electronics Article
Adhesion Control Strategy Based on the Wheel-Rail Adhesion State Observation for High-Speed Trains Xiaochun Fang *
ID
, Shuai Lin, Zhongping Yang, Fei Lin, Hu Sun and Liang Hu
School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China;
[email protected] (S.L.);
[email protected] (Z.Y.);
[email protected] (F.L.);
[email protected] (H.S.);
[email protected] (L.H.) * Correspondence:
[email protected]; Tel.: + 86-10-5168-4864 Received: 1 April 2018; Accepted: 10 May 2018; Published: 14 May 2018
Abstract: In this paper, an adhesion control strategy based on the wheel-rail adhesion state observation is proposed for high-speed trains. First, the high-speed train single axle dynamics model is established. Then, a modified adhesion control method is proposed. The scheme observes the tangential force coefficient between wheel and rail through full dimension observer and forecasts the slope of the adhesion-slip curve by the recursive least squares method with forgetting factor. Meanwhile, a feasibility analysis of the method and the control parameters tuning is conducted. Afterwards, the experimental study of the proposed adhesion control is carried out based on a 5.5 kW induction motor drag platform using dSPACE simulation technology. The experimental results confirm the feasibility of the adhesion control method proposed in this paper. Using the proposed adhesion control method can achieve high wheel-rail adhesion performance under variable complex road conditions. Keywords: adhesion control; tangential force coefficient; adhesion-slip slope; load simulation; high-speed train
1. Introduction Wheel-rail adhesion is one of the important factors affecting the normal traction-braking performance of high-speed trains. Wheel-rail adhesion force is restricted by road adhesion capacity. When traction-braking torque on the wheel over the maximum adhesion that wheel-rail can provide, idling-sliding phenomenon happens. This kind of phenomenon can lead to bad effects, such as a decline in passenger comfort, wheel-rail abrasion, train traction-braking performance degradation and so on [1]. Therefore, high speed trains are equipped with adhesion control devices to suppress the occurrence of idling-sliding, in order to ensure the normal operation of the train. In the field of high-speed train adhesion control, a main way is adopting the logic threshold control such as speed difference, creepage rate, acceleration/deceleration threshold, etc. But the method is a kind of control that acts after the occurrence of idling-sliding. So it cannot obtain the best use of adhesion, and it is affected by road surface conditions. Based on a zero order observer; literature [2,3] put forward a new torque adjustment control algorithm triggered by idling-sliding detection. Where, the control effect is better, but the utilization rate of adhesion remains need to be improved. Literature [4–6] present a fuzzy adhesion control method based on a zero order observer and achieves good results, but due to the complex fuzzy logic and programming difficulty, there are certain limitations in practical application. Literature [7] analyzes the performance influence of full dimension observer to re-adhesion optimization control system emphatically. Literature [8] proposes a torque feedback adhesion control method based on a zero order observer. The control in adhesion-slip stable region is effective, but in unstable region this control will fail. Literature [9] proposes a reduced-order observer, and adds an extra open-loop torque command C(t) to the output of Electronics 2018, 7, 70; doi:10.3390/electronics7050070
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torque regulator in literature [8]. Then literature [9] solves the failure problem in adhesion-slip unstable region of literature [8], but literature [9] does not give a reasonable method for judging whether the operation state is in the unstable region or not. The extra open loop torque command C(t) is obtained by experience instead of calculation. To suppress the occurrence of idling-sliding and get better use of adhesion, this paper proposes a modified algorithm of optimized adhesion control, on the basis of literature [8,9]. By building the full dimension observation of wheel-rail tangential force coefficient µ and Recursive Least Squares (RLS) estimation of adhesion-slip slope dµ/dvs with forgetting factor, the method uses torque feedback control to quickly implement train running near the adhesion peak point in complex road conditions and maintains high adhesion performance between wheel and rail. To confirm the feasibility of the proposed adhesion control method, based on adhesion control experimental research in literature [10–12], the experimental study is carried out based on a 5.5 kW induction motor drag platform using dSPACE simulation technology. The experimental results have confirm the feasibility of the proposed adhesion control method. 2. Model Analysis 2.1. Adhesion-Slip Characteristic
Tangential force coefficient μ
The wheel-rail adhesion-slip phenomenon of high-speed trains is essentially a kind of elastic contact interaction. Under the effect of axle load Wg, elastic deformation occurs in the contact area between the wheel-rail and leads to the formation of elliptical contact zone. When the wheel rolls forward by the drive torque T, tangential force can be produced between wheel-rail due to the relative motion or motion trend. The tangential force causes the movement of the wheel-rail contact surface; as a result, the train forward velocity will be smaller than the wheel line velocity and this phenomenon Electronics 2018, 7, x FOR PEER REVIEW 3 of 12 is slip. Figure 1 briefly shows the slip phenomenon. Peak point (μmax,vsopt) Stable region
Unstable region (sliding or idling) F Fd
w T
R
vt
Wg
F
Creep domain
Adhesion domain
Slip velocity vs Figure 1. Adhesion-slip phenomenon and adhesion-slip characteristic curve. Figure 1. Adhesion-slip phenomenon and adhesion-slip characteristic curve.
In order evaluate the degree 2.2. Train SingletoAxle Dynamics Model of slip and the value of adhesion force, the slip velocity vs and tangential force coefficient µ are defined as follows: Due to the complex dynamic characteristics of high-speed train running, it is difficult to build complex dynamic models considering various In this paper, the adhesion control study vs = ωfactors. (1) w · R − vt mainly aimed at the single axle dynamic model as shown in Figure 2. µ = Fµ /Wg (2)
rg 2
riving gear the n m o to r ω w Dexpresses ig where, R is the radius ofT racti theowheel; wheel angular velocity; vt is the velocity of the rg 1 F is the tangential force. train; W is the axls weight; g is the gravity acceleration; and µ
m
W heel
w W g
w R vt
Tangential force coefficient μ
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Stable
Unstable region (sliding or idling)
F region Numerous theoretical analyses and experimental tests have confirmed that the adhesion-slip F character between wheel and rail can be expressed by the relationship between tangential force w coefficient µ and the slip velocity vs . The relationship is called the adhesion-slip characteristic, T R and Figure 1 shows the typical adhesion-slip curve. The adhesion-slip curve has a peak point vt (µmax , vsopt ). The tangential force coefficient µmax at this point is called the adhesion coefficient. Wg The corresponding slip velocity vsopt at this point is called the optimal slip velocity. The curve is F divided into two areas by the vsopt . One is the stable area and the other is unstable area. The curve Creep Adhesion shows a positive slope of the adhesion-slip curve (dµ/dvs ≥ domain 0) in the stable area while a negative slope domain (dµ/dvs < 0) in the unstable area. Slip velocity vs When wheel-rail operates in the unstable region, the idling-sliding phenomenon happens easily. In order to avoid idling-sliding and use the maximum adhesion between the wheel-rail, optimized adhesion controls must be able to achieve wheel-rail running in the adhesion stablecurve. region and near Figure 1. Adhesion-slip phenomenon and adhesion-slip characteristic the peak point (µmax , vsopt ) under the variable condition of complex roads. d
2.2. Train Single Axle Dynamics Model 2.2. Train Single Axle Dynamics Model
Due to the complex dynamic characteristics of high-speed train running, it is difficult to build Due to the complex dynamic characteristics of high-speed train running, it is difficult to build complex dynamic considering various factors. this the paper, the control adhesion control complex dynamic models models considering various factors. In thisIn paper, adhesion study mainlystudy mainly aimed the single axle dynamic in Figure 2. aimed at theat single axle dynamic model asmodel shownas inshown Figure 2. T ractio n m o to r
D riving gear
ig
m
rg 2 rg 1 W heel
w R
w
vt
W g D riven gear R ail
Figure tractionforce forcetransferring transferring model for single Figure2.2.The Thesimplified simplified traction model for single axle. axle.
According adhesion characteristic, characteristic,driving driving system characteristic and the Accordingtotothe thewheel-rail wheel-rail adhesion system characteristic and the mechanical model Equation is gained as follows: mechanical modelofofthe thetrain, train, the the mathematical mathematical Equation (3)(3) is gained as follows: T − T − B · ω = J d dωmm m J m dt Bmm Tmm Twm wm m r g2m dt ig = r g1 r Tmw g2 = η gear · i g · Twm i g r w (3) Tmw − Fgµ1 · R − Bw · ωw = Jw dω dt M dvt − Fd ( ivt ) T= NM dt T Fµ mw gear g wm F µ = u ( vs ) · Wg d2w M FT(vt )= bvwt +Jcv · (Baw+ t ) (3) d mw F N R w M dt dvt where, M is train mass (including equipment andMpassenger quality, which is the load of motor Fd (vt ) Faxle; coaches); NM is the number of motor Jm is the traction motor rotor moment of inertia; Twm is N M dt the torque exerted to motor axle through F uthe (vs gear ) Wgbox by driven axle; Tmw is the torque exerted to driven axle through the gear box by motor axle; Jw is the driven axle moment of inertia; ig is the gear M transmission ratio; rg1 and rg2 are the Fradius gearand (vt ) of driving ( a bv cvt 2 )driven gear respectively; η gear is the d t NM
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gear transmission efficiency; R is the radius of the wheel; Bm , Bw are motor and driven axle rotational viscosity coefficient; Tm is the traction motor torque; ω m is motor angular speed; Fd is basic resistance of train, a, b and c are coefficients of resistance equation. Traction motor output side equivalent equation can be obtained by (3): Tm −
R Bw dωm Jw · Fµ − ( Bm + 2 ) · ωm = ( Jm + 2 ) i g · ηgear dt i g · ηgear i g · ηgear
(4)
Making Jequ = Jm + TL =
Jw i g 2 · ηgear
R · Fµ i g · ηgear
(5) (6)
and ignoring the Bm and Bw . Bm and Bw represent the internal rotational friction of the train drive system, which is relatively smaller than load torque and system moment of inertia torque. So Bm and Bw are often ignored in modelling [8,9]. Then Formula (4) can be represented as: Tm − TL =
dωm Jequ dt
(7)
3. The Modified Adhesion Control Method 3.1. Method Implementation Principle Literature [8,9] carry out torque feedback adhesion control based on the tangential force coefficient µ and dµ/dt. The key regulator function is: TA = K1 · dµ/dt + K2 · µ
(8)
where, TA is the torque command output by adhesion control, K1 and K2 are the control parameters. The essence of this regulator is a PI controller with dµ/dt as input. dµ/dt = 0 is the control objective with a suppose that dµ/dt = 0 is equivalent to dµ/dvs = 0. And dµ/dt is use to judge the operation area is stable or unstable in literature [9]. However, as shown in Figure 1, the operation area of the adhesion-slip characteristic is determined by dµ/dvs , not dµ/dt. dµ/dt isn’t equivalent to dµ/dvs as the criterion of operation area. This may cause inaccurate judgment of unstable areas, so that the torque command will get smaller and smaller as it moves along the stable parts of the adhesion-slip characteristic curve in Figure 1, and the train cannot run. As shown in Figure 1, f (µ, dµ/dvs ) can truly reflect the status of wheel-rail adhesion. So in this paper, based on the literature [8,9], replacing dµ/dt by dµ/dvs , torque feedback adhesion optimized control is proposed based on the tangential force coefficient µ and adhesion-slip slope dµ/dvs . The modified torque regulator function is shown in (9). TA = K1 · dµ/dvs + K2 · µ
(9)
Figure 3 shows the diagram of the modified adhesion control algorithm. The inputs in Figure 3 are drivers handle instruction T*, vehicle velocity vt , motor speed ω m and motor torque Tm . The output is the motor torque instruction Tm∗ Motor load torque TL is got through the state observer. Then combined with (2), (3), the wheel-rail tangential force coefficient µ and its differential value dµ/dt is calculated. Slip velocity vs is known by Formula (1), then the differential value dvs /dt can be calculated. Inputting dvs /dt and dµ/dt into the RLS module with forgetting factor, the estimated value of dµ/dvs can be got.
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calculated. Slip velocity vs is known by Formula (1), then the differential value dvs/dt can be calculated. Inputting dvs/dt and dμ/dt into the RLS module with forgetting factor, the estimated value Electronics 2018, 7, 70 5 of 12 of dμ/dvs can be got.
vt
m Tm
ig R
vs
Full dimension T L state observer
dvs dt
With forgetting factor RSL
ig g Wg R
d dt
d dvs
K1 K2
TA Min
Tm*
T* Figure 3. The diagram of modified adhesion control algorithm for high-speed train. Figure 3. The diagram of modified adhesion control algorithm for high-speed train.
According to torque regulator function (9), the adhesion control torque command TA is output. According to torque (9), the control torque command A is output. Comparing TA with T* andregulator choosingfunction the smaller oneadhesion as the motor vector control torqueTinstruction ∗ Comparing TA with the smaller one asstate the motor vector torque instruction value𝑇 (10)T*isand the choosing full dimension asymptotic observer of Tcontrol L [13,14]. Formula (11) is 𝑚 . Formula ∗ . Formula (10) is the full dimension asymptotic state observer of T [13,14]. Formula (11) is value T L m the principle of RLS estimation with forgetting factor [15]. the principle of RLS estimation with forgetting factor [15]. 1 B 1 " . # " # " ˆ# " ( p1 p2 ) 0 # " # " 1 # ˆ m p1 p21 B m m ˆ ω p + p − −( p + p ) − 0 J ωˆ m ωm J m 2 J equ 1 1 2 Jequ Jequ . T Tm Jequ Tm = ˆ ×equ Tˆ + × equ + ˆ L L − Jequ p1 p2 ˆL (10) L TL (10) TJequ T 0 0 0 T L p1 p2J pp 0 0 0 J equ p1 p2 Tˆ = R J p p (ωˆ − ω equ)dt1 2 m 1 2 m m L Tˆ J p p (ˆ m )dt L m 1 2 m where, p1 and p2 are the poles of full dimension observer. where, p1 and p2 are the poles of full dimension observer. y[k] = θˆ T [k]φ[k] y[ k ] ˆT [ k ][ k ] P [ k −1] φ [ k ] θˆ[k] = θˆ[k − 1] − 1+φT [k] P[k−1]φ[k] × (θˆ[k − 1]φ[k] − y[k ]) P [ k 1][ k ] ˆ[ k ] ˆ[ k 1] (11) T (ˆ[ k 1][ k ] y[ k ]) 1 T P [ k −1] φ [ k ] φ [ k ] P [ k −1] ] P [ k ] = [ P [ k − 1 ] − 1 [ k ] P [ k 1] [ k ] T κ 1+ φ [ k ] P [ k −1] φ [ k ] κ = 11 (11) P[ k 1][ k ] T [ k ]P[ k 1] 2 1+γφ [k[] k 1] [P ] P[ k ] T 1 [ k ]P[ k 1][ k ] where, γ is the exponential weighting factor, P is the error covariance matrix. 1 Making 1 [ k ]2 yP[kis] = where, γ is the exponential weighting factor, thedµ/dt error covariance matrix. ˆ[k] = dµ/dvs (12) θ Making φ[k ] = dv /dt s y[ k ] d dt The adhesion-slip slope ˆ dˆ dvs (12) [ kβ] = θ [k] (13) [ k ] dv dt s can be estimated accurately. The adhesion-slip slope 3.2. Theoretical Analysis and Parameter Setting of the Control Method ˆ[k] (13) Combined with the Formula (3), and ignoring Bm and Bw , adhesion state equation can be written as follows: can be estimated accurately. dvs R R2 NM N = · Tm − µ(vs ) · W · g + W · g + M Fd (vt ) (14) 2J dt i J M M i η g equ g equ g 3.2. Theoretical Analysis and Parameter Setting of the Control Method Because ofwith the great inertia of the actual train,Bthe variation of vehicle speed vt is can verybesmall in a Combined the Formula (3), and ignoring m and Bw, adhesion state equation written NM adhesion controller response action interval. So the F ( v ) in Formula (14) can be regarded as a t M d as follows: constant disturbance C. Discretization of Formula (14) is: v s [ k ] − v s [ k − 1] R R2 NM = Tm [k ] − W·g+ W · g · µ[k] + C Ts i g · Jequ M i g 2 Jequ · ηg
(15)
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By adhesion control algorithm block diagram shown in Figure 3, under good road conditions, the controller normally outputs driver instruction value T* (TA > T*). Under poor road conditions, the controller outputs adhesion control torque values TA (TA < T*). So in such condition, discretizing TA and putting the result into the Formula (15): −1]−µ[k−2] · K1 vµs [[kk− + 1]−vs [k −2] i W · g + NMM W · g · µ[k] + C
vs [k ]−vs [k −1] Ts
−
h
R2
i g 2 Jequ ·ηg
=
R i g · Jequ
R i g · Jequ
· K2 µ [ k − 1 ]
(16)
Within a control interval Ts , µ[k − 1] ≈ µ[k]. C is decided by vt and its value is still very small (C = ±0.198) when vtmax = 380 km/h. The proportion of C is very small during the process of adhesion control, so that it can be ignored. Therefore, further approximate processing of Formula (16) is: N v s [ k ] − v s [ k − 1] µ [ k − 1] − µ [ k − 2] R R R2 W · g + M W · g · µ[k] ≈ · K1 + · K2 − 2 Ts i g · Jequ v s [ k − 1] − v s [ k − 2] i g · Jequ M i g Jequ · ηg | {z } | {z } A
(17)
B
Based on Formula (17), we perform the feasibility analysis of the adhesion control method proposed in this paper and parameter setting of K1 and K2 . To realize running on the adhesion peak point (dvs /dt ≈ 0), the first requirement is A = 0, as a result B = 0, then we get the ideal K2 : K2 =
i g · Jequ NM R W·g+ W·g i g · ηg R M
(18)
At this time, K2 decided by system structure parameters is called its critical value K2TH . Determining the ideal K2 = K2TH , then B = 0, and A (decided by K1 ) plays the role of dynamic torque adjustment. The specific effect of K1 is to dynamically correct motor torque with small amplitude when road conditions change suddenly, and then to make the slip speed increase or decrease for rapid convergence to the peak point. Finally, to improve the utilization rate of adhesion. In actual control, in order to ensure the stability of adhesion control near the adhesion peak requires further analysis to the K2 . When K2 < K2TH and close to the K2TH , because of B < 0 and A + B = 0, so A ≈ 0 and A > 0. At this time, the operation point is in the left stable area and near the adhesion peak. When K2 > K2TH and close to the K2TH , because of B > 0 and A + B = 0, so A ≈ 0 and A < 0. At this time, the operation point is in the right unstable area and near the adhesion peak. Thus, K2 bounded by K2TH determines the final effect of adhesion control that wheel-rail operates in the stable area or in the unstable area near adhesion-slip peak point. In terms of adhesion control objectives, K2 actual value shall be the K2 = K2TH − K∆ < K2TH (K∆ is stability margin) to ensure that wheel-rail runs in stable area on the left side of the adhesion peak point. The value of K∆ must take into account both the adhesion control system stability and adhesion utilization. The value of K1 should be appropriately large (excessive K1 will lead to severe fluctuation of torque) to ensure the response speed and adhesion utilization. 4. Experimental Verification 4.1. The Load Simulation Test Platform Introduction According to the traction motor equivalent mechanical Equation (7), and using the scaling principle [16], the adhesion load simulation platform can be built with a motor drag platform [17]. The traction motor is simulated by a motor and the operation load is simulated by another motor. The two coaxial motors are dragged by each other. Therefore, this paper set up a 5.5 kW adhesion load simulation platform shown in Figures 4 and 5. Where, the dSPACE system controls the load motor and
both employ vector control. The train dynamics parameters refer to the CRH2A parameters [18]. both As employ vector control.4,The dynamics parameters refer to completes the CRH2Athe parameters [18].axle shown in Figure thetrain dSPACE control system mainly train single As shown in Figure 4, the dSPACE control system mainly completes the train single axle dynamics and the wheel-rail adhesion road conditions simulation, adhesion control, load torque dynamics and the wheel-rail adhesion road conditions simulation, adhesion control, load torque control and traction instruction calculation. Specifically, by calculation of the load torque, the control and traction instruction calculation. Specifically, byvalue calculation the load the dSPACE control system gets the load motor torque instruction 𝑇𝐿∗ andofcontrols the torque, load motor Electronics 2018, 7, 70 7 of 12 ∗ dSPACE control system gets the load motor torque instruction value 𝑇 and controls the load motor 𝐿 In addition, traction torque to simulate the traction motor equivalent load during train operation. to simulate the ∗ traction motor equivalent load during train operation. In addition, traction torque instruction 𝑇𝑚 calculated by dSPACE is sent to Myway platform through the CAN communication. ∗ instruction 𝑇system bythe dSPACE isreceiving sent to The Myway platform through CAN communication. 𝑚 calculated the Myway controls traction motor. motor andtraction thethe load motor both control. employ Myway control system mainly realizes 𝑇𝑚∗traction and completing motor vector ∗ Myway control system mainly realizes receiving 𝑇 and completing traction motor vector control. 𝑚 vector control. The train dynamics parameters refer to the CRH2A parameters [18]. The 5.5kW platform physical structure is shown in Figure 5. The 5.5kW platform physical structure is shown in Figure 5. dSPACE Control System dSPACE Control System
Myway Control System Myway Control System
*
Torque calculaTorque tion calculation
Level Level
vw vw
T* T
vt vt vt vt
Road simula Road -tion simula -tion
F F
Fd Fd
Adhesion control Adhesion control
Train model Train model
Resistance Resistance
vt vt
Tmrefref Tm
*
Tm * Tm
CAN CAN
m m
Load torque Load control torque control
Vector control Vector control
m m TL** TL
Traction motor Traction motor
IM IM
Speed sensor Speed sensor
Vector control Vector control
IM IM Load motor Load motor
Figure 4. The block diagram of the 5.5 kW adhesion load simulation experimental platform. Figure 4. 4. The The block block diagram diagram of of the the 5.5 5.5 kW kW adhesion adhesion load load simulation simulation experimental experimental platform. platform. Figure
Drag platform Drag platform
Figure 5. The 5.5 kW semi-physical adhesion load simulation platform. Figure Figure 5. 5. The The 5.5 5.5 kW kW semi-physical semi-physical adhesion adhesion load load simulation simulation platform. platform.
As shown in Figure 4, the dSPACE control system mainly completes the train single axle dynamics and the wheel-rail adhesion road conditions simulation, adhesion control, load torque control and traction instruction calculation. Specifically, by calculation of the load torque, the dSPACE control system gets the load motor torque instruction value TL∗ and controls the load motor to simulate the traction motor equivalent load during train operation. In addition, traction torque instruction Tm∗ calculated by dSPACE is sent to Myway platform through the CAN communication. Myway control system mainly realizes receiving Tm∗ and completing traction motor vector control. The 5.5kW platform physical structure is shown in Figure 5. 4.2. Experimental Results and Analysis To verify the effectiveness of the proposed adhesion control method, we designed adhesion-slip characteristics of three different road conditions as shown in Figure 6 [19,20].
verify the effectiveness of the proposed adhesion control method, we designed adhesion-slip 4.2.To Experimental Results and Analysis characteristics of three different road conditions as shown in Figure 6 [19,20]. To verify the effectiveness of the proposed adhesion control method, we designed adhesion-slip Electronics 2018, 7, 70 8 of 12 characteristics of three different road conditions as shown in Figure 6 [19,20]. μ force coefficient Tangential切向力系数 u μ force coefficient Tangential切向力系数 u
0.2
Road situation1(good) 路况1（良好） Road situation2(bad) 路况2（恶劣） Road situation3(bad) 路况3（恶劣）
0.2 0.15
Road situation1(good) 路况1（良好） Road situation2(bad) 路况2（恶劣） Road situation3(bad) 路况3（恶劣）
Road situation
0.15 0.1 Road situation Road situation
0.1 0.05
Road situation Road situation
0.05 0 0
5
0 0
10
15situation Road
20
[km/h] Slip蠕滑速度 velocity [km/h] 5
10
15
25 20
25
Figure 6. Adhesion-slip characteristic curves under different road conditions. [km/h] Slip蠕滑速度 velocity [km/h] Figure 6. Adhesion-slip characteristic curves under different road conditions. Figure 6. Adhesion-slip characteristic curves under different road conditions. The experimental platform simulates the whole process that a train speeds up from 0 to 130 km/h (10 level of traction), then uses regenerative braking to 25 km/h. In the traction condition, in the 55~85 The experimental platform thefrom whole process train up speeds from 0 to 130 km/h The experimental platformsimulates simulates the whole that athat trainaspeeds from 0up 130 km/h km/h section, road conditions rapidly change 1process (good road condition) to poortoroad condition 2; (10 level of traction), then uses regenerative braking to 25 km/h. In the traction condition, in the (10 level of traction), then uses regenerative braking to 25 km/h. In the traction condition, in the 55~85 in the 85~110 km/h section, road conditions deteriorate to poor road condition 3. In the braking 55~85 km/h section, road conditions rapidly change from 1 (good road condition) to poor road km/h section, conditions rapidlyroad change from 1 (good road condition) to poor road road condition) condition 2; condition, in theroad 105~70 km/h km/h section, conditions change from (good condition 2; in the 85~110 section, road conditionsrapidly deteriorate to poor road 1condition 3. In the theroad 85~110 km/h section, road km/h conditions deteriorate to poor road condition 3. In the braking toin poor condition 2.in the 105~70 braking condition, section, road conditions rapidly change from 1 (good road condition, km/h section, conditions rapidly 1 (good roadoperation condition) condition) to105~70 poor road condition Figure 7inisthe the change process of2.theroad wheel speed and vehiclechange speed from during the above to poor condition 2. control Figure is the change process of the wheel speed and vehicle speed during the above operation under theroad effect of 7adhesion (setting control parameters K1 = 19000, K2 = 7000). under the effect of adhesion control control parameters K1 = 19000, K2 =during 7000). the above operation Figure 7 is the change process of(setting the wheel speed and vehicle speed under the effect of adhesion control (setting control parameters K1 = 19000, K2 = 7000). 140
[km/h] Speed 速度 [km/h] [km/h] Speed 速度 [km/h]
120 140 100 120 80 100 60 80 40 60 20 40 0 020 0 0
Vehicle 车速 speed Wheel 轮速 speed Vehicle 车速 speed Wheel 轮速 speed
Road situation 1
25Road
situation 1
25
Road situation 2
Road situation 3
50 Road 75 situation 2
50
Road situation 1
Road100 situation 时间 [s] Time [s] 3
75
100
Road situation 2
Road 125 situation 1
125
Road situation 1
150Road 175 Road195 situation 2
150
situation 1
175
Figure 7. The changing speed and wheel speed. Figure 7. The changingof oftrain train speed wheel speed. 时间 [s] and Time [s]
195
7. The changing of train speed and wheel speed. According to Figure 7,Figure when the road became worse, either traction or braking, According to Figure 7, when the roadcondition condition became worse, either traction or braking, wheel wheel speed not sharply increase decrease .Idling/sliding is avoided effectively due to rapid of action speed did notdid sharply increase or or decrease .Idling/sliding is avoided effectively due action to rapid According to Figure 7, when the road condition became worse, either traction or braking, wheel adhesion controller. For further analysis, the changes of variables reflecting train running state, such of adhesion controller. For further analysis, the changes of variables reflecting train running state, as motor torque and adhesion or state, are shown in Figures 8–12.is avoided effectively due to rapid action speed did not sharply decrease .Idling/sliding such as motor torque andincrease adhesion state, are shown in Figures 8–12. Figure 8 shows the torque instructions, and Figure 9 shows actual value of torque.train According of adhesion controller. For further analysis, the changes ofthe variables reflecting running state, Figure 8 shows torque instructions, Figure 9 shows actual of torque. According to the figures,the when the road conditionsand become worse, due tothe a low roadvalue adhesion coefficient, as motor torque and adhesion state, are shown in Figures tosuch the figures, when road become worse, a8–12. low road adhesion the the wheel-rail isthe unable toconditions perform given adhesion ability. due Then,to the adhesion controller actscoefficient, rapidly. Figure 8 shows the torque instructions, and Figure shows the actual value of torque. According ∗ = T 9for The traction motor torque instruction is adjusted to T adapting to the current road adhesion wheel-rail is unable to perform given adhesion ability. the adhesion controller acts rapidly. The A m Then, to the figures, when the road conditions become to a poor lowtoroad road adhesion coefficient, the state and avoiding idling-sliding. In addition, in response different change ∗ worse,todue traction motor torque instruction is adjusted to 𝑇𝑚 = TA for adapting theconditions current road adhesion (roadisconditions 3), the adhesion controller can also achieve rapid adjustment of tractionacts motor wheel-rail unable to2,perform given adhesion Then, the adhesion rapidly. The state and avoiding idling-sliding. In addition, inability. response to different poorcontroller road conditions change ∗ traction motor torque instruction adjusted can to 𝑇also TA for adapting to the current road adhesion 𝑚 = achieve (road conditions 2, 3), the adhesioniscontroller rapid adjustment of traction motor state and avoiding ∗idling-sliding. In addition, in response to different poor road conditions change torque instruction 𝑇𝑚 (as shown in Figure 8, TA2 = 5.8 N·m and TA3 = 4.9 N·m). The controller has (road conditions 2, 3), the adhesion controller can also achieve rapid adjustment of traction motor good dynamic performance. torque instruction 𝑇𝑚∗ (as shown in Figure 8, TA2 = 5.8 N·m and TA3 = 4.9 N·m). The controller has good dynamic performance.
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m] [N· command Torque m] [N· command Torque m] [N· command Torque [N.m] 转矩指令 [N.m] 转矩指令 [N.m] 转矩指令
Figure Figure 10 10 shows shows the the results results of of the the tangential tangential force force coefficient coefficient μ μ full full dimensional dimensional observation observation and and ∗ the adhesion-slip slope dμ/dv ss RLS estimation. The observed values are in good agreement with the torque instruction Tmdμ/dv (as shown Figure 8, TA2 = 5.8 N·m and TA3 =are 4.9 in N·good m). The controllerwith has the the adhesion-slip slope s RLSin estimation. The observed values agreement actual values. The observation actual values. Theperformance. observation method method proposed proposed in in this this paper paper has has aa good good performance. performance. good dynamic 10 10 88 66 44 22 00 -2 -2 -4 -4 -6 -6 -8 -8 -10 -1000
Driver 司机指令（缩放系数200） Driverinstructions(zoom instructions(zoomfactor factor200) 200) 司机指令（缩放系数200） Driver instructions(zoom factor 200) 司机指令（缩放系数200） Traction 牵引转矩指令（引入黏着控制） Tractiontorque torquecommand(with command(withgelling gellingcontrol) control) 牵引转矩指令（引入黏着控制） Traction torque command(with gelling control) 牵引转矩指令（引入黏着控制） The 负载转矩指令（负载电机） Theload loadtorque torquecommand(traction command(tractionmotor) motor) 负载转矩指令（负载电机） The load torque command(traction motor) 负载转矩指令（负载电机）
TT TA2 A2 A2
25 25
TT TA3 A3 A3
50 50
75 75
100 125 100 125 时间 [s] time [s] time [s] 时间 [s] time [s]
150 150
175 175 195 195
Figure 8. torque traction motor and load motor. Figure 8. The The torque command of traction tractionmotor motorand and load motor. Figure 8. The torquecommand command of load motor. Figure 8. The torque command of traction motor and load motor.
m] [N· torque[N· Actualtorque m] Actual m] [N· torque Actual
10 10 10 888
traction traction traction load load load
666 444 222 000
-2 -2 -2 -4 -4 -4 -6 -6 -6 -8 -8 -8 -10 -10 -10 000
25 25 25
50 50 50
75 75 75
100 100 100
Time Time [s] [s] Time [s]
125 125 125
150 150 150
175 175 175
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Figure 9. The actual motor and load motor. Figure The actualtorque torque of traction load motor. Figure 9. 9. The actual torque of traction tractionmotor motorand and load motor. Figure 9. The actual torque of traction motor and load motor.
0.2 0.2 0.2
actual actual value value actual value observed observed value value observed value
μμμ
0.1 0.1 0.1
000 -0.1 -0.1 -0.1
dμ/dvsss dμ/dv dμ/dv
-0.2 -0.2 -0.2
000 0.2 0.2 0.2 0.1 0.1 0.1 000 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.3 -0.3 -0.3 000
25 25 25
50 50 50
75 75 75
100 100 100
125 125 125
150 150 150
175 175 175
195 195 195
actual actual value value actual value observed observed value value observed value
25 25 25
50 50 50
75 75 75
100 100 100
Time Time [s] [s]
125 125 125
150 150 150
Figure value and dμ/dv Figure10. 10.The The observed observed value and dµ/dv Figure 10. The observed valueofof ofµ μ μ and dμ/dv s . sss... Figure 10. The observed value of μ and dμ/dv
175 175 175
195 195 195
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u 切向力系数 coefficient forcecoefficient Tangential切向力系数 u μμ force Tangential
0.15 0.15 Road condition 1
0.1 0.1
Roadcondition condition21 Road
Road Roadcondition condition32
A A
Road condition 3 The actual trajectory The actual trajectory
0.05 0.05
B B
0 0 In bad road conditions, In bad road conditions, near the peak point, high near the peak point, high adhesion utilization adhesion utilization
-0.05 -0.05 C C
-0.1 -0.1 -25 -25 -20 -20
-15 -15
-10
-5 -5
00
55
10 10
蠕滑速度 [km/h] velocity[km/h] [km/h] [km/h] Slip蠕滑速度 velocity
1515
2020 2525
Figure 11. The actual running trackofofof μ-v Figure 11.11. track μ-v s. s. Figure Theactual actualrunning running track µ-v s. 88
velocity Slip [km/h] 蠕滑速度 [km/h] velocity[km/h] Slip [km/h] 蠕滑速度
vvs3s3=3.5km/h =3.5km/h
44 22 0 0
-2 -2 -4 -4
TheThe actual creep speed 实际蠕滑速度 actual creep speed 实际蠕滑速度
=5.3km/h vvs2s2=5.3km/h
66
peak point： peak point： umax2=0.063 umax2 =0.063 vsopt3=6.9km/h peak point： vsopt3=6.9km/h peak point： peak point： peak point： umax1=0.125 umax3=0.052 uvmax1=0.125 =0.052 max3=4.0km/h sopt1=6.9km/h vusopt3 vsopt1=6.9km/h vsopt3=4.0km/h Road Road Road situation Road Road Road situation situation Road 1 situation Road situation situation 1 1 situation 2 situation 1 3 2 3
-6 -6 -8 -8 0 0
20 20
40 40
60 60
80 100 120 80Time 100 时间[s] [s] 120
Road Road situation situation 2 2
140 140
时间[s][s] Time Figure 12. The change of vs. Figure Figure12. 12.The The change change ofofvsv. s.
160 160
Road Road situation situation 1 1
180 180
Unlike Figures 8 and 9 which verify adhesion control performance by output torque, Figures 11 Unlike Figures 8performance andthe 9 which verify adhesion control performance bystate output torque, Figures 11 Figure 10 resultsmainly of the tangential coefficient µ full dimensional and and 12 evaluate theshows from theforce wheel-rail adhesion-slip inobservation actual operation. the adhesion-slip slope dµ/dv RLS estimation. The observed values are in good agreement with the and 12 evaluate the performance mainly from the wheel-rail adhesion-slip state in actual operation. s Figure 11 describes the actual running state trajectory of μ and vs. It can be found from the figure that actual values. The observation method proposed in this has performance. Figure 11 describes the actual running state trajectory ofpaper μ and vs.acan Itgood can be found fromnear the the figure that despite in the bad conditions 2 or 3, the wheel-rail operation area achieve running peak Unlike Figures 8 and 9 which verify adhesion control performance by output torque, despite in the therespective bad conditions 2 or 3, the wheel-rail area can achieve running near the peak point in adhesion-slip conditions (A,operation B, C). Figures 11 and 12 evaluate the performance mainly from the wheel-rail adhesion-slip state in actual point in respective adhesion-slip conditions (A, B, C). Inthe addition, Figure 12 shows that in the traction condition, at a speed of 85 km/h, when road operation. Figure 11 describes the actual running state trajectory of µ and vs . It can be found from the Infigure addition, Figure 12 shows that in the traction condition, at aarea speed of 85 km/h, when road conditions deteriorate from poor road condition 2 to lower condition excessive that despite in the bad conditions 2 or 3, the wheel-railadhesion operationroad can achieve 3, running near slip conditions deteriorate from poortoroad condition 2than to lower road 3,rapidly, excessive slip velocity s2 = 5.3 km/h (vs2respective close vadhesion-slip sopt2 and bigger vsopt3 4 C). km/h) can be condition suppressed and the vpeak point in the conditions (A,=adhesion B, decreased vs3km/h = 3.5 Figure km/h close the peak point vsopt3condition, sopt3= < sopt2 That within arapidly, relatively velocity vs2 In =to5.3 (v s2 close to vtosopt2 and than v(v sopt3 4 vkm/h) can means be suppressed addition, 12 shows that inbigger the traction at a).speed of 85 km/h, when road and short period of time after the road conditions change, the operation point is located in the unstable conditions deteriorate from poor road condition 2 to lower adhesion road condition 3, excessive decreased to vs3 = 3.5 km/h close to the peak point vsopt3 (vsopt3 < vsopt2). That means within a relatively slip vs23after =and 5.3 the km/h (vs2 conditions closepoint to vsopt2 andto bigger than vregion 4by km/h) can be suppressed region of velocity condition operation moves the theisproposed control. This sopt3 =point short period of time road change, thestable operation located in the unstable rapidly, and decreased to v = 3.5 km/h close to the peak point v (v < v ). That means s3 sopt3 sopt3 sopt2 showsofthat the proposed adhesion control effective evenby if the the proposed wheel-rail operation region condition 3 and the operation pointmethod moves is to still the stable region control. This within a relatively short period of time after thescheme road conditions change, the operation point is located point is in an unsteady area, and the proposed can judge the operation area accurately. shows that the proposed adhesion control method is still effective even if the wheel-rail operation in the unstable region of condition 3 and the operation point moves to the stable region by the point isproposed in an unsteady area, and the proposed scheme can judge the operation area accurately. 5. Conclusionscontrol. This shows that the proposed adhesion control method is still effective even if the wheel-rail operation point is in an unsteady area, and the proposed scheme can judge the operation
5. Conclusions This paper briefly introduces the wheel-rail adhesion characteristic, and establishes simplified area accurately. single axle dynamic mathematical models of the CRH2A EMUs. Then, based on the literature [8,9], This paper briefly introduces the wheel-rail adhesion characteristic, and establishes simplified using the tangential force coefficient μ all dimension observation and the adhesion-slip slope dμ/dvs single axle dynamic mathematical models of the CRH2A EMUs. Then, based on the literature [8,9], RSL estimation, this paper proposes the modified torque feedback adhesion control. Besides, this using the tangential force coefficient μ all dimension observation and the adhesion-slip slope dμ/dvs paper analyzes the feasibility of the proposed method and the setting method of control parameters RSL estimation, this paper proposes the modified torque feedback adhesion control. Besides, this K1 and K2. The experimental study of the proposed adhesion control is carried out based on the 5.5 paper analyzes the feasibility of the proposed method and the setting method of control parameters
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5. Conclusions This paper briefly introduces the wheel-rail adhesion characteristic, and establishes simplified single axle dynamic mathematical models of the CRH2A EMUs. Then, based on the literature [8,9], using the tangential force coefficient µ all dimension observation and the adhesion-slip slope dµ/dvs RSL estimation, this paper proposes the modified torque feedback adhesion control. Besides, this paper analyzes the feasibility of the proposed method and the setting method of control parameters K1 and K2 . The experimental study of the proposed adhesion control is carried out based on the 5.5 kW induction motor drag platform using dSPACE simulation technology. According to the experimental results, the proposed adhesion control method can be achieved in different poor adhesion road conditions. The wheel-rail operation area stably nears peak point and the adhesion control is still effective in adhesion-slip unstable areas. The experimental results have confirmed the feasibility of the adhesion control method proposed in this paper. Author Contributions: X.F., Z.Y., F.L. and L.H. conceived and developed the ideas behind the research; X.F. carried out the experiments with support from S.L., L.H. and H.S.; X.F. wrote the paper. Z.Y. and F.L. supervised the research. Acknowledgments: This work was supported by The National Key Research and Development Program of China (No. 2017YFB1201105 and No. 2016YFB1200506-18). Conflicts of Interest: The authors declare no conflict of interest.
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