering (R > 0.5B) According to the vehicle dynamic balance, the following formula can be obtained from Figure1b:

( dv FL − FR − RR − RL = δm dt B B dω (8) (FL + FR) · 2 + (RR − RL) · 2 − Mµ = J dt where FL is tractive force. In steady-state steering conditions, the expressions of the driving force can be obtained and if we assume the FR is null:

1 µmgL 1 µ mgL F = − f mg + = − f mg + max = 0 (9) R 2 4B 2 3.7B + 0.6R

We thus obtain the solution R = R0 = 67.54 m. This situation can be also divided into three categories: 0.5B < R < R0, R = R0, R > R0. When R > R0, FR is traction force and is in the same direction with the track. When R = R0, FR = 0, PR = 0. At this moment, the inner propulsion motor is turned off, the track rotates freely, only the outer propulsion motor works. While when R < R0, FR is brake force, generated by motor. The direction between FR and VR is opposite in this situation. Similarly, during high-speed steering the internal resistance in crawler mechanism increases, so the decline of transmission efficiency cannot be ignored. Therefore, a factor k is proposed to correct Equation (1). The value of k, which is determined by simulation or experimental results, ranges from 0.0001 to 0.002: ηt = 0.95 − (0.0017 + k)v (v > 30 km/h) (10)

2.3. Calculation The steering process can be divided into two periods: dynamic steering and static steering, the motor torque and power required vary with the steering radius and speed. This paper focuses on the steering performance of the vehicle at high speeds. Usually, the yaw rate of ETV is 45~75◦/s, we choose w = 1.3 rad/s. During high-speed steering, in order to prevent the crew from feeling discomfort due to the excessive centripetal acceleration, the centripetal acceleration is limited to 1 g. According to the calculation results, several representative cases are selected, as shown in Table3. It can be seen from Table3 that during low-speed small radius steering, the demand torque of the vehicle is large due to the large steering resistance moment, which exceeds the maximum torque that the motor can provide. This has been confirmed in the previous study. Energies 2018, 11, 1538 6 of 17

Table 3. Torque and power required by two motors in stationary steering.

1 2 R TL TR nL nL P’L PL PR V w (mm) (N·m) (N·m) (r/min) (r/min) (kW) (kW) (kW) (km/h) (rad/s) 0B 278.7 −278.7 344 −344 10.0 10.0 10.0 0 1.3 2B 214.9 −178.1 1720 1032 38.7 38.7 −19.2 13.0 1.3 5B 162.1 −125.3 3549 2904 60.3 60.3 −38.1 28.8 1.2 10B 117.7 −80.9 4791 4335 59.0 64.2 −36.7 40.7 0.87 20B 84.2 −45.3 6295 6618 55.3 64.8 −29.9 57.5 0.6 30B 68.0 −28.1 7992 7730 52.9 66.0 −22.8 70.4 0.5 1 2 P’L: required power (internal loss ignored). PL: required power (internal loss considered).

During high-speed steering, the vehicle’s power requirements (60.3/64.2/64.8/66 kW) exceed the maximum power (50 kW) that the motor can provide, so two motors with at least 70 kW are required for a vehicle without a coupling device, whereas during straight driving the required power is only half of the motor maximum power [4]. If the arrangement with coupling device (50 + 50 + 20 kW) is applied, the peak power will reduce to 20 kW less than the arrangement with two independent propulsion motors (70 + 70 kW). It is noteworthy that the values shown in Table3 are calculated with k = 0. If k 6= 0, the lateral power demand can be determined by Equation (11). As k increases, the power demand actually for the outside motor will be further increased:  53.17 + 3.843 (R = 10B)  −40.65k+0.8809  = 49.74 PL −57.49k+0.8523 + 6.397 (R = 20B) (11)   41.2 −60.98k+0.8463 + 8.741 (R = 30B)

3. Steering System Design

3.1. Steering Coupling Drive System With the deepening of research and advances in power electronics technology, the AC-DC-AC electric transmission structure is mainly used in electric drive systems. The unilateral (propulsion) motor is mainly an induction motor or permanent magnet motor with reliable control technology [27]. In general, the engine-generator generates energy, and the energy is allocated to the propulsion motors through the energy conversion unit. According to the control strategy, the speed, torque, power and other parameters of the motor is adjusted by the motor controller to drive the sprocket. In the regenerative braking mode, the energy regenerated from the wheel is distributed by the energy conversion and distribution unit, partially or completely to the energy battery pack. And the rest part of the energy flows to the outside track or energy absorb unit, thereby improving the energy utilization and stability of the vehicle. The steering coupling drive system is composed of a new type of center steering motor, two electromagnetic , two planetary gear couplers, and two propulsion motors, as shown in Figure2. The steering motor is smaller with lower rated power 10 kW (maximum power 20 kW). A reverse mechanism is designed in the steering motor to achieve positive and negative rotation direction. When the torque or power is insufficient, the electromagnetic is engaged and the torque or power of the driving wheel is satisfied by the coupling between the steering motor and the propulsion motor. Energies 2018, 11, 1538 7 of 17 Energies 2018, 11, x FOR PEER REVIEW 7 of 16

Energies 2018, 11, x FOR PEER REVIEW 7 of 16

Figure 2. Steering coupling drive system configuration and power flow. Figure 2. Steering coupling drive system configuration and power flow. Figure 2. Steering coupling drive system configuration and power flow. 3.2. Planetary Planetary Gear Coupler Design 3.2. Planetary Gear Coupler Design The planetary gear couplers consists of two electromagnetic (EM) clutches, two gear pairs and a planetaryThe gear planetary unit, which gear couplersconsists consists consistsof of a a sun sun of gear, gear,two electromagnetic a ring gear, a planet (EM) clutches, carrier twoand gear three pairs planet and agears, , as shown planetary in Figure gear unit, 33.. GearGear which pairpair consists 11 containscontains of a sun geargear gear, 11 andand a ring geargear gear, 22 (ring(ring a planet gear),gear), carrier whereaswhereas and three geargear planet pairpair 2gears,2 containscontains gear 3 as and shown gear in 4. Figure The 3.driving Gear pair disc disc 1 containsof electromagnetic gear 1 and gear clutch clutch 2 (ring is is connected connectedgear), whereas with with gear steering steering pair 2 containsmotor motor shaft, shaft, gear 3 and gear 4. The driving disc of electromagnetic clutch is connected with steering motor shaft, while clutch plate plate is is connected connected with with gear. gear. It’s It’s worth worth noting noting that that gear gear 1 and 1 and gear gear 3 are 3 aremounted mounted on the on while clutch plate is connected with gear. It’s worth noting that gear 1 and gear 3 are mounted on the steeringthe steering motor motor shaft shaft without without a , a spline, transmitting transmitting the thepower power only only when when one one of the of the EM EM clutches clutches is engaged.steering motor shaft without a spline, transmitting the power only when one of the EM clutches is is engaged.engaged.

Figure 3. Components of the planetary gear coupler. Figure 3. Components of the planetary gear coupler. Figure 3. Components of the planetary gear coupler.

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Energies 2018, 11, x FOR PEER REVIEW 8 of 16 When the vehicle is driving straight, the ring gear (R) is fixed by brake 1 while both the EM clutch 1 andWhen the the EM vehicle clutch is driving 2 are disengaged. straight, the ring The ge powerar (R) is fixed transmitted by brake to 1 thewhile sun both gear the (S)EM of the planetaryclutch gear1 and unit the(transmission EM clutch 2 are ratio disengaged. 6.35) from The the power propulsion is transmitted motor, andto the outputted sun gear to(S) the of sprocketthe planetary gear unit (transmission ratio 6.35) from the propulsion motor, and outputted to the through the planet carrier(C), as shown in Figure4a. The device works in different modes according to sprocket through the planet carrier(C), as shown in Figure 4a. The device works in different modes different steering conditions. Figure4b–d shows the power transmission routes during some typical according to different steering conditions. Figure 4b–d shows the power transmission routes during steeringsome conditions. typical steering conditions.

(a)

(b)

(c)

(d)

Figure 4. (a) Transmission mode during straight running; (b) Transmission mode during low speed steering; (c) Transmission mode during medium speed steering; (d) Transmission mode during high speed steering. Energies 2018, 11, 1538 9 of 17

During low-speed steering, if the torque demand for the sprocket is too large, the torque coupling mode is active. The torque of the steering motor and the propulsion motor is coupled via the gear pair 2, and this drives the sprocket through the planet carrier. This mode was discussed in previous studies [22]. If the torque demand does not exceed the peak torque of the propulsion motor, the steering motor is turned off and the EM clutches are disconnected. The outer propulsion motor provides the required torque for steering, while the inner motor is in the regenerative braking mode, converting the mechanical energy from the crawler into electrical energy. The power transmission path is shown in Figure4b. The power demand for the outer sprocket may be larger during medium-speed steering. If it exceeds the maximum power of the propulsion motor, the steering motor works and the device works in the power coupling mode. The EM clutch 1 is engaged while the EM clutch 2 is disconnected and the brake 1 is disengaged. The power of the steering motor is transferred to ring gear (R) through the gear pair1, and the power of propulsion motor is transmitted to the sun gear (S). Then the power is coupled and transmitted to the sprocket through the planet carrier (C). In this case, the inner motor is still in regenerative braking mode. The corresponding power transmission route is shown in Figure4c. During high-speed steering, the propulsion motors on both sides are in the drive mode for high-speed steering. The outer coupling device is in power coupling mode due to the high power requirements for the outer track, and the steering motor provides auxiliary power to keep the vehicle steering at high speed. The inner motor also outputs power to maintain the vehicle speed. The power transmission route is shown in Figure4d. In general, the device works in torque coupling mode during low speed steering and in power coupling mode during high speed steering. The operation of components in different coupling modes is listed in Table4. In this paper, we focused more on high speed steering while the low speed steering had been discussed yet [22,23].

Table 4. Coupling mode and the operation of each component.

Mode Brake 1 EM Clutch 1 EM Clutch 2 Steering Motor Propulsion Motor straight running engaged disconnected disconnected off working torque coupling engaged disconnected combined working working power coupling disengaged combined disconnected working working

4. Control Strategy A closed-loop control strategy based on torque control of motor is proposed and shown in Figure5. The strategy proposed for a 2MDTV is designed as a three-level structure, including an ideal model level, a dynamics upper-level controller and a torque distribution lower-level controller. In the reference model level, a dynamic reference model is established and discussed in Section2 to obtain the desired yaw rate or other dynamics parameters, according to the driver inputs and the actual state of the vehicle. The upper-level controller consists of a speed tracking controller and a yaw moment controller with the PID control method and fuzzy PID control, respectively. The controller in this level aims to guarantee the capability of speed following and basic steering performance. The lower-level controller adopts the optimal allocation algorithm to assign the optimal torque (TL, TR) to desired torque (TL-des, Ts-des, TR-des) generated by propulsion motors and steering motor under the constraints of the planetary coupling device. Based on the above calculation, the output torque of two propulsion motors and steering motor can be directly distributed to three motor controllers by a CAN bus, respectively. Finally, the torque or power is coupled through the electromechanical coupling device and transmitted to sprockets to improve the stability of the 2MDTV. Energies 2018, 11, 1538 10 of 17 Energies 2018, 11, x FOR PEER REVIEW 10 of 16

4.1. Yaw Moment FuzzyFuzzy PIDPID ControllerController The yawyaw momentmoment controller controller is is designed designed based based on on the the error error between between the the actual actual angular angular speed speed and theand desired the desired angular angular speed speed to calculate to calculate the target the yawtarget moment yaw momentMz-des by M thez-des fuzzyby the PID fuzzy control PID method.control Thismethod. controller This controller is activated is activated when the when yaw ratethe erroryaw rate∆ω errorbeyond Δω the beyond constant the 0.1.constant 0.1.

Figure 5. Control strategy schematic based on torque.

4.2. Speed Tracing ControllerController The speed tracking controller is always activatedactivated and designed based on the PID control method to calculate the desired traction force of vehicle Fx-des for the purpose of following the desired vehicle to calculate the desired traction force of vehicle Fx-des for the purpose of following the desired vehicle speed. Usually during high speed steering, the speedspeed of the vehicle declines rapidly and the steering mode isis translatedtranslated intointo low low speed speed steering, steering, so so the th speede speed tracking tracking controller controller is importantis important especially especially for highfor high speed speed steering. steering.

4.3. Optimization-Based Distribution Controller To improveimprove thethe performanceperformance ofof thethe speedspeed andand yawyaw raterate following,following, anan optimization-basedoptimization-based distribution controller is designed to obtain the optimal torque TL and TR ofof the bilateral sprockets. According to FigureFigure5 5,, the the torque torque TTLL,, TTRR and Ts,, which are supposed to bebe generatedgenerated byby propulsionpropulsion motors andand steeringsteering motor,motor, are are allocated allocated by by the the coupling coupling distribution distribution controller controller under under the the constraint constraint of planetaryof planetary coupling coupling to trackto trac desiredk desired steering steering radius. radius. The rollingrolling resistance resistance is assumedis assumed to beto zerobe zero and thenand thethen matrix the formmatrixH canform be H obtained can be accordingobtained toaccording the dynamic to the balance dynamic analysis balance in analysis Section2 in and Section expressed 2 and as expressed follows: as follows: κ =⋅H u (12) κ = H · u (12) 11 −  " #  − 1 1 rr ≤≤r r ( ≤ R ≤ R )  ,(0B BRR, 0 )0 0 BB 2r 2r " # " #  " # 22rr 1 Fx TR 0 r where: κ = , u = ,H = B , (R = R0) . Mz TL 1 0 2r F T  0  " # x R  r 1 1 where: κ ==,u , HRR== ,(r r ) .     0 , (R > R0) M z TL B B B  0  − 2r 2r  where κ are the control inputs, uare the2r torque of the sprockets, and H, the control effectiveness  11 matrix, is chosen depending on the steering radius. The optimization object to minimize is chosen as rr distribution error, kH × u − εk, for control accuracy,(RR> ) and u, for efficient driving. We thus obtain the  BB 0 optimization objective function: − 22rr h 2 2i where κ are the control uinputs,= argmin u are thek Wtorqueu · uk of+ theξ · k sprockets,Wv · (H · u and− κ) Hk , the control effectiveness(13) matrix, is chosen depending uonmin the≤u≤ steeringumax radius. The optimization object to minimize is chosen as distribution error, Hu×−ε , for control accuracy and u, for efficient driving. We thus obtain the optimization objective function:

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This is a weighted least-squares (WLS) problem, and where Wu is the weighting matrix for efficient driving, Wv is the diagonal weighting matrix of the inputs, ξ is the weighting factor whose value is chosen depending on how important the distribution error is. The objective function is determined by the following constraints:  |T | ≤ T , |T | ≤ T  L L,max R R,max   −Tmax−brake ≤ TL,R,s ≤ Tmax−drive (14)  |T | ≤ f rmg , |T | ≤ f rmg  L 2 R 2   εm ≥ 90% where ε is the efficiency of motor obtained by map diagram of speed-torque.

4.4. Coupling Distribution Controller

The coupling distribution controller allocate the torque TL, TR and Ts according to the torque TL and TR received form the optimization-based distribution controller in different situations. The torque distribution is based on following constraints:  −T ≤ T ≤ T  max−brake L,R max−drive   |Ts| ≤ Ts,max (15)  Tsun : T : T = 1 : i − 1 : i  ring carrier   nsun + (i − 1)nring − incarrier = 0

In order to reduce the complexity of the control system, the priority for dual motor operating mode is the highest. The desired torque (TL-des, Ts-des, TR-des) can be obtain according to Equation (15) and coupling judgment module [23]. The steering motor works only when the propulsion motor can’t generate enough torque or power during some steering situations.

5. Modeling and Simulation Results We build the steering co-simulation model using the multi-body software Recurdyn and control software Matlab/Simulink. The vehicle model and ground model are developed in Recurdyn, as shown in Figure6. The driver inputs model, the control strategy model and the motor system model are developed in Simulink. The multi-body dynamic model in Recurdyn is seamlessly interfaced with Matlab/Simulink. The parameters of the dynamic simulation parameters are shown in Table5.

Table 5. Dynamic simulation parameters.

Inertia (kg·mm2) Component Number Stiffness Coefficient Damping Coefficient Ixx Iyy Izz Sprocket 2 237,774 237,774 279,379 10,000 10 Road Wheel 10 495,799 495,799 685,898 10,000 10 Idler 2 495,799 495,799 685,898 10,000 10 Carrier 6 16,169 16,169 5121 10,000 10 Balance Arm 10 1157 3987 5056 17,319,000 60 Track link 198 5425 5493 1989 1,000,000 1000

The RecurDyn software can define soil parameters according to the user’s needs. The road is divide into rectangular elements for calculation. Therefore, the contact force between the track and the ground can be automatically calculated by the software. The calculation is based on the following two models: a hard pavement model established by general contact force, and a soft pavement model based on Baker’s theory. We choose the hard pavement model in this paper. EnergiesEnergies 20182018,, 1111,, x 1538 FOR PEER REVIEW 1212 of of 16 17 two models: a hard pavement model established by general contact force, and a soft pavement model basedThe on Baker’s pressure theory. between We the choose track the shoes hard and pavement the ground model on hardin this pavement paper. is defined by the track contact.The Thepressure contact-collision between the force track in shoes RecurDyn and the is calculatedground on as:hard pavement is defined by the track contact. The contact-collision force in RecurDyn is calculated as: n F = −k(q − q0) − cq =− −n − Fkqqcq()0 where q is ground contact position before contact, q0 is ground contact position after contact, q − q0 is where q is ground contact position before contact, q0 is ground contact position after contact, q − q0 is the subsidence. the subsidence. According to relevant theories and experiments, the convergence speed of the simulation is According to relevant theories and experiments, the convergence speed of the simulation is obtained optimally when the soil deformation index n is ranged from 2 to 3. The friction between the obtained optimally when the soil deformation index n is ranged from 2 to 3. The friction between the track and the ground is calculated by Coulomb’s law. The parameters of the hard pavement used in track and the ground is calculated by Coulomb’s law. The parameters of the hard pavement used in the simulation are shown in Table6. the simulation are shown in Table6. Table 6. Hard pavement parameters. Table 6. Hard pavement parameters. Parameter Value Parameter Value Road springRoad coefficient spring coefficient 10,000 10,000 Road dampingRoad damping coefficient coefficient 1010 Max frictionMax coefficient friction coefficient 0.7 0.7 Soil deformation index 2.0 Soil deformation index 2.0

AA real-time real-time electronic electronic steering steering control control simulation simulation by by the the Hardware-in-the-Loop Hardware-in-the-Loop (HIL) (HIL) method method is constructedis constructed with with rapid rapid simulation simulation prototyping prototyping te technology,chnology, as as shown shown in in Figure Figure 77.. The SimulinkSimulink modelsmodels of electronic differentialdifferential steering steering control control strategy strategy and and motor motor control control strategy strategy are are compiled compiled into intoexecutable executable codes codes via RT-LAB via RT-LAB software. software. Then theThen executable the executable codes are codes loaded are to loaded RT-LAB to hardwareRT-LAB hardware1 and RT-LAB 1 and hardware RT-LAB hardware 2 respectively 2 respectively to run the to real-timerun the real-time simulation. simulation. The required The required output output torque torquesignal ofsignal four of motors four motors obtained obtained from HIL from simulation HIL simulation of ECU of are ECU input are to input RT-LAB to RT-LAB hardware hardware 2 for HIL 2 forsimulation HIL simulation of motors. of motors. The output The output torque torque signals signals from from HIL simulationHIL simulation of motors of motors are givenare given to the to theSimulink Simulink vehicle vehicle model model built built by by Recurdyn. Recurdyn. Some Some typical typical high-speed high-speed steering steering cases cases are are simulated simulated to toverify verify the the feasibility feasibility of of the the coupling coupling device device and and the the strategy strategy proposed. proposed.

Vehicle Body

Track Subsystem

Carrier

sprocket

Idler Road Wheel Track Balance Arm

(a) (b)

Figure 6. (a) Vehicle model in RecurDyn; (b) Vehicle model during simulation. Figure 6. (a) Vehicle model in RecurDyn; (b) Vehicle model during simulation.

Energies 2018, 11, 1538 13 of 17 Energies 2018, 11, x FOR PEER REVIEW 13 of 16

Co-Simulation RT-Lab Software Energies 2018, 11, x FOR PEER REVIEW 13 of 16

RT-Lab Hardware 1 Co-Simulation RT-Lab SoftwareEthernet RT-Lab Hardware 2

RT-Lab Hardware 1 Ethernet PC RT-Lab Hardware 2

Driving Simulator PC FigureDriving 7. Hardware-in-the-LoopSimulator simulation for electronic steering control. Figure 7. Hardware-in-the-Loop simulation for electronic steering control.

5.1. 5B Steering 5.1. 5B Steering Figure 7. Hardware-in-the-Loop simulation for electronic steering control. At first, the vehicle is stationary for 2 s. After that, the vehicle starts running straight for 5 s and At5.1. first, 5B Steering the vehicle is stationary for 2 s. After that, the vehicle starts running straight for 5 s accelerates to 28.8 km/h. The steering wheel is turned to the right at 7 s and manipulated to output R and accelerates to 28.8 km/h. The steering wheel is turned to the right at 7 s and manipulated to = 5B. The trajectory,At first, the yaw vehicle rate is and stationary speed forof the2 s. vehiclAfter that,e are the shown vehicle in starts Figure running 8a–c. Withoutstraight for the 5 scoupling and output R = 5B. The trajectory, yaw rate and speed of the vehicle are shown in Figure8a–c. Without the system,accelerates the vehicle to 28.8 speed km/h. declines The steering continually, wheel is turnwhilede towith the theright coupling at 7 s and device manipulated the vehicle to output speed R is coupling= 5B system,. The trajectory, the vehicle yaw rate speed and declinesspeed of the continually, vehicle are shown while within Figure the 8a–c. coupling Without device the coupling the vehicle higher, which can maintain near the theoretical value, as shown in Figure 8c. The torque, rotation speedsystem, is higher, the whichvehicle canspeed maintain declines nearcontinually, the theoretical while with value, the coupling as shown device in Figurethe vehicle8c. Thespeed torque, is speed and power of the sprocket are shown in Figure 8d–f. Limited by the motor power, the speed higher, which can maintain near the theoretical value, as shown in Figure 8c. The torque, rotation rotationof the sprocket speed andis lower power without of the the sprocket coupling are device shown. Figure in Figure 8f shows8d–f. that Limited the output by the power motor of power, outer the speedspeed of and the power sprocket of the is lower sprocket without are shown the coupling in Figure device.8d–f. Limited Figure by8f the shows motor that power, the output the speed power sprocketof the is improvedsprocket is lowerfrom without50 to 60 the kW, coupling and the device vehicle. Figure speed 8f shows can be that maintained the output withpower the of outercoupling of outer sprocket is improved from 50 to 60 kW, and the vehicle speed can be maintained with the device.sprocket It is worth is improved mentioning from 50 that, to 60 seen kW, fromand the Fi gurevehicle 8b, speed the yawcan be rate maintained of the vehicle with the cannot coupling be too coupling device. It is worth mentioning that, seen from Figure8b, the yaw rate of the vehicle cannot large device.during Ithigh is worth speed mentioning steering, that, and seen otherwise from Fi gurethe 8b,vehicle the yaw is easyrate ofto the be vehicle instability cannot or be rollover. too beAlthough toolarge large the during during yaw highrate high isspeed speedlower steering, steering,than what and and weotherwise otherwise assume thed, thebutvehicle vehicleat this is easysituation is easy to be to theinstability be power instability ordemand rollover. or rollover. is still Althoughhigh (largerAlthough the than yaw the the yaw rate calculated rate is lower is lower thanvalue). than what what we we assumed, assumed, butbut at this situation situation the the power power demand demand is still is still high (largerhigh (larger than than the calculatedthe calculated value). value).

60 0.8 36 60 Trajectory(w/o) 0.8 36 50 Trajectory(w)Trajectory(w/o) 0.7 50 Trajectory(w) 0.7 28.8 0.6 28.8 40 0.6 Yaw rate(w/o) 40 Yaw rate(w/o) 0.5 Yaw rate(w) ） 0.5 Yaw rate(w) ） 21.6 ） ） 21.6 ） 30 Vehicle speed(w/o)

） 30 Vehicle speed(w/o) m m 0.4 0.4 VehicleVehicle speed(w) speed(w) rad/s km/h rad/s km/h （ 20 （ 20 （ Y （ Y （ 14.4 （ 14.4 v w

0.3 v w 0.3 10 10 0.2 0.2 7.27.2 0 0 0.1 0.1 -10 0 -10 -10 0 10 20 30 40 50 60 0 0 0 5 10 15 20 -10 0 10 20 30 40 50 60 0 0 5 10 15 20 0 5 10 15 20 X（m） 0 5 10 15 20 t（s） X（m） t（s） t（s） t（s） (a) (b) (c) (a) (b) (c) 200 100 70 Inner side(w/o) Inner side(w/o) 200 100 70 0 Inner side(w/o)Outer side(w/o) 0 InnerOuter side(w/o) side(w/o) 60 Inner side(w) Outer side(w/o) 0 OuterInner side(w/o)side(w) 0 Outer side(w) -100 Outer side(w) 60 -200 Inner side(w) Inner side(w) 50 Outer side(w) -100-200 Outer side(w) -200 -400 4050

） Inner side(w/o) ） -200-300 ） Outer side(w/o) -400 40

-600 kW 30

） Inner side(w/o) N*m Outer side(w) ） r/min -400 ） -300 （ （ Inner Outerside(w) side(w/o) （ P T

-800 n 20

-600 kW 30

N*m Outer side(w) r/min -400-500 （

（ Inner side(w) （ P

T -1000 10

-800 n -600 20 -500 -1200 0 -1000 -700 10 -600 -1400 -800 -10 -1200 0 5 10 15 20 -700 0 5 10 15 20 0 0 5 10 15 20 t（s） t（s） t（s） -1400 -800 -10 0 5 10 (d) 15 20 0 5 (10e) 15 20 0 5 (f) 10 15 20 t（s） t（s） t（s） Figure (8.d Simulation) results of 5B steering: (a) Trajectory;(e) (b) Vehicle yaw rate; (c) Vehicle(f )speed; (d) Figure 8. Simulation results of 5B steering: (a) Trajectory; (b) Vehicle yaw rate; (c) Vehicle speed; Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power. (Figured) Sprocket 8. Simulation torque; ( eresults) Sprocket of 5B rotation steering: speed; (a) Trajectory; (f) Sprocket (b) power. Vehicle yaw rate; (c) Vehicle speed; (d) Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power.

Energies 2018, 11, 1538 14 of 17 Energies 2018, 11, x FOR PEER REVIEW 14 of 16

5.2.5.2. 10B 10B Steering Steering AtAt first, first, the the vehicle vehicle is is stationary stationary for for 2 2 s. s. After After that, that, the the vehicle vehicle starts starts running running straight straight for for 5 5 s s and and acceleratesaccelerates to to 40.7 40.7 km/h. km/h. The steering wheel is is turn turneded to to the the right right at at 7 7 s s and and manipulated manipulated to to output output R R== 10 10BB. The. The trajectory, trajectory, yaw yaw rate rate and and speed speed of of the the vehicl vehiclee are shown inin FigureFigure9 a–c.9a–c. From From Figure Figure9b 9b we we knowknow that that without without the the coupling coupling device, device, the fluctuation the fluctuation of the vehicleof the yawvehicle rate yaw deteriorate rate deteriorate the trajectory the controllability,trajectory controllability, also the vehicle also the speed vehicle fluctuates speed andfluctuates declines and at declines the same at time. the same While time. the While speed the of thespeed vehicle of the with vehicle coupling with devicecoupling is closedevice to is the close target to the value. target The value. torque, The rotation torque, rotation speed and speed power and ofpower the sprocket of the sprocket are shown are in shown Figure in9d–f. Figure The 9d–f. graph The shows graph that shows the torque that the varies torque smoothly varies withsmoothly the couplingwith the device.coupling Without device. the Without coupling the device, coupling the rotationdevice, the speed rotation is lower speed and is there lower are and fluctuations there are duefluctuations to the limitation due to ofthe the limitation motor power of the according motor po tower Figure according9e. However, to Figure the 9e. output However, power the increases output withpower the increases coupling device,with the therefore coupling the device, vehicle therefore can turn the in highvehicle speed. can Itturn is worth in high noting speed. that It theis worth yaw ratenoting is a littlethat the lower yaw to ensurerate is thea little stability lower of to the ensure vehicle, the however, stability the of powerthe vehicle, demand however, is still quitethe power high especiallydemand is during still quite dynamic high steering.especially during dynamic steering.

100 0.7 54 Yaw rate(w/o) Vehicle speed(w/o) Yaw rate(w) Vehicle speed(w) 80 0.6

0.5 60 36 ）

0.4 ） ）

m 40 m/s rad/s （ 0.3 （ （ Y v 20 w 18 0.2

0 0.1 Trajectory(w/o) Trajectory(w) 0 -20 0 -20 0 20 40 60 80 0 5 10 15 20 25 0 5 10 15 20 25 X（m） t（s） t（s） (a) (b) (c)

0 200 80 Inner side(w/o) Outer side(w/o) 70 -200 0 Inner side(w) Outer side(w) 60 -400 -200 50 ） ） -600 ） 40

-400 kW N*m r/min 30 -800 （ （ （ P T n -600 20 -1000 Inner side(w/o) 10 Inner side(w/o) Outer side(w/o) Outer side(w/o) -1200 -800 Inner side(w) 0 Inner side(w) Outer side(w) Outer side(w) -1400 -1000 -10 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 t（s） t（s） t（s） (d) (e) (f)

Figure 9. Simulation results of 5B steering: (a) Trajectory; (b) Vehicle yaw rate; (c) Vehicle speed; (d) Figure 9. Simulation results of 5B steering: (a) Trajectory; (b) Vehicle yaw rate; (c) Vehicle speed; Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power. (d) Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power.

5.3. 20B Steering 5.3. 20B Steering At first, the vehicle is stationary for 2 s. After that, the vehicle starts running straight for 8 s and At first, the vehicle is stationary for 2 s. After that, the vehicle starts running straight for 8 s and accelerates to 57.5 km/h. The steering wheel is turned to the right at 10 s and manipulated to output accelerates to 57.5 km/h. The steering wheel is turned to the right at 10 s and manipulated to output R = 20B. The trajectory, yaw rate and speed of the vehicle are shown in Figure 10a–c. We can see from R = 20B. The trajectory, yaw rate and speed of the vehicle are shown in Figure 10a–c. We can see Figure 10a that the steering radius is quite large due to the slip between tracks and the ground during from Figure 10a that the steering radius is quite large due to the slip between tracks and the ground high-speed steering. To avoid the rollover or instability of the vehicle, the yaw rate is not as high as during high-speed steering. To avoid the rollover or instability of the vehicle, the yaw rate is not as the value we assumed. However, the yaw rate of the vehicle with coupling device is still higher. The high as the value we assumed. However, the yaw rate of the vehicle with coupling device is still vehicle speed is higher with the coupling device while 11% lower than the theoretical value according higher. The vehicle speed is higher with the coupling device while 11% lower than the theoretical to Figure 10c. The torque, rotation speed and power of the sprocket are shown in Figure 10d–f. It can value according to Figure 10c. The torque, rotation speed and power of the sprocket are shown in be seen that the output torque and the speed of the sprocket are not changed greatly during stationary Figure 10d–f. It can be seen that the output torque and the speed of the sprocket are not changed steering due to the limitation of the motor power. The output torque and the speed of the sprocket is greatly during stationary steering due to the limitation of the motor power. The output torque and lower without the coupling device. While with the coupling device the output power is improved the speed of the sprocket is lower without the coupling device. While with the coupling device the and the vehicle speed can be maintained at higher level. Although the yaw rate is not large, the power demand is still larger than the calculated value to maintain the high speed during steering.

Energies 2018, 11, 1538 15 of 17 output power is improved and the vehicle speed can be maintained at higher level. Although the yaw rate is not large, the power demand is still larger than the calculated value to maintain the high speed duringEnergies steering.2018, 11, x FOR PEER REVIEW 15 of 16

200 0.35 60

0.3 50 150 0.25 40 ） 100 ）

） 0.2

m 30 rad/s km/h （ 0.15 （ Y

50 （ v w 20 0.1 0 10 Trajectory(w/o) 0.05 Yaw rate(w/o) Vehicle speed(w/o) Trajectory(w) Yaw rate(w) Vehicle speed(w) -50 0 0 -50 0 50 100 150 0 5 10 15 20 25 0 5 10 15 20 25 X（m） t（s） t（s） (a) (b) (c)

0 200 100 Inner side(w/o) -200 0 Outer side(w/o) Inner side(w) 80 Outer side(w) -400 -200 60 ） ） -600 -400 ）

kW 40 N*m r/min

-800 -600 （ （ （ P T n 20 -1000 -800 Inner side(w/o) Inner side(w/o) Outer side(w/o) 0 Outer side(w/o) -1200 Inner side(w) -1000 Inner side(w) Outer side(w) Outer side(w) -1400 -1200 -20 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 t（s） t（s） t（s） (d) (e) (f)

Figure 10. Simulation results of 5B steering: (a) Trajectory; (b) Vehicle yaw rate; (c) Vehicle speed; (d) Figure 10. Simulation results of 5B steering: (a) Trajectory; (b) Vehicle yaw rate; (c) Vehicle speed; Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power. (d) Sprocket torque; (e) Sprocket rotation speed; (f) Sprocket power.

6. Conclusions 6. Conclusions In this paper, according to the dynamic analysis of the 2MDTV, we found that the power In this paper, according to the dynamic analysis of the 2MDTV, we found that the power required required by the propulsion motor is quite large during high-speed steering situations. As the existing by the propulsion motor is quite large during high-speed steering situations. As the existing research research focused more on low-speed conditions, we considered the vehicle performance during high focused more on low-speed conditions, we considered the vehicle performance during high speed speed steering in this work and supplemented the calculations about the power demand. In order to steering in this work and supplemented the calculations about the power demand. In order to solve solve the problem of understeer and speed decline of the vehicle caused by insufficient power during the problem of understeer and speed decline of the vehicle caused by insufficient power during high speed steering, a new electromechanical coupling device is proposed. The device is used to high speed steering, a new electromechanical coupling device is proposed. The device is used to couple the power of the steering motor and the propulsion motor to satisfy the requirements for high- couple the power of the steering motor and the propulsion motor to satisfy the requirements for speed steering. The coupling system can increase the power of outer track by 20 kW during high- high-speed steering. The coupling system can increase the power of outer track by 20 kW during speed steering. Furthermore, an optimized torque distribution control strategy is proposed. In the high-speed steering. Furthermore, an optimized torque distribution control strategy is proposed. Hardware-in-the-Loop (HIL) simulation of 5B, 10B, and 20B steering with RecurDyn and In the Hardware-in-the-Loop (HIL) simulation of 5B, 10B, and 20B steering with RecurDyn and Matlab/Simulink models, the coupling device can improve the output power of the vehicle, and the Matlab/Simulink models, the coupling device can improve the output power of the vehicle, and the proposed strategy can improve the steering stability and achieve smoother steering response of the proposed strategy can improve the steering stability and achieve smoother steering response of the vehicle at high speed. vehicle at high speed. Author Contributions: L.Z. proposed the innovation of the overall system and designed the control methods, Author Contributions: L.Z. proposed the innovation of the overall system and designed the control methods, H.H.H.H. are are responsible responsible for for the the improvement improvement ofof coupledcoupled systemssystems andand thethe simulationsimulation ofof thethe system,system, Z.W.Z.W. andand H.H.H.H. builtbuilt the the mathematic mathematic model model and and performed performed the calculation.the calculat L.Z.ion.and L.Z. H.H. and wrote H.H. thewrot manuscripte the manuscript and Z.W. and polished Z.W. thepolished manuscript. the manuscript. All authors All read authors and approvedread and approved the manuscript. the manuscript.

Acknowledgments:Acknowledgments:This This work work was was supported supported by the by National the National Natural Natural Science FoundationScience Foundation of China forof financiallyChina for supporting this project (51475045). financially supporting this project (51475045). Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

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