Abstract
When the permanent magnet high-speed Electrical Multiple Unit (EMU) train runs at extremely high speeds, it is necessary to solve the problem of optimal exertion of wheel-rail adhesion to ensure the adhesion utilization rate of the train and the smooth and safe operation of the vehicle. To improve the adhesion utilization rate of the train and passenger comfort, this paper proposes an adaptive adhesion utilization control strategy for permanent magnet high-speed EMU trains. This method automatically identifies the wheel-rail state, matches the wheel-rail adhesion characteristics, automatically adjusts the adhesion control parameters according to the wheelset idling and sliding state, reduces the fluctuation range of traction force, improves the stability of traction force exertion and effectively improves the adhesion utilization control performance of the permanent magnet high-speed EMU train. Both simulation and experimental tests demonstrate this method's superiority over traditional control methods. It has been shown to enhance adhesion utilization efficiency by over 5% and to significantly narrow the traction force adjustment range by more than 10%. It also improves passenger comfort indicators such as train stability and comfort, and enhances the safety of train operation.
1. Introduction
In wheel-rail transportation, adhesion is the physical basis for rail transit vehicles to achieve traction, braking and steering. The formation of traction/braking force in rail transit trains relies on the adhesion between the wheels and rails. The adhesion coefficient between the wheels and rails is significantly reduced by the influence of third media such as rain, snow, falling leaves and oil stains. When the required traction/braking force exceeds the adhesion coefficient limit between the wheels and rails during train operation, it will cause the wheelset to idle/slide. The traction/braking force that can be transmitted between the wheels and rails drops sharply, severely affecting the train's operating performance. Adhesion control has always been one of the difficulties of high-speed train traction control [1, 2]. If the adhesion control system does not timely suppress idling and sliding on low-adhesion track surfaces, it may cause wheel-rail damage and even serious safety accidents.
There has been a lot of research carried out by many scholars on adhesion control methods, such as the combined correction method [3, 4], the acceleration differentiation method [5, 6], the intelligent control method [7, 8] and the observer method [9–15]. The combined correction method is currently the most widely used and mature adhesion control method. It mainly adjusts the traction motor torque according to indicators such as creep speed and acceleration of the train and wheelset during traction/braking. This algorithm has the advantages of simplicity, reliability and fast response, but it requires preset thresholds for creep speed and acceleration. Once the selected reference value differs too much from the actual optimal creep speed, the adhesion utilization will be low. The acceleration differentiation method performs adhesion control based on the acceleration of the wheelset. This algorithm can adapt to transient changes in the track surface, and the motor torque adjustment is timely, but this method is susceptible to noise interference. With the development of control technology, various intelligent control methods have also begun to be applied to various control fields, such as fuzzy control and neural network control methods. Although this algorithm does not require the establishment of an accurate mathematical model, it requires a large amount of actual operational data to establish a database. In the field of adhesion control, the relationship between wheels and rails is affected by factors such as weather and routes, which are nonlinear and time-varying. Therefore, although this algorithm seems advanced, it has not yet been maturely applied in the field of adhesion control.
With the development of permanent magnet control technology, permanent magnet synchronous motors have higher efficiency and power density, and enable higher train speeds. However, this also brings further challenges to adhesion control: permanent magnet motors generally use position sensors, and their output signals have periodic pulsations, or they adopt a speed sensorless method to obtain speed signals through speed identification. Differences in speed signals from different sources bring greater challenges to the setting of adhesion parameters and control performance improvement. Currently, observers are used in research to estimate wheel-rail adhesion forces, such as disturbance observers [9], full-order observers [10, 11], Kalman observers [12, 13] and sliding mode observers [14–17]. These methods have excellent stability and robustness. However, due to the characteristics of permanent magnet motor speed signals, such as periodic disturbances in the resolver speed signals, the engineering applicability of these methods is relatively low; the optimal creep search method [18] based on asynchronous motors has certain engineering application effects in the adhesion control of conventional asynchronous motors, but it is difficult to achieve good results in the adhesion control of permanent magnet motors due to the characteristics of permanent magnet motor speed signals. The performance of adhesion control directly affects the stability and comfort of high-speed train operation. If the control effect is poor, under extreme circumstances there may even be a bad influence of wheel scratching and track damage. Therefore, there is an urgent need to study adhesion control enhancement techniques that can be applied in engineering to improve the safety, stability and comfort of permanent magnet high-speed train operation.
During extremely high-speed operation, permanent magnet high-speed EMU trains need to address the challenge of optimizing wheel-rail adhesion to ensure efficient utilization of wheel-rail adhesion and smooth, safe operation. To enhance the utilization of wheel-rail adhesion and passenger comfort, this paper proposes an adaptive adhesion utilization control strategy for permanent magnet high-speed EMU trains. Utilizing an expert experience database, this method evaluates the current wheel-rail adhesion characteristics by analysing the maximum torque and the associated creep speed during the adhesion control process. It then refines the adhesion control parameters based on the instantaneous outcomes of the control. Additionally, it refines the transient result evaluation indicators through a comprehensive assessment of the overall results. With this approach, adaptive control has been successfully implemented across various wheel-rail adhesion conditions. This approach reduces fluctuations in traction force, improves the stability of traction force delivery, and effectively enhances the adhesion utilization control performance of permanent magnet high-speed EMU trains.
The remainder of this paper is organized as follows. Section 2 discusses the adhesion control principle. Section 3 presents and discusses the adaptive adhesion control principle. Next, Section 4 presents the experiments and the analysis of results, and finally Section 5 states the conclusions of this paper.
2. Principles of adhesion control
2.1 Adhesion characteristics
Due to factors such as weather conditions, track conditions, and foreign objects on the track surface, the adhesion conditions between wheel pairs are complex and variable. In practical applications of rail transit trains, it is impossible to accurately measure the actual wheel-rail contact conditions. Through extensive testing and research conducted by numerous experts and scholars in laboratories and on actual track tests, the correspondence between the wheel-rail adhesion force and creep ratio has been summarized, which is called the adhesion characteristic curve. Although the wheel-rail adhesion characteristics differ under different wheel-rail contact conditions, their trends and patterns are basically consistent. The adhesion characteristic curve is shown in Fig. 1.
Adhesion characteristic curve.
The adhesion characteristic graph's extreme point (μ, Vs) signifies the maximum adhesion coefficient μ for that condition, with Vs being the corresponding creep speed at this peak adhesion. The four adhesion characteristics depicted in Fig. 1 are detailed as follows:
Adhesion characteristic curve 1 illustrates the dry track conditions, with an extreme point at (0.01, 0.15), indicating the maximum adhesion coefficient and associated creep speed for a dry rail surface.
Adhesion characteristic curve 2 corresponds to rainy track conditions, with its extreme point at (0.03, 0.09), reflecting the maximum adhesion coefficient and creep speed in wet conditions.
Adhesion characteristic curve 3 is indicative of snowy track conditions, with the extreme point at (0.04, 0.05), showing the maximum adhesion coefficient and creep speed for a snow-covered rail surface.
Adhesion characteristic curve 4 represents the conditions of an oiled track surface, with the extreme point at (0.07, 0.035), denoting the maximum adhesion coefficient and creep speed for oily rail conditions.
This optimized description provides clarity and conciseness while maintaining the technical accuracy of the original content.
In this curve, the extreme point corresponds to the maximum adhesion coefficient and the optimal creep ratio for the respective adhesion characteristic curve. The area to the left of the extreme point is known as the adhesion region, while the area to the right is called the sliding region. When the actual creep ratio is close to the optimal creep ratio, the maximum adhesion coefficient can be achieved, and the corresponding creep ratio range can be referred to as the optimal creep ratio range.
When the wheel-rail adhesion state is within the adhesion region, as the creep speed increases, the adhesion force between the wheel and rail also increases. However, when the adhesion state is in the sliding region, as the creep speed increases, the adhesion force decreases. The goal of adhesion control is to keep the wheel-rail adhesion state close to the extreme point of the adhesion characteristic, minimizing and suppressing the occurrence of idle spinning and sliding, while fully utilizing the wheel-rail adhesion limit to ensure maximum traction/braking force.
2.2 Traditional adhesion control methods
Currently, the most widely used and mature adhesion control method in traditional adhesion utilization control systems is the combined correction method. As shown in Fig. 2, this method mainly adjusts the traction motor torque based on indicators such as creep speed and acceleration during traction/braking of the train and wheelset. This algorithm has the advantages of simplicity, reliability and fast response. It primarily uses wheelset acceleration and creep speed as key indicators to determine whether wheel spin or slide occurs and to control accordingly.
Wheelset acceleration protection
Logic block diagram of the combination correction method.
The principle of the acceleration protection strategy is to detect whether the wheelset acceleration exceeds a set threshold. When the wheelset acceleration exceeds the set threshold, the motor adhesion torque setting is reduced based on the acceleration value to suppress idle spinning and sliding.
When the adhesion conditions on the track surface change, and the adhesion state between the wheel and rail transitions from an adhesion to a sliding region, the actual adhesion force between the wheel and rail decreases. This is characterized by a sudden increase in the acceleration signal, indicating wheel spin or slide. The acceleration protection strategy detects the wheelset acceleration signal to predict the trend of wheel spin and adjusts the adhesion torque accordingly [6].
Wheelset creep speed protection
The creep speed protection strategy uses the current creep speed of the wheelset as feedback and aims to control the minimum overshoot with a preset creep speed threshold as the control target. Based on this, the corresponding adhesion torque adjustment is made [7].
The combined correction method is simple and convenient to implement but may not meet the demand for efficient adhesion utilization under complex wheel-rail conditions around the clock. Especially for permanent magnet trains, due to the influence of the speed signal of the permanent magnet motor, the control effect of the conventional combined correction method is not satisfactory.
3. Adaptive adhesion control
The conventional combined correction method has fixed parameters, which may not be fully applicable under different wheel-rail conditions. This can lead to overly sensitive or sluggish control, neither of which can achieve optimal control effects. If the adhesion control is too sensitive, it may judge the occurrence of idle spinning or sliding when the adhesion characteristic is still in the adhesion region, which prevents the full utilization of the wheel-rail adhesion limit and affects the acceleration and deceleration capabilities of the vehicle. On the other hand, if the adhesion control is too sluggish, it may judge the occurrence of idle spinning or sliding only after the adhesion characteristic has entered the sliding region. This can lead to the continuous development of idle spinning or sliding, resulting in significant traction/braking force loss and affecting the stability and comfort of the train operation.
To achieve excellent adhesion control effects under different wheel-rail adhesion conditions, it is essential to ensure that the adhesion control parameters are suitable for various wheel-rail conditions. Therefore, an adaptive adhesion control strategy is adopted, and an online adhesion control evaluation system is established. As shown in Fig. 3, this system assesses the adhesion control effect through both instantaneous and comprehensive results evaluation. Based on the evaluation results, the adhesion control parameters (acceleration protection threshold and creep speed protection threshold) are adjusted adaptively online to achieve excellent adhesion control effects under different wheel-rail adhesion conditions.
Logic block diagram of adaptive adhesion control.
3.1 Evaluation of wheel-rail adhesion conditions
As shown in Fig. 1, the adhesion conditions between wheel and rail vary under different track conditions and weather conditions. According to theoretical research and engineering application experience, under dry and clean rail surface conditions, the maximum adhesion coefficient between wheel and rail is higher, and the slope of the adhesion coefficient is greater in both the adhesion region on the left and the sliding region on the right. Under wet or even oily conditions, the maximum adhesion coefficient between wheel and rail is lower, and the slope of the adhesion coefficient is smaller in both the adhesion region on the left and the sliding region on the right.
Under different wheel-rail adhesion conditions, due to differences in wheel-rail adhesion characteristics, there are variations in optimal creep and maximum adhesion torque. Based on the utilization of adhesion, the wheel-rail adhesion state is evaluated in real time, and an expert experience library approach is adopted to set the corresponding expected creep speed and desired torque adjustment range according to different wheel-rail adhesion states.
As shown in Fig. 4, the process of evaluation of the wheel-rail adhesion status is as follows:
Detect the maximum traction force: before the occurrence of wheel slip, ascertain the maximum traction force and equate it to the maximum adhesion force under the current wheel-rail conditions. Compute the corresponding adhesion coefficient.
Measure the creep speed: prior to wheel slip, identify the creep speed of the wheel pair, calculate the current creep ratio and deem it the optimal ratio that corresponds to the maximum adhesion coefficient.
Determine the optimal adhesion point: employ the maximum adhesion coefficient and the optimal wheel pair creep ratio to establish the optimal adhesion point, which will be the foundation for the recognition of wheel-rail status.
Expert database matching: align the optimal adhesion point with the expert database of wheel-rail adhesion characteristics to facilitate accurate and informed matching.
Evaluation process of wheel-rail adhesion state.
3.2 Instantaneous result evaluation and parameter adjustment
Instantaneous result evaluation measures the effectiveness of individual adhesion control from two perspectives: maximum creep speed and torque adjustment range.
Maximum creep speed can be used to measure the final degree of creep and confirm the location of the wheel-rail adhesion state within the adhesion characteristic regions. A low maximum creep speed may indicate overly sensitive control, while a high maximum creep speed may suggest overly sluggish control.
The torque adjustment range characterizes the current adhesion torque adjustment scope through the difference between the motor torque before and after slip occurs (before and after unloading) as a ratio of the motor torque before slip occurs. According to adhesion characteristics, if the torque adjustment range is very small, the control may be too sensitive; if the torque adjustment range is very large, the control may be too sluggish.
As shown in Fig. 5, the specific process of instantaneous result evaluation is as follows:
When slip is detected, record the motor torque Tm1 before slip occurs.
During spin-up control, record the current creep speed Smax and St in real time according to the control cycle, and determine the relationship between the maximum creep speed and a preset threshold. If the maximum creep speed is less than the threshold, update the threshold with the maximum creep speed; otherwise, keep the threshold unchanged.
After slip elimination, record the motor torque Tm2 after slip elimination and calculate the torque adjustment range |$({{{T}_{m1} - {T}_{m2}}})/{{{T}_{m1}}}$|.
Estimate the current wheel-rail adhesion characteristics based on the records Tm1 and match them with the desired creep speed Sref and torque adjustment range γref.
Calculate evaluation indices based on recorded data ΔS = Smax–Sref, Δγ = γmax–γref. Select variables (ΔS and Δγ) as fuzzy rule inputs, fuzzify the input variables, divide the input variables into three fuzzy subsets represented by negative small (NS), zero (ZO) and positive small (PS); divide the input variables into five fuzzy subsets represented by negative big (NB), negative small (NS), zero (ZO), positive small (PS) and positive big (PB). Choose their membership functions as Gaussian (gaussmf). The control parameter adjustment coefficient is represented by negative small (NS), zero (ZO) and positive small (PS). A positive value indicates that the control parameter needs to be increased, while a negative value suggests that the control parameter should be decreased. The membership function is selected as triangular (trimf). Based on practical application experience, a fuzzy rule table for adjusting the control parameter is developed as shown in Table 1.
Flowchart of instantaneous result evaluation.
Fuzzy rule table for control parameter η adjustment coefficients.
| Δγ | ΔS | ||
|---|---|---|---|
| NS | ZO | PS | |
| NB | PS | PS | PS |
| NS | PS | PS | ZO |
| ZO | NS | ZO | PS |
| PS | NS | NS | ZO |
| PM | NS | NS | NS |
| Δγ | ΔS | ||
|---|---|---|---|
| NS | ZO | PS | |
| NB | PS | PS | PS |
| NS | PS | PS | ZO |
| ZO | NS | ZO | PS |
| PS | NS | NS | ZO |
| PM | NS | NS | NS |
Fuzzy rule table for control parameter η adjustment coefficients.
| Δγ | ΔS | ||
|---|---|---|---|
| NS | ZO | PS | |
| NB | PS | PS | PS |
| NS | PS | PS | ZO |
| ZO | NS | ZO | PS |
| PS | NS | NS | ZO |
| PM | NS | NS | NS |
| Δγ | ΔS | ||
|---|---|---|---|
| NS | ZO | PS | |
| NB | PS | PS | PS |
| NS | PS | PS | ZO |
| ZO | NS | ZO | PS |
| PS | NS | NS | ZO |
| PM | NS | NS | NS |
This method obtains the control parameter adjustment coefficient through fuzzy rule reasoning, and adjusts the control parameters (acceleration protection threshold and creep speed protection threshold) in real time.
3.3 Comprehensive result evaluation and parameter adjustment
Comprehensive result evaluation comprehensively measures the overall adhesion control effect during continuous wheel slipping by considering the average torque adjustment range. At the same time, it can determine whether the desired creep speed Sref setting is appropriate.
As shown in Fig. 6, the specific process of comprehensive result evaluation is as follows:
Within a certain time T1, if continuous slip occurs more than N times, judge that the continuous slip phenomenon appears and start timing.
Within a certain time T2, if no slip occurs, the comprehensive evaluation cumulative count ends.
Calculate the average torque Tave within the statistical time period. Calculate the average upper limit T2_ave and lower limit of the actual torque T1_ave during wheel slipping.
Calculate the average torque adjustment range based on the above data |${\gamma }_{ \mathrm{ ave}} = \left({{{T}_{2\_{\mathrm{ ave}}} - {\mathit{ T}}_{1\_{\mathrm{ ave}}}}}\right)/{{{\mathit{ T}}_{\mathrm{ ave}}}}$|.
Compare the calculated average torque γave adjustment range with the desired average torque adjustment range γave1, γave2.
If γave<γave1, so the calculated average torque adjustment range is lower than the desired range, it indicates that the adjustment range is too low, and the desired creep speed Sref needs to be increased accordingly. Conversely, if γave>γave2, it is higher than the desired range, suggesting that the adjustment range is too high and the desired creep speed Sref should be reduced.
Flowchart of comprehensive result evaluation.
The transient result evaluation assesses the control outcome of each slip event and adjusts the control parameters in real time to achieve the optimal anticipated control effect. The comprehensive result evaluation judges the overall effectiveness of slip control over a period of time, allowing for timely adjustments to the expected creep speed and ensuring the stability of the control effect. Through dual evaluations of transient and comprehensive results, and parameter adjustments, adaptive adhesion control is achieved, enhancing the adhesion control effect of rail transit permanent magnet trains under complex line conditions around the clock.
4. Simulations and experiments
4.1 Simulation analysis
As shown in Fig. 7, a simulation model was established to conduct a single-axis adhesion control simulation test and validate the adaptive control algorithm. The simulation analysis is conducted in Matlab, and the simulation model is mainly divided into six parts:
The ‘Smc Torque Control' module: this processes input from the driver controller, simulates changes in the driver controller's handle position and outputs the corresponding traction/braking force based on the handle position.
The ‘Adh Control' module: this handles adhesion control by acquiring speed signals, setting torque signals, etc., and outputs the adhesion torque.
The ‘Motor Control' module: this handles motor control based on the output torque signal from the adhesion control and the motor speed signal.
The ‘Adh Coef Cal' module: establishes a Polach wheel-rail model, and outputs the current wheel-rail adhesion coefficient based on changes in wheelset creep speed and set wheel-rail adhesion characteristics.
The ‘Axle Mode' module: represents the wheel-rail model, which obtains wheelset speed and actual adhesion force based on changes in motor driving force and adhesion coefficient. The wheel-rail contact model is established based on the Polach method's wheel-rail adhesion characteristic curve. By modifying this curve, changes in the wheel-rail adhesion state are simulated.
The ‘Train Mode' module: represents the train model, which acquires train speed based on the wheel-rail adhesion force using a train dynamics model.
Adaptive adhesion control simulation model.
Assuming a high-speed permanent magnet train model, validation was performed using the following parameters as shown in Table 2:
Control model parameters.
| Parameter | Value/Unit |
|---|---|
| Axle load | 14.5 t |
| Wheel diameter | 860 mm |
| Transmission ratio | 3.04 |
| Drive-to-trailer ratio | 1:1 |
| Parameter | Value/Unit |
|---|---|
| Axle load | 14.5 t |
| Wheel diameter | 860 mm |
| Transmission ratio | 3.04 |
| Drive-to-trailer ratio | 1:1 |
Control model parameters.
| Parameter | Value/Unit |
|---|---|
| Axle load | 14.5 t |
| Wheel diameter | 860 mm |
| Transmission ratio | 3.04 |
| Drive-to-trailer ratio | 1:1 |
| Parameter | Value/Unit |
|---|---|
| Axle load | 14.5 t |
| Wheel diameter | 860 mm |
| Transmission ratio | 3.04 |
| Drive-to-trailer ratio | 1:1 |
Set up four adhesion characteristic curves as shown in Fig. 1. The adhesion characteristics in the simulation model changed according to the sequence of adhesion characteristic curves 1, 2, 3, 4, 3 and 2.
The optimal creep rates ratiom and optimal adhesion φm coefficients are provided separately.
As shown in Fig. 8(a), the original combined correction control method exhibited significant differences in control effects under different wheel-rail conditions. Specifically, under adhesion characteristics (0.07, 0.035), the traction force adjustment range was significantly smaller than under other adhesion characteristics, making it unsuitable for higher adhesion control demands under loaded wheel-rail adhesion conditions.
Simulation result of adaptive adhesion control: (a1) and (a2) the simulation results before optimization; (b1) and (b2) the simulation results after optimization.
As shown in Fig. 8(b), after applying the adaptive control method, the adhesion software sets different expected parameters based on changes in the track surface conditions. It self-evaluates the real-time control effects during the control process and adjusts the control parameters in real time. Compared to the original method, there was a noticeable improvement under different adhesion characteristics. The traction force adjustment range was smaller, and the stability of traction force exertion was higher. As shown in Fig. 9, by adjusting the target value of creep speed based on the evaluation results, the parameter adjustment process can quickly converge to the vicinity of the optimal creep speed for the current rail surface.
Simulation result of the parameter adjustment process.
In the simulation test results of the original control method, the single-axis adhesion utilization coefficient was 0.88. After adopting the adaptive control algorithm, the single-axis adhesion utilization coefficient increased to 0.92, representing a 4% improvement in adhesion utilization compared to the original adhesion control. It should be noted that the adhesion utilization rate is represented by the ratio of the integral value of the actual motor torque to the integral value of the maximum torque envelope of the motor before the occurrence of wheel slip.
4.2 Experimental verification
A certain type of permanent magnet EMU was selected for the experiment. A low-friction liquid was sprayed on the track surface to simulate a low-adhesion state. The following parameters were monitored and recorded: wheelset linear speed, train speed, traction force and operating time. The adhesion control effects before and after optimization were compared and analysed through data.
As shown in Fig. 10, according to data comparison, the original control method cannot meet the higher control requirements of different wheel-rail adhesion conditions due to its inability to set parameters. During the process of idling judgement and control, the adhesion utilization ratio is approximately 86%, and the traction force adjustment range is relatively large, resulting in significant traction force loss, which is not conducive to the smooth and comfortable operation of the permanent magnet high-speed EMU. After adopting the adaptive adhesion control algorithm based on the adhesion control effect evaluation method, the adhesion utilization ratio increases to 91%, effectively reducing the traction adjustment range by more than 10%. The traction force becomes more stable, which is more conducive to the smooth, safe and comfortable operation of the permanent magnet high-speed train. It should be noted that the adhesion utilization rate is represented by the ratio of the integral value of the actual motor torque to the integral value of the maximum torque envelope of the motor before the occurrence of wheel slip.
Test result of adaptive adhesion control: (a1), (a2) and (a3) the test results before optimization; (b1), (b2) and (b3) the test results after optimization.
As shown in Fig. 11, the maximum speed of EMU reached 450 km/h. After applying adaptive control, the traction force performs exceptionally well, and the control is extremely stable across the entire speed range.
Optimized vehicle operation data: (a) speed and (b) torque.
5. Conclusions
The adaptive adhesion control method provides real-time evaluation of the wheel-rail adhesion state, matching the corresponding wheel-rail adhesion characteristics. Through transient control evaluation and comprehensive control evaluation, it comprehensively evaluates the adhesion control effect online and adjusts the control parameters based on the evaluation results. By optimizing the adhesion control effect online, the method achieves optimal adhesion control for permanent magnet high-speed trains under different speed signal inputs and wheel-rail adhesion conditions. Simulation analysis and field tests have shown that the adaptive adhesion control method comprehensively evaluates the torque adjustment range and creep speed variation during the adhesion control process to adjust the adhesion control parameters. This enables quick searching for optimal control parameters when wheel-rail conditions change, achieving optimal adhesion control under complex wheel-rail conditions. The adhesion utilization ratio is increased by 5%, and the traction adjustment range is reduced by more than 10%, which is more conducive to the smooth, safe and comfortable operation of the permanent magnet high-speed EMU trains.
Conflict of interest statement
None declared.
