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Coupler force reduction method for multiple-unit trains using a new hierarchical control system

Coupler force reduction method for multiple-unit trains using a new hierarchical control system Rail. Eng. Science (2021) 29(2):163–182 https://doi.org/10.1007/s40534-021-00239-w Coupler force reduction method for multiple-unit trains using a new hierarchical control system Jacek Jackiewicz Received: 13 December 2020 / Revised: 27 April 2021 / Accepted: 28 April 2021 / Published online: 23 June 2021 The Author(s) 2021 Abstract During traction and braking of multiple-unit with the longitudinal movement of any train holistically trains, substantial longitudinal dynamic forces might occur and to a certain extent with relative longitudinal motions of in couplers due to the non-optimal distribution of traction train components. Within the LTD, both lateral and vertical and braking forces generated by self-propelled carriages. movements of carriages, or locomotives, can be omitted. These dynamic forces might create shocks affecting the In an overview article, Wu et al. [2] presented the his- reduction of endurance of the weakest train structural com- torical approach to issues of LTD since 1831, when, for the ponents primarily. Thus, the overall operational safety of the first time, Mohawk and Hudson had observed the dynamic train is also lowered. The purpose of the paper is to develop a behavior of ‘slack’ actions, referred to as a series of train new control system to supervise the activities related to the vehicle impacts (during state transitions of connections— longitudinal dynamics of each train carriage in a multiple- from tension to compression—or vice versa). The authors unit train to reduce the longitudinal coupler forces acting [2] focused, mainly, on the issues of longitudinal train during train traction and braking. The hierarchical structure dynamics, which cover the following problems: numerical of the control system consists of two levels. The first master solvers, vehicle connection systems, air brake systems, level of control works like standard cruise control. However, wagon dumper systems, locomotives, resistance forces, the reduction of longitudinal coupler forces is achieved by gravitational components, vehicle in-train instabilities, and applying a second level of slave control systems with a computing schemes. control configuration of feedback compensation. For long heavy-haul trains besides the LTD, some meaningful progress has been accomplished in the carriage Keywords Longitudinal train dynamics  Control system  system dynamics and coupled dynamics of vehicle-track Multiple-unit train  Railway coupler systems. However, there are still some difficulties during the simulation of longitudinal impulse interactions such, as changes in momentum of railway carriages on the elastic track structure [3]. Oprea [4] pointed out that studies on start-up dynamics of railway trains helped to ensure comfort for passengers 1 Introduction and, also, running safety of trains. Ansari et al. [5] comprehensively discussed the influ- The longitudinal train dynamics (LTD) studies motions of ences of stiffness and damping of couplers and load dis- all types of rolling stock vehicles moving in the longitu- tribution pattern on the train longitudinal dynamic dinal track direction [1]. This branch of mechanics deals behaviors. They also determined the optimum placement of the second locomotive to obtain the lowest longitudinal & Jacek Jackiewicz forces. jaceksnd@aim.com In recent years, modeling and simulations as research methods of rail vehicle-track dynamics have been inten- Faculty of Mechatronics, Kazimierz Wielki University in sively developed. Sharma et al. [6] presented an overview Bydgoszcz, Kopernika 1, 85-074 Bydgoszcz, Poland 123 164 J. Jackiewicz of applications of rail vehicle-track dynamic modeling. same speed while maintaining simultaneously fixed inter- They noted that relative motions between two adjacent vals between individual carriages. This solution requires carriages known as ‘slack actions’ had been caused due to the application of a new method for distributed power. The looseness and horizontal displacements in spring and MUTs have no locomotives, and their drive system consists damper connections. According to them, a coupling ‘free of several self-propelled units in a fixed formation, thus slack’ is defined as the free movement allowed by the sum providing that the traction is distributed along the train of clearances in wagon connections. They emphasized that length. The new control system will supervise the dis- these clearances occurred in the auto-coupler knuckles and tributed power to reduce the longitudinal coupler forces. draft gear assembly pins. In railways, not only passive damping systems with non- linear stiffness characteristics are used, especially in the 2 Functionality of advanced railway couplers suspension, but also magnetorheological dampers inte- grated with the secondary vertical suspension system. Different types of couplers have been used to connect Parameters of magnetorheological dampers are dependent adjoining carriages. Most used couplers allow a certain on current, amplitude, and frequency of excitations, as amount of slack to occur between wagons. In the case of described in Refs. [7, 8]. It naturally results in improved heavy-haul trains, the slack presence helps the train start. In ride quality and passenger comfort in comparison to the the heavy-haul train, its lack causes that the locomotive existing passive system. needs to pull the full load of the train at once, and hence the Sharma [9] modeled longitudinal train dynamics of the locomotive may not have sufficient power to start. How- locomotive-hauled passenger train of Rajdhani Express ever, in the high-speed train, the slack presence is unfa- based on experimental results and some data from the lit- vorable. It allows individual vehicles to move erature. He evaluated the performance of the rail vehicle in independently of each other, and thus they can end up its five braking phases. He noticed that the maximum traveling at different speeds to each other. If the speed compressive coupler force of 1.49 MN occurred in the third difference is high enough between individual vehicles, then quarter of the train. the forces acting in the coupler between adjoining carriages The traction and braking actions can cause large longi- may be high enough to break it [12]. tudinal forces in inter-vehicle coupling systems, especially Advanced tight-lock inter-vehicle connections [13] in long and heavy-haul trains. This paper focuses on installed on adjacent vehicles of a high-speed train provide electric multiple units (EMUs) with the distributed power, running stability during acceleration or deceleration. They blended and (or) electronic braking, advanced slip controls, have insignificantly small slackness. The tight-lock railway and permanently coupled carriages, for which LTD prob- connections themself represent coupler systems that consist lems may seem not to be such an essential issue. In prac- of springs and dampers, as shown in Fig. 1, where k and iðÞ 1 tice, things are not quite so effortless because quite large c are stiffness and damping coefficients. Elements of iðÞ 1 longitudinal forces may occur in EMUs by the improper these connection systems are parallel as they should share use of the distributed power control [10]. The EMU across the same absolute values of variables (such as rel- requires no separate locomotive, as electric traction motors ative displacements and velocities). are incorporated within one or a number of its vehicles. Let us notice that it is not easy to determine the non- The asynchrony of EMU vehicles’ traction or braking linear dynamic characteristic of the advanced coupler. As action may lead to large forces due to longitudinal vibra- described in Fig. 2a, this characteristic can often be rep- tions. Such vibrations may ultimately lead to a failure of resented by the three-zone displacement model. Figure 2b the coupler or even superstructure [11]. shows the damping force characteristic of the longitudinal To the best of the author’s knowledge in the field of inter-vehicle damper. This damper reduces longitudinal longitudinal train dynamics, the object of this work is to impacts and also can improve the lateral stability and ride improve a method for reduction of the longitudinal coupler comfort of the train. forces present during the traction and braking of the pas- For advanced inter-vehicle connections, active isolation senger train for outer suburban and long-distance config- of longitudinal vibration is proposed as a target solution. urations. This train should travel at high speeds and However, both characteristics of the semi-permanent tight- accelerate/brake quickly to increase average travel veloci- lock coupler and longitudinal inter-vehicle damper are ties and lower door-to-door trip time. nonlinear. Moreover, if the system is highly nonlinear over Depending on operator needs, there are several ways to the full range of operation, its adaptive schemes associated reduce the maximum of coupler forces. The most preferred with the control algorithm may show severe limitations. hi solution is a simple solution based on the assumption that Therefore, stroke limitations defined by x ; x for s s 1ðÞ i 1ðÞ i all vehicles of a multiple-unit train (MUT) move at the Rail. Eng. Science (2021) 29(2):163–182 c /3 i 1 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 165 tight-lock couplers are adopted, as well as velocity-jump hi constraints set by x_ ; x_ for longitudinal inter-ve- d d 1ðÞ i 1ðÞ i hicle dampers. Thus, due to automatic control, the coupler forces will have values within the range of their linear characteristics. In consequence, the coupler forces of this advanced connection system will not exceed the estab- lished admissible values. Structural failure of railway couplers may cause acci- dents and even lead to catastrophic damages. Therefore, it is critical to ensure that the couplers are in healthy struc- tural condition. The measurement of coupler-force values can be performed within the structural health monitoring (SHM) system for railway couplers [14]. This system Fig. 1 Adjacent vehicles of a high-speed train joined via the consists of, among others, accelerometers, which determine advanced inter-vehicle connection coupler movements, and digital strain sensors, which measure deformation strains on coupler bodies. vehicle. Similarly, model B consists of three vehicles with masses of m and four bogies. m (k ¼ 1; 2; 3; 4) are i k masses of Jacob bogies and q are their coordinates. 3 Modeling of longitudinal dynamics of multiple- Although various external loads act on each train car- unit trains riage, only these loads, related solely to the longitudinal direction, are significant to model the LTD, as assumed A system of differential equations can describe the longi- here. When the train moves on along a straight line, the tudinal dynamic behavior of the MUT. Assuming that there rolling resistance forces are independent of the train speed. is no vertical or lateral movement of each train vehicle, the They act on each carriage and occur as the results of wheel- MUT model has a much simpler structure. rail friction and friction in bearings. These forces, however, The EMUs can be divided into two broad categories are functions of various types of frictional resistance. [15]. The EMUs of the first category consist of independent Furthermore, for further analysis, certain forms of velocity- vehicles, each of which rests on two bogies (see model A of dependent rolling resistance forces are negligibly small Fig. 3). Such EMU vehicles, which do not share bogies, except for those forces, which may occur due to track can be longer. However, they need more bogies and must deflection. Without any cross-wind effect and in the open- be equipped with additional anti-overlap systems between air conditions, the total drag on the traveling train is usually the two adjacent vehicles to reduce the consequences of a calculated by the use of the following Davis’ formula railway accident. Each of the two adjacent vehicles of the [16, 17]: second category EMUs shares at least one the same bogie (see model B of Fig. 3). The advantage of this category is F ¼ a þ bv þ cv ; ð1Þ that the EMU has a reduced number of bogies in the train. where F is the train resistance (i.e., the total drag); a, b, Besides, shared boogies assure reduction of their lateral and c are constants, which depend upon the type of train; oscillations, less rolling, and pitching at high speeds. On and v is the train speed. Note that bearing and contact the other hand, it is necessary to use shorter vehicle bodies frictions vary with the weight of the train and the number to meet the limit requirements concerning the smallest of axles. The second term of this equation is proportional to permissible radii of railway track curves. train speed. This term expresses increased rolling The LTD model of MUT is necessary to design control resistance at high speed despite that it also includes some algorithms. This model allows testing different control components of laminar airflow. The last corresponds in size strategies without the need to use a physically available to speed-squared and expresses the aerodynamic drag. As EMU. indicated in [18], the aerodynamic drag of MUT consists of As shown in Fig. 3, x (i ¼ 1; 2; 3) describe the position separate drag forces with a different value for each of vehicle centers. Model A consists of three vehicles with carriage. Equation (1), therefore, has been converted to masses of m connected by stiffness and damping couplers. the form, which estimates the total drag force, R , acting A A Note that k and c (j ¼ 1; 2) are the stiffness and jðÞ 1 jðÞ 1 only on the ith carriage of the train: damping coefficients, respectively. F are the tractive R ¼ A þ B v þ C v ; ð2Þ A i i i i forces. R are the forces, which resist the motion of each Rail. Eng. Science (2021) 29(2):163–182 2c /3 i 1 Left inter-vehicle damper Right inter-vehicle damper Vehicle i Vehicle i+1 Semi-permanent tight-lock coupler 2k i 1 c /3 i 1 166 J. Jackiewicz The master level of the control system is an innovative closed-loop negative feedback control system. This control system has an unconventional solution through the appli- cation of the arrangement of two parallel-connected PID controllers. These controllers have the possibility of weighing their output signals, as demonstrated in Fig. 4a. As in the past, PID controllers are readily used in control applications due to their universality and simple structure [16, 17]. They are used not only in low-order systems but even in high-order systems owing to their advantageous properties. One of the disadvantages of these standardized controllers is that they, in some cases, cannot place all the poles as desired when controlling higher-order plant models. To deal with this problem, Persson and Astro¨m introduced the dominant pole placement method, refer to [18]. For a structurally complex system, system delay is usually variable during the control process. Therefore, the hierarchical control system is structured as least compli- cated as possible element arrangement. The second PID controller with time-delay compensation is wherefore applied and, thus, reduces the time-delay effect in the closed control system with negative feedback. Besides, separate tuning rules for both PID controllers provide smooth control action when switching signals between their different working points. There is also a possibility of Fig. 2 Characteristics of inter-vehicle connection components: a shows a relationship between spring force and displacement of an online adaptation of the multipliers for their output- the semi-permanent tight-lock coupler, whereas b demonstrates a weighting. Due to this adaptation, the closed-loop response damping force characteristic of the longitudinal inter-vehicle damper error disappears more rapidly than in the case of using only (in both cases, the sub-index i stands for the sequence number of the one single PID controller [19]. advanced inter-vehicle connection) The controller output signal is the tractive force F , def def where A ¼ðÞ a þ b g W and B ¼ c W , in which W driving the first bogie of MUT. The motor starting current i i i i i i i i i (i ¼ 1; 2; ...; p) is the weight of the ith carriage and p and the wheel-rail adhesions during the startup process limit the maximum value for F . Because any one of the denotes the number of train carriages, a is the rolling i 1 resistance coefficient assigned to the ith carriage, b is its processing signals cannot exceed its allowable physical limits, the saturation effects are taken into account in the bearing resistance coefficient, c is its flange resistance (in the case of a curved track), and g denotes the axles’ master control system. As depicted in Fig. 4a, through the saturation function, the limiters of F are F . It is worth number counted for the ith carriage; C is the aerodynamic i 1 max resistance coefficient of the ith carriage. The sample noting that slave negative feedback controllers establish other tractive forces. The saturation thresholds also apply coefficient values of Davis’s constants for some trains are given in Ref. [1]. to braking forces. Thus, it is possible to model the power transmission system without going into more details, how one, a few, or all of the electric motors of MUT can create 4 Design of master control system to supervise torques applied to the wheels. To include the process effects of the digital controller MUT activities related to the LTD delay and the analog-to-digital (A/D) conversion, and the digital-to-analog (D/A) conversion, standard block dia- The two-level control system for multiple-unit electric trains has a slightly complex structure. It consists of a grams for the continuous-time control systems need to be modified [20]. The master controller block diagram for master control level, which works similar to standard cruise control, and a lower control level, which compose of speed regulation, shown in Fig. 4, consists of blocks of associated together slave negative feedback controllers for continuous-time transfer functions. At the second input to process variables to decrease the longitudinal coupler for- the master controller, the continuous-time transfer function ces in the MUTs. denoted as A/D mimics the operation of the A/D converter. In the case under consideration, it is the second-order Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 167 A A A A A F R F x R x R F x 3 1 1 1 2 2 2 3 3 (a) A A A A c c m 1(1) m 2(1) m 1 2 A A k k 1(1) 2(1) B B x R x R R x 2 3 (b) 1 1 2 3 1(1) B B B B B B B m B B m m 1 c 3 c c c c c 2 c 8(1) 2(1) 3(1) 4(1) 6(1) 7(1) 5(1) B B B B B B B k k k k k 6(1) k k 4(1) k 7(1) 8(1) 2(1) 3(1) 5(1) 1(1) q q q 1 2 3 4 B Q B Q B B Q Q F m F m F F m m 1 1 2 2 3 4 3 4 Fig. 3 LTD models of MUTs: a model A; b model B Butterworth filter, which is an analog low pass filter to Even for linear plants, however, with actuator satura- prevent aliasing. The term, 1=T, is the filter cut off fre- tion, if, during the control design, the constraints on the quency. The cut off frequency has to be below one-half of actuator input are not accounted for, the results can the sampling frequency. The replacement block for the D/A sometimes give undesired effects [21]. A saturation link is converter in the form of a continuous-time transfer function often placed in the front of the PID controller integration emulates the conversion of the controller digital output branch to prevent windup. When the plant model represents signal back to an analog signal and performs a zero-order a double integration processing, the saturation link is also hold function. In Fig. 4a, the labeled ‘Delay’ block mimics placed in the PID controller proportional branch. the delay effects caused by the parallel system of two A modified PID controller with back-calculation and digital PID controllers. This block has the continuous-time clamping, as well as a tracking mode, represents another transfer function with the constant parameter, k. The value built-in anti-windup method. This controller is used to of k is the transfer function order for the parallel system of prevent integration windup in the PID controller [22]. two digital PID controllers. This value is established in A technique related to the anti-windup methods is the mathematical terms of the Z-transform. The block diagram so-called bumpless transfer method [21]. In the bumpless of Fig. 4a is the starting point for building the master transfer method, a supervising system supervises multiple discrete controller for speed regulation. The PID continu- controllers designed for the same linearized control system ous-time transfer functions of this master controller can be and switches among them. Inputs of three controllers, C , easily converted to discrete-time transfer functions (Z- C , and C , are connected to the same output of the feed- 2 3 transform transfer function). back summing point, as illustrated in Fig. 4b. These con- The developed method of active vibration reduction in trollers are hot (i.e., all the time, they process the error). the railway couplers is to be a compromise solution Switching between the controllers’ outputs occurs when the between its implementation costs and its operational per- error magnitude achieves a specified threshold value, with formance. An additional task for the two-level automatic some hysteresis to avoid frequent switching back and forth. control system is to keep force values of every railway Besides, to reduce the windup and improve the transient coupler element within the linearized range limited by its response, the master controller can be built upon nonlinear thresholds. If the full range of non-linear characteristics of dynamic compensators (C and C ) with two parallel chan- 1 2 any railway connection is needed, the active vibration nels [22], as shown in Fig. 4c. Nonlinear nondynamic isolation system will be turned off, leaving only passive links are placed here in both channels. The first channel damping in operation. The assumption adopted in this way starts with a saturation link with a unity threshold (when enables a significant simplification of the structure of the the signal amplitude is less than 1), and the second, with a control system. unity dead-zone (when the signal amplitude is higher than 1). Rail. Eng. Science (2021) 29(2):163–182 168 J. Jackiewicz The first version of the master controller, shown in this block is to encapsulate nested block diagrams for LTD Fig. 4a, was selected for further considerations due to its equations and slave control systems. least complex structure and satisfactory results obtained The design of robust control systems involves choosing during the LTD computer simulations. the controller structure and then adjusting the controller The master speed control system of the MUT to super- setting parameters to achieve acceptable performance in vise the activities related to the LTD is represented by a the presence of uncertainty. The controller structure should block diagram shown in Fig. 5. This negative feedback provide that the control system response can meet founded control system allows to maintain a prescribed relationship performance criteria. The first objective of the designing c c _ _ _ of x to x , where x represents the desired speed of the first control system is that this system output should very 1 1 MUT vehicle called the ‘leader’ in the distribute power accurately track the input desired speed, x_ . The second operation, and x_ is the measured (i.e., actual) speed of this objective is maintaining the internal forces in the advanced s d vehicle. The return signal x_ goes into the summing point inter-vehicle connections, F and F , within the given from the feedback path. In the summing point, the differ- range of permissible values. Note that F is the vector of ence between x_ and x_ becomes the error speed. reduced spring forces in semi-permanent tight-lock cou- The master controller for speed regulation amplifies this plers (or secondary suspensions), for which k are equiva- error and produces the output signal transmitted to an lent stiffnesses. F is the vector of reduced damping forces actuator. In the considering case, the actuator is to be the in advanced inter-vehicle connections (or secondary sus- traction motor of the first vehicle. When the traction motor pensions) with equivalent damping coefficients c . Another powered by electrical energy receives a control signal, it crucial goal of the control system design is minimizing the responds by converting its driving torque into the wheel effect of disturbances on system output signals. tractive force F . The MUT has no locomotives, but power To explain why there are no adverse couplings between is distributed along this train by multiple traction motors. the master control system and slave control systems of this Slave control systems control the distribution of tractive hierarchical control structure, let us consider the operation forces, F , driving other vehicles. The distribution of F i i of simplified forms of both these control levels. Albeit not depends on F . 1 only frequency-domain but also time-domain performance The block diagram of Fig. 5 has the subsystem block measures can describe the closed-loop feedback control labeled ‘LTD model ? Slave control systems.’ The role of system performances, the description in frequency-domain terms will merely be considered. (a) + Continuous ∑ PID 0.5 fix delay 2nd PID controller Gain ∑ Out 1 In 1 ∑ PID 0.5 In 2 1st PID controller Gain (b) (c) 1 C −1 In 1 + + In 1 ∑ ∑ Out 1 Out 1 ∑ C In 2 − In 2 − + −1 1 Command 1st Input Delay D/A In 1 Output A/D F max 1/ kg T 2/T Out 1 2 s + 1/ kg T s + 2/T −F 1/T max In 2 0.707 0.707 Saturation function 2 2 s + + 2nd Input T T with limits of -F and max F for F max 1 Fig. 4 Block diagram of the master controller for speed regulation built upon a parallel arrangement of two PID controllers, b bumpless transfer method, and c two nonlinear dynamic compensators connected in parallel Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 169 The objective of any one of the negative-feedback Disturbance controllers, which are represented by, widely used in the industry, PID controllers, is to respond to the error. How- s d F, F , F ever, the purpose of compensators, such as the lead, lag, Reference input 1st Input and lag-lead compensators, is to change the original c 2nd Input Desired speed, x dynamics of the plant. In the considering case, an appro- MCSR priate master-compensator should be interconnected with Master controller for speed regulation the LTD model to form the master nonlinear control-affine LTDM + SCSs system to control the speed x . LTD model + slave control systems The closed-loop master control system is based on the series compensation. For this compensation type, the con- Fig. 5 Block diagram of the master control system to supervise MUT troller, , is inserted into the forward path in series activities related to the LTD with the controlled system, , which describes the LTD model with slave control systems. Both and controller in the form of an adjusting gain parameter ,is are state-dependent transfer functions of the com- placed in the feedback path. Therefore, such a control plex variable s, and the state vector . To guarantee the configuration is referred to as feedback compensation. The stable closed-loop control system, the design of the master controlled system only consists of the LTD model. controller is based on a pole-placement algorithm. is the state-dependent transfer function inserted As shown in Fig. 5, the input signal to the block labeled without anything else into the forward path (i.e., between ‘LTDM ? SCSs’ is the tractive force F . The actual output the summing point and the take-off point). The input to the x_ is feedback, compared with the reference input x_ (i.e., slave-system transfer function is the tractive force F . The 1 1 the velocity command). The error, e ¼ x_  x_ ,atthe transfer function of the closed-loop system is given by summing point output is passed into the compensator, . The primary task of such a type of master control ð4Þ system is to keep the control variable x_ to the desired value x , despite external disturbances d in some frequency range. Since the master-system (state-dependent) transfer function of the closed-loop system is the following form: In this case, the output signal (i.e., one of the three process control variables, e.g., Dx ) tracks the setpoint equal to zero in the frequency range when . ð3Þ The primary task of the slave control system is to control the tractive force of the ith drive unit, F , in correlation to the tractive force of the ‘leader’ drive unit, F . the output signal x_ tracks the input signal x_ accurately (i.e., x_ ’ x_ ) in the frequency range when 5 Typical applications of train dynamics models and, therefore, is close to 1. together with the slave control structure However, the master control system does not perform selection to reduce coupler forces in the MUTs directly and alone tasks of active vibration damping, con- cerning the maintenance of zero values for the following EMU configurations can include various combinations of process control variables: power carriages. The power carriages with motored bogies, • Dx —the distance change between both ends of the like electric locomotives, are self-propelled and not used as selected inter-vehicle connection, which connects two passenger carriages in a locomotive-hauled train. Usually carriages, used connections between carriage bodies of MUT are • Dx_ —the difference of velocities of both ends of the couplers (i.e., mechanisms used to connect rolling stock in considering railway connection, a train) or Jacobs’ bogies. • Dx ds—the integral over time (s) of the distance j The posed task is to design a new hierarchical control change between both ends of this connection. system to bring the MUT smoothly up to speed 50 m/s, followed by braking to 0 m/s, utilizing an electric or hybrid The design of slave control systems enabling the real- traction system with the possibility of energy recovery. The ization of the active vibration damping in the MUT inter- command signal for the MUT speed is broken down into vehicle connections is different from the master speed- the following stages: (i) start-up (the MUT speed varies control system design. In each slave control system, a slave Rail. Eng. Science (2021) 29(2):163–182 170 J. Jackiewicz continuously from standstill to the cruising speed), (ii) Numerical simulations carried out with the help of cruising (the MUT speed is maintained constant at the Scilab/Xcos toolbox for modeling and simulation of cruising value), (iii) braking (the MUT speed is reduced dynamic (continuous and discrete) systems mimic opera- from cruising to a standstill), and (iv) stop (the MUT speed tions of the master control system of the MUT to supervise is zero). The performance task requires establishing a the activities related to the LTD. method of MUT tractive effort control and then selecting the controller characteristics. The software package of 5.1 Test simulations for the MUT with couplers Scilab, called Xcos, provides functionalities to determine used as connections between carriage bodies control strategies for both open and closed control systems with negative feedback. Let us consider a train consisting of one electric locomotive and two individual passenger wagons, as shown in Fig. 3a (a) A A A F (Ex.1) F (Ex.1) F (Ex.1) 1 2 3 A A A F (Ex.2) F (Ex.2) F (Ex.2) 1 2 3 A A A F (Ex.3) F (Ex.3) F (Ex.3) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -100 -200 -300 -400 Time (s) (b) Fig. 6 Numerical results based on the LTD for model A of the MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 1 and 2, passive vibration damping is only used; in Ex. 3 both passive and active vibration damping are used) Rail. Eng. Science (2021) 29(2):163–182 Tractive forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 171 s(A) s(A) F (Ex. 1) F (Ex. 1) 1 2 s(A) s(A) F (Ex. 2) F (Ex. 2) 1 2 s(A) s(A) F (Ex. 3) F (Ex. 3) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -50 -100 -150 -200 -250 Time (s) (a) d(A) d(A) d(A) F (Ex. 1) F (Ex. 1) F (Ex. 2) 1 2 1 d(A) d(A) d(A) F (Ex. 2) F (Ex. 3) F (Ex. 3) 2 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -50 -100 -150 Time (s) (b) sAðÞ sAðÞ Fig. 7 Numerical results based on the LTD for model A of the MUT: a coupler spring forces F and F vs. time; b coupler damping forces 1 2 dAðÞ dAðÞ F and F vs. time (in Ex. 1 and 2, passive vibration damping is only used; in Ex. 3 both passive and active vibration damping are used) 1 2 (i.e., model A), with the following assumptions made: x_ , are also correlated. Both connections consist of the A A A parallel connection systems of the spring connectors with F 6¼ 0, F ¼ 0, and F ¼ 0. Train model parameters are 1 2 3 the viscous dampers. They are placed between the 1st and selected based on data from [23]. Note that in Figs. 6 and 7, 2nd carriages as well as between the 2nd and 3rd carriages. the results of computer simulations for this example are The use of viscous dampers with the following damping labeled by Ex. 1. Figure 6a shows train acceleration to the A A line speed of 50 m/s at full power, motoring at the line coefficients, b and b , provides passive damping of lon- 1 2 speed, and then train braking at standard service rate. gitudinal vibrations. The passive vibration damping Figure 6b illustrates the dependence on the time of the method based on energy dissipation can be very efficient in tractive forces F . Time courses of changes of the train damping out high-frequency excitations. However, passive damping of dynamic forces in train couplers can be speed x_ and any one of the tractive forces F correspond insufficient in the case of an uncorrelated traction distri- to each other. bution in the MUT, especially in the range of low-fre- Figure 7 shows variations of coupler forces in both quency vibrations. The active damping method ensures advanced inter-vehicle connections. Changes in the coupler sAðÞ dAðÞ more effective damping of low-frequency vibrations. forces, F and F ðÞ i ¼ 1; 2 , as well as the train speed i i Rail. Eng. Science (2021) 29(2):163–182 Spring forces (kN) Damping forces (kN) 172 J. Jackiewicz Disturbance A . F R x , x i i i s d F, F , F Vehicle i d(A) A d(A) i − 1 m F i i s(A) s(A) i − 1 i LTDM + SCSs 1 + Expression: ∑ 1/s i − K ·∫(x − x )dτ + I(A) 1 i K ·(x − x )+ P(A) 1 i 1 + . . Saturation K ·(x − x ) . D(A) 1 i Saturation i − Fig. 8 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the MUT inter- vehicle connections (all MUT carriages are self-propelled) However, this method requires the application of additional systems are nested in the block diagram of the master actuators. The actuators generate second forces or con- control system, which is depicted in Fig. 5. trolled displacements to compensate for the effects of The computer simulations’ results are labeled by Ex. 2, response on the action of external forces or kinematic when all MUT carriages are self-propelled (i.e., F 6¼ 0, A A excitations directly acting on components of the MUT. F 6¼ 0, and F 6¼ 0), and the only passive vibration 2 3 Unfortunately, this method requires an external power damping is used. In the case of the application of both source, which should supply energy of quite considerable passive and active vibration damping, they are designated amounts. It is a crucial disadvantage of this method. by Ex. 3. For a value of the leader tractive force F , Therefore, active vibration isolators are not used widely in determined by the master control system, the slave control practice. Bearing in mind that the cost reduction of the systems gently adjust the appropriate distribution of the active damping usage, both actuators and the energy supply forces acting simultaneously as tractive and compensative, A A for them will be created by the distributed traction system F and F . Such adjustment makes it possible to signifi- 2 3 with all vehicles (or bogies) motored, i.e., via the distri- cantly decrease close to zero the following longitudinal bution of the traction or braking forces in the MUT. sAðÞ sAðÞ dAðÞ dAðÞ coupler forces: F , F , F , and F . When the 1 2 1 2 To verify the correctness of actions of slave control MUT has all motored vehicles (even when passive vibra- systems enabling the realization of the active vibration tion damping is only employed), the coupler forces are damping in the MUT inter-vehicle connections and to much smaller than in the case labeled as Ex. 1. check their ability to cooperate with the master control level without adverse couplings, ponder once again the 5.2 Active vibration damping in the MUT inter- A A A MUT shown in Fig. 3a. F 6¼ 0, F 6¼ 0, and F 6¼ 0, since 1 2 3 vehicle connections under external disturbances all carriages of this train are self-propelled. For the MUT with all vehicles motored, the slave con- The control systems of the MUT are often subjected to trol systems are based on the feedback compensation. Note unwanted external disturbance signals, for example, sudden that the loop of the negative-feedback slave control system, gusts of wind tending to change LTD conditions, distur- as illustrated in Fig. 8, is closed by the LTD model. Fig- bances that emerge from the time variation of carriages’ ure 8 shows that the block diagrams of the slave control masses, disruptions raised from braking with degraded Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 173 Total drag force Multiplier 10 2.50 2.00 1.50 1.00 0 25 50 75 100 125 150 175 200 225 250 275 -2 0.50 -4 -6 0.00 Time (s) (a) A A A F (Ex. 4) F (Ex. 4) F (Ex. 4) 1 2 3 A A A F (Ex. 5) F (Ex. 5) F (Ex. 5) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -2 -4 -6 Time (s) (b) Fig. 9 Analysis of the slave control systems. a Time course of the variability of external disturbances acting on the second carriage of the MUT; b compensating action of tractive forces during active vibration damping adhesion, and those caused by the time variation of the the 2nd vehicle, R , and the second is in the form of step track curvature, etc. changes in the weight of the 2nd vehicle as illustrated in Let us investigate how the feedback of the active Fig. 9a. vibration damping system of the MUT (model A of Fig. 3a) During computer simulations, both active and passive provides support in mitigating the effect of these distur- vibration damping systems are used. The results of the bances on the overall hierarchical control system response. numerical calculations are shown in Figs. 9, 10 and 11.In For the MUT, the identical desired speed profile, shown in these figures, the outcomes influenced by disturbances in Fig. 6a, is assumed. All MUT carriages are self-propelled the form of the changing force R are marked by Ex. 4. The A A A rest of them, which concern the operation of disturbances (i.e., F 6¼ 0, F 6¼ 0, and F 6¼ 0). The MUT is subjected 1 2 3 caused by the second vehicle weight with a variable value, to two types of external disturbances. The first of them is in are marked as Ex. 5. Figure 9b shows the compensating the form of the variable in time total drag force acting on Rail. Eng. Science (2021) 29(2):163–182 Tractive forces (kN) Total drag force acting on the second vehicle (kN) Multiplier of change in weight for the second vehicle 174 J. Jackiewicz s(A) s(A) s(A) F (Ex. 4, passive) F (Ex. 4, active) F (Ex. 4, passive) 1 1 2 s(A) s(A) s(A) F (Ex. 4, active) F (Ex. 5, passive) F (Ex. 5, active) 2 1 1 s(A) s(A) F (Ex. 5, passive) F (Ex. 5, active) 2 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -5 -15 -25 Time (s) (a) d(A) d(A) d(A) F (Ex. 4, passive) F (Ex. 4, active) F (Ex. 4, passive) 1 1 2 d(A) d(A) d(A) F (Ex. 4, active) F (Ex. 5, passive) F (Ex. 5, active) 2 2 1 d(A) d(A) F (Ex. 5, passive) F (Ex. 5, active) 2 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -5 -10 -15 -20 Time (s) (b) sAðÞ sAðÞ Fig. 10 Response action of the passive and active vibration damping systems: a coupler spring forces F and F vs. time; b coupler 1 2 dAðÞ dAðÞ damping forces F and F vs. time 1 2 A A A disturbances on the MUT with only passive vibration action of tractive forces F , F , and F during active 1 2 3 damping, the coupler forces’ values are significant con- vibration damping. cerning those shown in Fig. 11 (and unnoticed in Fig. 10), For active vibration damping, the feedback action which express the effective response action of the active introduced in slave control systems makes the response of vibration damping systems from Fig. 8. these systems relatively insensitive to external distur- For the MUTs with all self-propelled 10 ? carriages, bances, as shown in Figs. 10 and 11. Figure 10 shows the computer simulations of the action effectiveness for active passive vibration damping system cannot so effectively vibration damping systems have also been carried out. The reduce external disturbances. During the impact of these Rail. Eng. Science (2021) 29(2):163–182 Spring forces (kN) Damping forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 175 s(A) s(A) F (Ex. 4, active) F (Ex. 4, active) 1 2 s(A) s(A) F (Ex. 5, active) F (Ex. 5, active) 1 2 3.0 2.0 1.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -1.0 -2.0 -3.0 Time (s) (a) d(A) d(A) F (Ex. 4, active) F (Ex. 4, active) 1 2 d(A) d(A) F (Ex. 5, active) F (Ex. 5, active) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 Time (s) (b) sAðÞ sAðÞ Fig. 11 Response action of the active vibration damping systems: a coupler spring forces F and F vs. time; b coupler damping forces 1 2 dAðÞ dAðÞ F and F vs. time 1 2 5.3 MUT operating in the push–pull configuration simulation results have shown that the values of the cou- plers forces are included in the following ranges: sAðÞ dAðÞ EMU configurations can include various combinations of 3N\F \3 N and 80 N\F \80 N. It should be i i power carriages. The push–pull MUT (represented by emphasized that the use of systems for active vibration model A of Fig. 3a) has the first and the third (in this case damping allows substantially to eliminate the risk of such the last) motored vehicles. It means that the traction forces events as pitches of rail vehicle bodies and bogies due to A A A are as follows: F 6¼ 0, F ¼ 0, and F 6¼ 0. Figure 12a coupler impact forces. 1 2 3 shows a course of velocity change over time of the MUT Rail. Eng. Science (2021) 29(2):163–182 Spring forces (N) Damping forces (N) 176 J. Jackiewicz c (A) Speed command v Output speed v (Ex. 6) (A) (A) Output speed v (Ex. 7) Output speed v (Ex. 8) 1 1 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -10.0 Time (s) (a) A A A F (Ex. 6) F (Ex. 6) F (Ex. 6) 1 2 3 A A A F (Ex. 7) F (Ex. 7) F (Ex. 7) 1 2 3 A A A F (Ex. 8) F (Ex. 8) F (Ex. 8) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -100 -200 -300 -400 Time (s) (b) Fig. 12 Simulation results based on the LTD for model A of the push–pull MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 6, passive vibration damping is only used) for the following successive stages: the acceleration to the systems based on the feedback compensation have been set velocity of 50 m/s, the cruising at the constant speed, employed to achieve this goal. Note that the loop of the then the deceleration during braking. The simulation results negative-feedback slave control system shown in Fig. 14 is for the push–pull MUT are summarized in Figs. 12 and 13. based on differently defined inputs of reference signal than During these simulations, both active and passive vibration in the case of active vibration damping systems for all damping systems are used. motored carriages of the MUT (as depicted in Fig. 8). It is In Fig. 12 and 13, the outcomes are marked by Ex. 6 caused by that the coupler between the 1st and 2nd car- when the passive vibration damping is only used. An riages is stretched. In turn, the coupler between the 2nd and attempt has been made to reduce the forces in the railway 3rd carriages is compressed. In such a case, only the couplers using active vibration damping. The slave control respective equalization of the absolute values of the com- Rail. Eng. Science (2021) 29(2):163–182 Speed (m/s) Tractive forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 177 s(A) s(A) F (Ex. 6) F (Ex. 6) 1 2 s(A) s(A) F (Ex. 7) F (Ex. 7) 1 2 s(A) s(A) F (Ex. 8) F (Ex. 8) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 -100 -120 Time (s) (a) d(A) d(A) d(A) F (Ex. 6) F (Ex. 6) F (Ex. 7) 1 2 1 d(A) d(A) d(A) F (Ex. 7) F (Ex. 8) F (Ex. 8) 2 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 -100 Time (s) (b) sAðÞ sAðÞ Fig. 13 Simulation results based on the LTD for model A of the push–pull MUT: a coupler spring forces F and F vs. time; b coupler 1 2 dAðÞ dAðÞ damping forces F and F vs. time (in Ex. 6, passive vibration damping is only used) 1 2 pressive and tensile forces is possible. And, this goal has Due to the established limits, the hierarchical control sys- been achieved according to results labeled by Ex. 7 of tem, which consists of two control levels, has reduced the Fig. 13. tractive force, F (produced by the leader drive unit). The However, the values of the forces in the railway cou- ability of MUT to accelerate and decelerate has also plers remain too large. Therefore, for both tractive and decreased. The outcomes labeled by Ex. 8 of such control braking forces, the allowable value set is limited by are illustrated in Figs. 12 and 13. sAðÞ dAðÞ 42:5kNF 42:5kN and 42:5kNF 42:5kN. i i Rail. Eng. Science (2021) 29(2):163–182 Damping forces (kN) Spring forces (kN) 178 J. Jackiewicz Disturbance A . A 3 x , x 3 3 3 s d F, F , F 3rd vehicle d(A) F m s(A) LTDM + SCSs x − x 1 2 + Expression: + ∑ 1/s x − x + ∑ 3 2 − K ·∫(x − x )dτ + I(A) 1 3 ∑ + . . K ·(x − x )+ P(A) 1 3 x − x 1 2 Saturation . ∑ K ·(x − x ) Saturation D(A) 1 3 x − x 3 2 Fig. 14 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the push–pull MUT 5.4 Test simulations for the MUT with Jacobs’ vibration damping method only slightly improves the bogies used as connections between carriages’ evenness of the distribution of forces transmitted by springs bodies and dampers of the bogies’ second suspensions compared to the passive vibration damping method. The active Let us consider a train shown in Fig. 3b (model B), which vibration damping method might be a bit more effective has two standard bogies situated on both its ends, of which during acting external disturbances on the MUT (such, for only the first is with an electrically powered traction motor. instance, as combined excitations or wind gusts). In this The other two Jacobs’ bogies of the train connect the three case, the employed active vibration damping method is B B B carriage bodies. Therefore, F 6¼ 0, F ¼ 0, F ¼ 0, and also based on slave control systems with the feedback 1 2 3 compensation configuration (Figs. 15, 16). F ¼ 0. Train model parameters are also selected based on The loops of the negative-feedback slave control sys- data from [23]. This example is labeled by Ex. 9, kept the tems, shown in Fig. 17, are tailored to vibration damping in same as the simulation scenario of the ride by the MUT the MUT with Jacobs’ bogies used as connections between (see Fig. 12a), for which Figs. 12 and 13 show the sum- carriages’ bodies. This adaptation consists of choosing the mary results of numerical calculations The label Ex. 10 is appropriate reference input signals. The assumption is assigned to such simulations, during which all MUT bogies B B B made that the coordinates, q (see Fig. 17), have zero initial are self-propelled (i.e., F 6¼ 0, F 6¼ 0, F 6¼ 0, and 1 2 3 values. The springs of the second suspensions are non- F 6¼ 0), and simultaneously the method of passive vibra- deformed at the initial time, typically denoted t ¼ 0. This tion damping is solely applied. When besides the passive assumption allows keeping the desired initial distances vibration damping method, the active vibration damping between the bogies with uniform deformation of the method is employed, the simulation outcomes are desig- springs during the simulation ride. nated by the label Ex. 11. It can be noticed that the active Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 179 c (B) Speed command v Output speed v (Ex. 9) 1 1 (B) (B) Speed v (Ex. 10) Output speed v (Ex. 11) 1 1 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -10.0 Time (s) (a) (b) Fig. 15 Simulation results based on the LTD for model B of the MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 9 and 10, passive vibration damping is only used; in Ex. 11 both passive and active vibration damping are used) but, most of all, properties of the distributed traction sys- 6 Conclusions tems themselves. Nevertheless, by applying the original method for coupler force reduction in the MUTs composed The paper examines an original method for coupler force reduction in both distributed and concentrated traction of separate self-propelled carriages with couplers used as connections between carriage bodies, an even better result systems [24]. The results show that the most efficient way for reducing coupler forces is the method based on active is achieved. Namely, the values of dynamic forces carried through railway couplings are closely reduced to zero. vibration damping applied in the distributed traction sys- However, for load-bearing structures of the MUTs sup- tems. The obtained substantial reduction of coupler forces, ported on all motored Jacobs’ bogies, the method of active wherein, is not solely caused by active vibration damping Rail. Eng. Science (2021) 29(2):163–182 Speed (m/s) 180 J. Jackiewicz (a) (b) sBðÞ sBðÞ Fig. 16 Simulation results based on the LTD for model A of the MUT: a secondary suspension spring forces F and F vs. time; 1 2 dBðÞ dBðÞ b secondary suspension damping forces F and F vs. time (in Ex. 9 and 10, passive vibration damping is only used; in Ex. 11 both passive 1 2 and active vibration damping are used) vibration damping is not so very effective. As the traction The innovative two-level control system is applied to and braking forces transmitted by Jacobs’ bogies are only reduce vibration amplitudes of dynamic forces in couplers slightly more evenly distributed. Therefore, their load- of the MUTs. This developed control system consists of the bearing structures can carry only slightly smaller stresses, master control level, which performs like standard cruise which are a little more uniformly distributed in the longi- control, and the secondary control level implemented to tudinal direction. reduce the dynamic vibrations in couplers. Between the Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 181 Disturbance s d Vehicle j F, F , F d(B) d(B) F F j m j j + 1 s(B) s(B) 1 F + 1 q q j + 1 j LTDM + SCSs m Q j + 1 B B F F j + 1 ∑ 1/s Expression: q + K ·(q − q )dτ + I(A) 1 j + + ∑ F K ·(q − q )+ . P(A) 1 j + . . K ·(q − q ) ∑ D(A) 1 j Saturation . Saturation j − (avg) n = #vehicle j − 1 N = #bogies Expression: ∑ 1/s j = 1, ..., N j − (avg) K ·∫(x − q )dτ + I(A) j − 1 j (avg) No x = x (avg) j j K ·∫(x − q )dτ + j < n .. (avg) P(A) j − 1 j (avg) x = x j j x + j − 1 . . Yes (avg) . ∑ Saturation K ·∫(x − q ) D(A) j − 1 j (avg) j − x = 1/2(x + x ) j j j+1 .. . (avg) x = 1/2(x + x ) j j j+1 Fig. 17 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the MUT with Jacobs’ bogies (all MUT bogies are self-propelled) Acknowledgements The author would like to express his gratitude to higher and lower control levels of this system, there are no the editorial committee of Railway Engineering Science for help. I noticeable adverse couplings. would especially like to thank Professor Wanming Zhai (editor-in- The correctness of the new hierarchical control system chief). has been successfully validated for LTD problems of the Open Access This article is licensed under a Creative Commons MUT. This system has a simple structure that can be Attribution 4.0 International License, which permits use, sharing, modified. Besides, this system allows considering combi- adaptation, distribution and reproduction in any medium or format, as nations of diverse traction control models for the MUTs long as you give appropriate credit to the original author(s) and the using computationally efficient numerical methods. These source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this models are essential for the prevention of wheels from article are included in the article’s Creative Commons licence, unless excessive slip (for traction) or sliding (for braking) indicated otherwise in a credit line to the material. If material is not [25, 26]. included in the article’s Creative Commons licence and your intended This system makes it possible to find compromise use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright solutions for control issues, which represent, for instance, holder. To view a copy of this licence, visit http://creativecommons. setting the compromise between the possibility of obtain- org/licenses/by/4.0/. ing simultaneously the low overshoot and the close to zero value of the steady-state error. Most of all, it is also sus- ceptible to modifications, which lead to the much better performance obtained with the adopted additional nonlin- References ear feedforward action or by the possibility of self-tuning implementation [27]. The developed method of active 1. Allenbach JM, Chapas P, Comte M, Kaller R (2008) Electric traction. 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Coupler force reduction method for multiple-unit trains using a new hierarchical control system

Jackiewicz, Jacek
Railway Engineering Science , Volume 29 (2) – Jun 23, 2021
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10.1007/s40534-021-00239-w
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Rail. Eng. Science (2021) 29(2):163–182 https://doi.org/10.1007/s40534-021-00239-w Coupler force reduction method for multiple-unit trains using a new hierarchical control system Jacek Jackiewicz Received: 13 December 2020 / Revised: 27 April 2021 / Accepted: 28 April 2021 / Published online: 23 June 2021 The Author(s) 2021 Abstract During traction and braking of multiple-unit with the longitudinal movement of any train holistically trains, substantial longitudinal dynamic forces might occur and to a certain extent with relative longitudinal motions of in couplers due to the non-optimal distribution of traction train components. Within the LTD, both lateral and vertical and braking forces generated by self-propelled carriages. movements of carriages, or locomotives, can be omitted. These dynamic forces might create shocks affecting the In an overview article, Wu et al. [2] presented the his- reduction of endurance of the weakest train structural com- torical approach to issues of LTD since 1831, when, for the ponents primarily. Thus, the overall operational safety of the first time, Mohawk and Hudson had observed the dynamic train is also lowered. The purpose of the paper is to develop a behavior of ‘slack’ actions, referred to as a series of train new control system to supervise the activities related to the vehicle impacts (during state transitions of connections— longitudinal dynamics of each train carriage in a multiple- from tension to compression—or vice versa). The authors unit train to reduce the longitudinal coupler forces acting [2] focused, mainly, on the issues of longitudinal train during train traction and braking. The hierarchical structure dynamics, which cover the following problems: numerical of the control system consists of two levels. The first master solvers, vehicle connection systems, air brake systems, level of control works like standard cruise control. However, wagon dumper systems, locomotives, resistance forces, the reduction of longitudinal coupler forces is achieved by gravitational components, vehicle in-train instabilities, and applying a second level of slave control systems with a computing schemes. control configuration of feedback compensation. For long heavy-haul trains besides the LTD, some meaningful progress has been accomplished in the carriage Keywords Longitudinal train dynamics  Control system  system dynamics and coupled dynamics of vehicle-track Multiple-unit train  Railway coupler systems. However, there are still some difficulties during the simulation of longitudinal impulse interactions such, as changes in momentum of railway carriages on the elastic track structure [3]. Oprea [4] pointed out that studies on start-up dynamics of railway trains helped to ensure comfort for passengers 1 Introduction and, also, running safety of trains. Ansari et al. [5] comprehensively discussed the influ- The longitudinal train dynamics (LTD) studies motions of ences of stiffness and damping of couplers and load dis- all types of rolling stock vehicles moving in the longitu- tribution pattern on the train longitudinal dynamic dinal track direction [1]. This branch of mechanics deals behaviors. They also determined the optimum placement of the second locomotive to obtain the lowest longitudinal & Jacek Jackiewicz forces. jaceksnd@aim.com In recent years, modeling and simulations as research methods of rail vehicle-track dynamics have been inten- Faculty of Mechatronics, Kazimierz Wielki University in sively developed. Sharma et al. [6] presented an overview Bydgoszcz, Kopernika 1, 85-074 Bydgoszcz, Poland 123 164 J. Jackiewicz of applications of rail vehicle-track dynamic modeling. same speed while maintaining simultaneously fixed inter- They noted that relative motions between two adjacent vals between individual carriages. This solution requires carriages known as ‘slack actions’ had been caused due to the application of a new method for distributed power. The looseness and horizontal displacements in spring and MUTs have no locomotives, and their drive system consists damper connections. According to them, a coupling ‘free of several self-propelled units in a fixed formation, thus slack’ is defined as the free movement allowed by the sum providing that the traction is distributed along the train of clearances in wagon connections. They emphasized that length. The new control system will supervise the dis- these clearances occurred in the auto-coupler knuckles and tributed power to reduce the longitudinal coupler forces. draft gear assembly pins. In railways, not only passive damping systems with non- linear stiffness characteristics are used, especially in the 2 Functionality of advanced railway couplers suspension, but also magnetorheological dampers inte- grated with the secondary vertical suspension system. Different types of couplers have been used to connect Parameters of magnetorheological dampers are dependent adjoining carriages. Most used couplers allow a certain on current, amplitude, and frequency of excitations, as amount of slack to occur between wagons. In the case of described in Refs. [7, 8]. It naturally results in improved heavy-haul trains, the slack presence helps the train start. In ride quality and passenger comfort in comparison to the the heavy-haul train, its lack causes that the locomotive existing passive system. needs to pull the full load of the train at once, and hence the Sharma [9] modeled longitudinal train dynamics of the locomotive may not have sufficient power to start. How- locomotive-hauled passenger train of Rajdhani Express ever, in the high-speed train, the slack presence is unfa- based on experimental results and some data from the lit- vorable. It allows individual vehicles to move erature. He evaluated the performance of the rail vehicle in independently of each other, and thus they can end up its five braking phases. He noticed that the maximum traveling at different speeds to each other. If the speed compressive coupler force of 1.49 MN occurred in the third difference is high enough between individual vehicles, then quarter of the train. the forces acting in the coupler between adjoining carriages The traction and braking actions can cause large longi- may be high enough to break it [12]. tudinal forces in inter-vehicle coupling systems, especially Advanced tight-lock inter-vehicle connections [13] in long and heavy-haul trains. This paper focuses on installed on adjacent vehicles of a high-speed train provide electric multiple units (EMUs) with the distributed power, running stability during acceleration or deceleration. They blended and (or) electronic braking, advanced slip controls, have insignificantly small slackness. The tight-lock railway and permanently coupled carriages, for which LTD prob- connections themself represent coupler systems that consist lems may seem not to be such an essential issue. In prac- of springs and dampers, as shown in Fig. 1, where k and iðÞ 1 tice, things are not quite so effortless because quite large c are stiffness and damping coefficients. Elements of iðÞ 1 longitudinal forces may occur in EMUs by the improper these connection systems are parallel as they should share use of the distributed power control [10]. The EMU across the same absolute values of variables (such as rel- requires no separate locomotive, as electric traction motors ative displacements and velocities). are incorporated within one or a number of its vehicles. Let us notice that it is not easy to determine the non- The asynchrony of EMU vehicles’ traction or braking linear dynamic characteristic of the advanced coupler. As action may lead to large forces due to longitudinal vibra- described in Fig. 2a, this characteristic can often be rep- tions. Such vibrations may ultimately lead to a failure of resented by the three-zone displacement model. Figure 2b the coupler or even superstructure [11]. shows the damping force characteristic of the longitudinal To the best of the author’s knowledge in the field of inter-vehicle damper. This damper reduces longitudinal longitudinal train dynamics, the object of this work is to impacts and also can improve the lateral stability and ride improve a method for reduction of the longitudinal coupler comfort of the train. forces present during the traction and braking of the pas- For advanced inter-vehicle connections, active isolation senger train for outer suburban and long-distance config- of longitudinal vibration is proposed as a target solution. urations. This train should travel at high speeds and However, both characteristics of the semi-permanent tight- accelerate/brake quickly to increase average travel veloci- lock coupler and longitudinal inter-vehicle damper are ties and lower door-to-door trip time. nonlinear. Moreover, if the system is highly nonlinear over Depending on operator needs, there are several ways to the full range of operation, its adaptive schemes associated reduce the maximum of coupler forces. The most preferred with the control algorithm may show severe limitations. hi solution is a simple solution based on the assumption that Therefore, stroke limitations defined by x ; x for s s 1ðÞ i 1ðÞ i all vehicles of a multiple-unit train (MUT) move at the Rail. Eng. Science (2021) 29(2):163–182 c /3 i 1 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 165 tight-lock couplers are adopted, as well as velocity-jump hi constraints set by x_ ; x_ for longitudinal inter-ve- d d 1ðÞ i 1ðÞ i hicle dampers. Thus, due to automatic control, the coupler forces will have values within the range of their linear characteristics. In consequence, the coupler forces of this advanced connection system will not exceed the estab- lished admissible values. Structural failure of railway couplers may cause acci- dents and even lead to catastrophic damages. Therefore, it is critical to ensure that the couplers are in healthy struc- tural condition. The measurement of coupler-force values can be performed within the structural health monitoring (SHM) system for railway couplers [14]. This system Fig. 1 Adjacent vehicles of a high-speed train joined via the consists of, among others, accelerometers, which determine advanced inter-vehicle connection coupler movements, and digital strain sensors, which measure deformation strains on coupler bodies. vehicle. Similarly, model B consists of three vehicles with masses of m and four bogies. m (k ¼ 1; 2; 3; 4) are i k masses of Jacob bogies and q are their coordinates. 3 Modeling of longitudinal dynamics of multiple- Although various external loads act on each train car- unit trains riage, only these loads, related solely to the longitudinal direction, are significant to model the LTD, as assumed A system of differential equations can describe the longi- here. When the train moves on along a straight line, the tudinal dynamic behavior of the MUT. Assuming that there rolling resistance forces are independent of the train speed. is no vertical or lateral movement of each train vehicle, the They act on each carriage and occur as the results of wheel- MUT model has a much simpler structure. rail friction and friction in bearings. These forces, however, The EMUs can be divided into two broad categories are functions of various types of frictional resistance. [15]. The EMUs of the first category consist of independent Furthermore, for further analysis, certain forms of velocity- vehicles, each of which rests on two bogies (see model A of dependent rolling resistance forces are negligibly small Fig. 3). Such EMU vehicles, which do not share bogies, except for those forces, which may occur due to track can be longer. However, they need more bogies and must deflection. Without any cross-wind effect and in the open- be equipped with additional anti-overlap systems between air conditions, the total drag on the traveling train is usually the two adjacent vehicles to reduce the consequences of a calculated by the use of the following Davis’ formula railway accident. Each of the two adjacent vehicles of the [16, 17]: second category EMUs shares at least one the same bogie (see model B of Fig. 3). The advantage of this category is F ¼ a þ bv þ cv ; ð1Þ that the EMU has a reduced number of bogies in the train. where F is the train resistance (i.e., the total drag); a, b, Besides, shared boogies assure reduction of their lateral and c are constants, which depend upon the type of train; oscillations, less rolling, and pitching at high speeds. On and v is the train speed. Note that bearing and contact the other hand, it is necessary to use shorter vehicle bodies frictions vary with the weight of the train and the number to meet the limit requirements concerning the smallest of axles. The second term of this equation is proportional to permissible radii of railway track curves. train speed. This term expresses increased rolling The LTD model of MUT is necessary to design control resistance at high speed despite that it also includes some algorithms. This model allows testing different control components of laminar airflow. The last corresponds in size strategies without the need to use a physically available to speed-squared and expresses the aerodynamic drag. As EMU. indicated in [18], the aerodynamic drag of MUT consists of As shown in Fig. 3, x (i ¼ 1; 2; 3) describe the position separate drag forces with a different value for each of vehicle centers. Model A consists of three vehicles with carriage. Equation (1), therefore, has been converted to masses of m connected by stiffness and damping couplers. the form, which estimates the total drag force, R , acting A A Note that k and c (j ¼ 1; 2) are the stiffness and jðÞ 1 jðÞ 1 only on the ith carriage of the train: damping coefficients, respectively. F are the tractive R ¼ A þ B v þ C v ; ð2Þ A i i i i forces. R are the forces, which resist the motion of each Rail. Eng. Science (2021) 29(2):163–182 2c /3 i 1 Left inter-vehicle damper Right inter-vehicle damper Vehicle i Vehicle i+1 Semi-permanent tight-lock coupler 2k i 1 c /3 i 1 166 J. Jackiewicz The master level of the control system is an innovative closed-loop negative feedback control system. This control system has an unconventional solution through the appli- cation of the arrangement of two parallel-connected PID controllers. These controllers have the possibility of weighing their output signals, as demonstrated in Fig. 4a. As in the past, PID controllers are readily used in control applications due to their universality and simple structure [16, 17]. They are used not only in low-order systems but even in high-order systems owing to their advantageous properties. One of the disadvantages of these standardized controllers is that they, in some cases, cannot place all the poles as desired when controlling higher-order plant models. To deal with this problem, Persson and Astro¨m introduced the dominant pole placement method, refer to [18]. For a structurally complex system, system delay is usually variable during the control process. Therefore, the hierarchical control system is structured as least compli- cated as possible element arrangement. The second PID controller with time-delay compensation is wherefore applied and, thus, reduces the time-delay effect in the closed control system with negative feedback. Besides, separate tuning rules for both PID controllers provide smooth control action when switching signals between their different working points. There is also a possibility of Fig. 2 Characteristics of inter-vehicle connection components: a shows a relationship between spring force and displacement of an online adaptation of the multipliers for their output- the semi-permanent tight-lock coupler, whereas b demonstrates a weighting. Due to this adaptation, the closed-loop response damping force characteristic of the longitudinal inter-vehicle damper error disappears more rapidly than in the case of using only (in both cases, the sub-index i stands for the sequence number of the one single PID controller [19]. advanced inter-vehicle connection) The controller output signal is the tractive force F , def def where A ¼ðÞ a þ b g W and B ¼ c W , in which W driving the first bogie of MUT. The motor starting current i i i i i i i i i (i ¼ 1; 2; ...; p) is the weight of the ith carriage and p and the wheel-rail adhesions during the startup process limit the maximum value for F . Because any one of the denotes the number of train carriages, a is the rolling i 1 resistance coefficient assigned to the ith carriage, b is its processing signals cannot exceed its allowable physical limits, the saturation effects are taken into account in the bearing resistance coefficient, c is its flange resistance (in the case of a curved track), and g denotes the axles’ master control system. As depicted in Fig. 4a, through the saturation function, the limiters of F are F . It is worth number counted for the ith carriage; C is the aerodynamic i 1 max resistance coefficient of the ith carriage. The sample noting that slave negative feedback controllers establish other tractive forces. The saturation thresholds also apply coefficient values of Davis’s constants for some trains are given in Ref. [1]. to braking forces. Thus, it is possible to model the power transmission system without going into more details, how one, a few, or all of the electric motors of MUT can create 4 Design of master control system to supervise torques applied to the wheels. To include the process effects of the digital controller MUT activities related to the LTD delay and the analog-to-digital (A/D) conversion, and the digital-to-analog (D/A) conversion, standard block dia- The two-level control system for multiple-unit electric trains has a slightly complex structure. It consists of a grams for the continuous-time control systems need to be modified [20]. The master controller block diagram for master control level, which works similar to standard cruise control, and a lower control level, which compose of speed regulation, shown in Fig. 4, consists of blocks of associated together slave negative feedback controllers for continuous-time transfer functions. At the second input to process variables to decrease the longitudinal coupler for- the master controller, the continuous-time transfer function ces in the MUTs. denoted as A/D mimics the operation of the A/D converter. In the case under consideration, it is the second-order Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 167 A A A A A F R F x R x R F x 3 1 1 1 2 2 2 3 3 (a) A A A A c c m 1(1) m 2(1) m 1 2 A A k k 1(1) 2(1) B B x R x R R x 2 3 (b) 1 1 2 3 1(1) B B B B B B B m B B m m 1 c 3 c c c c c 2 c 8(1) 2(1) 3(1) 4(1) 6(1) 7(1) 5(1) B B B B B B B k k k k k 6(1) k k 4(1) k 7(1) 8(1) 2(1) 3(1) 5(1) 1(1) q q q 1 2 3 4 B Q B Q B B Q Q F m F m F F m m 1 1 2 2 3 4 3 4 Fig. 3 LTD models of MUTs: a model A; b model B Butterworth filter, which is an analog low pass filter to Even for linear plants, however, with actuator satura- prevent aliasing. The term, 1=T, is the filter cut off fre- tion, if, during the control design, the constraints on the quency. The cut off frequency has to be below one-half of actuator input are not accounted for, the results can the sampling frequency. The replacement block for the D/A sometimes give undesired effects [21]. A saturation link is converter in the form of a continuous-time transfer function often placed in the front of the PID controller integration emulates the conversion of the controller digital output branch to prevent windup. When the plant model represents signal back to an analog signal and performs a zero-order a double integration processing, the saturation link is also hold function. In Fig. 4a, the labeled ‘Delay’ block mimics placed in the PID controller proportional branch. the delay effects caused by the parallel system of two A modified PID controller with back-calculation and digital PID controllers. This block has the continuous-time clamping, as well as a tracking mode, represents another transfer function with the constant parameter, k. The value built-in anti-windup method. This controller is used to of k is the transfer function order for the parallel system of prevent integration windup in the PID controller [22]. two digital PID controllers. This value is established in A technique related to the anti-windup methods is the mathematical terms of the Z-transform. The block diagram so-called bumpless transfer method [21]. In the bumpless of Fig. 4a is the starting point for building the master transfer method, a supervising system supervises multiple discrete controller for speed regulation. The PID continu- controllers designed for the same linearized control system ous-time transfer functions of this master controller can be and switches among them. Inputs of three controllers, C , easily converted to discrete-time transfer functions (Z- C , and C , are connected to the same output of the feed- 2 3 transform transfer function). back summing point, as illustrated in Fig. 4b. These con- The developed method of active vibration reduction in trollers are hot (i.e., all the time, they process the error). the railway couplers is to be a compromise solution Switching between the controllers’ outputs occurs when the between its implementation costs and its operational per- error magnitude achieves a specified threshold value, with formance. An additional task for the two-level automatic some hysteresis to avoid frequent switching back and forth. control system is to keep force values of every railway Besides, to reduce the windup and improve the transient coupler element within the linearized range limited by its response, the master controller can be built upon nonlinear thresholds. If the full range of non-linear characteristics of dynamic compensators (C and C ) with two parallel chan- 1 2 any railway connection is needed, the active vibration nels [22], as shown in Fig. 4c. Nonlinear nondynamic isolation system will be turned off, leaving only passive links are placed here in both channels. The first channel damping in operation. The assumption adopted in this way starts with a saturation link with a unity threshold (when enables a significant simplification of the structure of the the signal amplitude is less than 1), and the second, with a control system. unity dead-zone (when the signal amplitude is higher than 1). Rail. Eng. Science (2021) 29(2):163–182 168 J. Jackiewicz The first version of the master controller, shown in this block is to encapsulate nested block diagrams for LTD Fig. 4a, was selected for further considerations due to its equations and slave control systems. least complex structure and satisfactory results obtained The design of robust control systems involves choosing during the LTD computer simulations. the controller structure and then adjusting the controller The master speed control system of the MUT to super- setting parameters to achieve acceptable performance in vise the activities related to the LTD is represented by a the presence of uncertainty. The controller structure should block diagram shown in Fig. 5. This negative feedback provide that the control system response can meet founded control system allows to maintain a prescribed relationship performance criteria. The first objective of the designing c c _ _ _ of x to x , where x represents the desired speed of the first control system is that this system output should very 1 1 MUT vehicle called the ‘leader’ in the distribute power accurately track the input desired speed, x_ . The second operation, and x_ is the measured (i.e., actual) speed of this objective is maintaining the internal forces in the advanced s d vehicle. The return signal x_ goes into the summing point inter-vehicle connections, F and F , within the given from the feedback path. In the summing point, the differ- range of permissible values. Note that F is the vector of ence between x_ and x_ becomes the error speed. reduced spring forces in semi-permanent tight-lock cou- The master controller for speed regulation amplifies this plers (or secondary suspensions), for which k are equiva- error and produces the output signal transmitted to an lent stiffnesses. F is the vector of reduced damping forces actuator. In the considering case, the actuator is to be the in advanced inter-vehicle connections (or secondary sus- traction motor of the first vehicle. When the traction motor pensions) with equivalent damping coefficients c . Another powered by electrical energy receives a control signal, it crucial goal of the control system design is minimizing the responds by converting its driving torque into the wheel effect of disturbances on system output signals. tractive force F . The MUT has no locomotives, but power To explain why there are no adverse couplings between is distributed along this train by multiple traction motors. the master control system and slave control systems of this Slave control systems control the distribution of tractive hierarchical control structure, let us consider the operation forces, F , driving other vehicles. The distribution of F i i of simplified forms of both these control levels. Albeit not depends on F . 1 only frequency-domain but also time-domain performance The block diagram of Fig. 5 has the subsystem block measures can describe the closed-loop feedback control labeled ‘LTD model ? Slave control systems.’ The role of system performances, the description in frequency-domain terms will merely be considered. (a) + Continuous ∑ PID 0.5 fix delay 2nd PID controller Gain ∑ Out 1 In 1 ∑ PID 0.5 In 2 1st PID controller Gain (b) (c) 1 C −1 In 1 + + In 1 ∑ ∑ Out 1 Out 1 ∑ C In 2 − In 2 − + −1 1 Command 1st Input Delay D/A In 1 Output A/D F max 1/ kg T 2/T Out 1 2 s + 1/ kg T s + 2/T −F 1/T max In 2 0.707 0.707 Saturation function 2 2 s + + 2nd Input T T with limits of -F and max F for F max 1 Fig. 4 Block diagram of the master controller for speed regulation built upon a parallel arrangement of two PID controllers, b bumpless transfer method, and c two nonlinear dynamic compensators connected in parallel Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 169 The objective of any one of the negative-feedback Disturbance controllers, which are represented by, widely used in the industry, PID controllers, is to respond to the error. How- s d F, F , F ever, the purpose of compensators, such as the lead, lag, Reference input 1st Input and lag-lead compensators, is to change the original c 2nd Input Desired speed, x dynamics of the plant. In the considering case, an appro- MCSR priate master-compensator should be interconnected with Master controller for speed regulation the LTD model to form the master nonlinear control-affine LTDM + SCSs system to control the speed x . LTD model + slave control systems The closed-loop master control system is based on the series compensation. For this compensation type, the con- Fig. 5 Block diagram of the master control system to supervise MUT troller, , is inserted into the forward path in series activities related to the LTD with the controlled system, , which describes the LTD model with slave control systems. Both and controller in the form of an adjusting gain parameter ,is are state-dependent transfer functions of the com- placed in the feedback path. Therefore, such a control plex variable s, and the state vector . To guarantee the configuration is referred to as feedback compensation. The stable closed-loop control system, the design of the master controlled system only consists of the LTD model. controller is based on a pole-placement algorithm. is the state-dependent transfer function inserted As shown in Fig. 5, the input signal to the block labeled without anything else into the forward path (i.e., between ‘LTDM ? SCSs’ is the tractive force F . The actual output the summing point and the take-off point). The input to the x_ is feedback, compared with the reference input x_ (i.e., slave-system transfer function is the tractive force F . The 1 1 the velocity command). The error, e ¼ x_  x_ ,atthe transfer function of the closed-loop system is given by summing point output is passed into the compensator, . The primary task of such a type of master control ð4Þ system is to keep the control variable x_ to the desired value x , despite external disturbances d in some frequency range. Since the master-system (state-dependent) transfer function of the closed-loop system is the following form: In this case, the output signal (i.e., one of the three process control variables, e.g., Dx ) tracks the setpoint equal to zero in the frequency range when . ð3Þ The primary task of the slave control system is to control the tractive force of the ith drive unit, F , in correlation to the tractive force of the ‘leader’ drive unit, F . the output signal x_ tracks the input signal x_ accurately (i.e., x_ ’ x_ ) in the frequency range when 5 Typical applications of train dynamics models and, therefore, is close to 1. together with the slave control structure However, the master control system does not perform selection to reduce coupler forces in the MUTs directly and alone tasks of active vibration damping, con- cerning the maintenance of zero values for the following EMU configurations can include various combinations of process control variables: power carriages. The power carriages with motored bogies, • Dx —the distance change between both ends of the like electric locomotives, are self-propelled and not used as selected inter-vehicle connection, which connects two passenger carriages in a locomotive-hauled train. Usually carriages, used connections between carriage bodies of MUT are • Dx_ —the difference of velocities of both ends of the couplers (i.e., mechanisms used to connect rolling stock in considering railway connection, a train) or Jacobs’ bogies. • Dx ds—the integral over time (s) of the distance j The posed task is to design a new hierarchical control change between both ends of this connection. system to bring the MUT smoothly up to speed 50 m/s, followed by braking to 0 m/s, utilizing an electric or hybrid The design of slave control systems enabling the real- traction system with the possibility of energy recovery. The ization of the active vibration damping in the MUT inter- command signal for the MUT speed is broken down into vehicle connections is different from the master speed- the following stages: (i) start-up (the MUT speed varies control system design. In each slave control system, a slave Rail. Eng. Science (2021) 29(2):163–182 170 J. Jackiewicz continuously from standstill to the cruising speed), (ii) Numerical simulations carried out with the help of cruising (the MUT speed is maintained constant at the Scilab/Xcos toolbox for modeling and simulation of cruising value), (iii) braking (the MUT speed is reduced dynamic (continuous and discrete) systems mimic opera- from cruising to a standstill), and (iv) stop (the MUT speed tions of the master control system of the MUT to supervise is zero). The performance task requires establishing a the activities related to the LTD. method of MUT tractive effort control and then selecting the controller characteristics. The software package of 5.1 Test simulations for the MUT with couplers Scilab, called Xcos, provides functionalities to determine used as connections between carriage bodies control strategies for both open and closed control systems with negative feedback. Let us consider a train consisting of one electric locomotive and two individual passenger wagons, as shown in Fig. 3a (a) A A A F (Ex.1) F (Ex.1) F (Ex.1) 1 2 3 A A A F (Ex.2) F (Ex.2) F (Ex.2) 1 2 3 A A A F (Ex.3) F (Ex.3) F (Ex.3) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -100 -200 -300 -400 Time (s) (b) Fig. 6 Numerical results based on the LTD for model A of the MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 1 and 2, passive vibration damping is only used; in Ex. 3 both passive and active vibration damping are used) Rail. Eng. Science (2021) 29(2):163–182 Tractive forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 171 s(A) s(A) F (Ex. 1) F (Ex. 1) 1 2 s(A) s(A) F (Ex. 2) F (Ex. 2) 1 2 s(A) s(A) F (Ex. 3) F (Ex. 3) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -50 -100 -150 -200 -250 Time (s) (a) d(A) d(A) d(A) F (Ex. 1) F (Ex. 1) F (Ex. 2) 1 2 1 d(A) d(A) d(A) F (Ex. 2) F (Ex. 3) F (Ex. 3) 2 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -50 -100 -150 Time (s) (b) sAðÞ sAðÞ Fig. 7 Numerical results based on the LTD for model A of the MUT: a coupler spring forces F and F vs. time; b coupler damping forces 1 2 dAðÞ dAðÞ F and F vs. time (in Ex. 1 and 2, passive vibration damping is only used; in Ex. 3 both passive and active vibration damping are used) 1 2 (i.e., model A), with the following assumptions made: x_ , are also correlated. Both connections consist of the A A A parallel connection systems of the spring connectors with F 6¼ 0, F ¼ 0, and F ¼ 0. Train model parameters are 1 2 3 the viscous dampers. They are placed between the 1st and selected based on data from [23]. Note that in Figs. 6 and 7, 2nd carriages as well as between the 2nd and 3rd carriages. the results of computer simulations for this example are The use of viscous dampers with the following damping labeled by Ex. 1. Figure 6a shows train acceleration to the A A line speed of 50 m/s at full power, motoring at the line coefficients, b and b , provides passive damping of lon- 1 2 speed, and then train braking at standard service rate. gitudinal vibrations. The passive vibration damping Figure 6b illustrates the dependence on the time of the method based on energy dissipation can be very efficient in tractive forces F . Time courses of changes of the train damping out high-frequency excitations. However, passive damping of dynamic forces in train couplers can be speed x_ and any one of the tractive forces F correspond insufficient in the case of an uncorrelated traction distri- to each other. bution in the MUT, especially in the range of low-fre- Figure 7 shows variations of coupler forces in both quency vibrations. The active damping method ensures advanced inter-vehicle connections. Changes in the coupler sAðÞ dAðÞ more effective damping of low-frequency vibrations. forces, F and F ðÞ i ¼ 1; 2 , as well as the train speed i i Rail. Eng. Science (2021) 29(2):163–182 Spring forces (kN) Damping forces (kN) 172 J. Jackiewicz Disturbance A . F R x , x i i i s d F, F , F Vehicle i d(A) A d(A) i − 1 m F i i s(A) s(A) i − 1 i LTDM + SCSs 1 + Expression: ∑ 1/s i − K ·∫(x − x )dτ + I(A) 1 i K ·(x − x )+ P(A) 1 i 1 + . . Saturation K ·(x − x ) . D(A) 1 i Saturation i − Fig. 8 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the MUT inter- vehicle connections (all MUT carriages are self-propelled) However, this method requires the application of additional systems are nested in the block diagram of the master actuators. The actuators generate second forces or con- control system, which is depicted in Fig. 5. trolled displacements to compensate for the effects of The computer simulations’ results are labeled by Ex. 2, response on the action of external forces or kinematic when all MUT carriages are self-propelled (i.e., F 6¼ 0, A A excitations directly acting on components of the MUT. F 6¼ 0, and F 6¼ 0), and the only passive vibration 2 3 Unfortunately, this method requires an external power damping is used. In the case of the application of both source, which should supply energy of quite considerable passive and active vibration damping, they are designated amounts. It is a crucial disadvantage of this method. by Ex. 3. For a value of the leader tractive force F , Therefore, active vibration isolators are not used widely in determined by the master control system, the slave control practice. Bearing in mind that the cost reduction of the systems gently adjust the appropriate distribution of the active damping usage, both actuators and the energy supply forces acting simultaneously as tractive and compensative, A A for them will be created by the distributed traction system F and F . Such adjustment makes it possible to signifi- 2 3 with all vehicles (or bogies) motored, i.e., via the distri- cantly decrease close to zero the following longitudinal bution of the traction or braking forces in the MUT. sAðÞ sAðÞ dAðÞ dAðÞ coupler forces: F , F , F , and F . When the 1 2 1 2 To verify the correctness of actions of slave control MUT has all motored vehicles (even when passive vibra- systems enabling the realization of the active vibration tion damping is only employed), the coupler forces are damping in the MUT inter-vehicle connections and to much smaller than in the case labeled as Ex. 1. check their ability to cooperate with the master control level without adverse couplings, ponder once again the 5.2 Active vibration damping in the MUT inter- A A A MUT shown in Fig. 3a. F 6¼ 0, F 6¼ 0, and F 6¼ 0, since 1 2 3 vehicle connections under external disturbances all carriages of this train are self-propelled. For the MUT with all vehicles motored, the slave con- The control systems of the MUT are often subjected to trol systems are based on the feedback compensation. Note unwanted external disturbance signals, for example, sudden that the loop of the negative-feedback slave control system, gusts of wind tending to change LTD conditions, distur- as illustrated in Fig. 8, is closed by the LTD model. Fig- bances that emerge from the time variation of carriages’ ure 8 shows that the block diagrams of the slave control masses, disruptions raised from braking with degraded Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 173 Total drag force Multiplier 10 2.50 2.00 1.50 1.00 0 25 50 75 100 125 150 175 200 225 250 275 -2 0.50 -4 -6 0.00 Time (s) (a) A A A F (Ex. 4) F (Ex. 4) F (Ex. 4) 1 2 3 A A A F (Ex. 5) F (Ex. 5) F (Ex. 5) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -2 -4 -6 Time (s) (b) Fig. 9 Analysis of the slave control systems. a Time course of the variability of external disturbances acting on the second carriage of the MUT; b compensating action of tractive forces during active vibration damping adhesion, and those caused by the time variation of the the 2nd vehicle, R , and the second is in the form of step track curvature, etc. changes in the weight of the 2nd vehicle as illustrated in Let us investigate how the feedback of the active Fig. 9a. vibration damping system of the MUT (model A of Fig. 3a) During computer simulations, both active and passive provides support in mitigating the effect of these distur- vibration damping systems are used. The results of the bances on the overall hierarchical control system response. numerical calculations are shown in Figs. 9, 10 and 11.In For the MUT, the identical desired speed profile, shown in these figures, the outcomes influenced by disturbances in Fig. 6a, is assumed. All MUT carriages are self-propelled the form of the changing force R are marked by Ex. 4. The A A A rest of them, which concern the operation of disturbances (i.e., F 6¼ 0, F 6¼ 0, and F 6¼ 0). The MUT is subjected 1 2 3 caused by the second vehicle weight with a variable value, to two types of external disturbances. The first of them is in are marked as Ex. 5. Figure 9b shows the compensating the form of the variable in time total drag force acting on Rail. Eng. Science (2021) 29(2):163–182 Tractive forces (kN) Total drag force acting on the second vehicle (kN) Multiplier of change in weight for the second vehicle 174 J. Jackiewicz s(A) s(A) s(A) F (Ex. 4, passive) F (Ex. 4, active) F (Ex. 4, passive) 1 1 2 s(A) s(A) s(A) F (Ex. 4, active) F (Ex. 5, passive) F (Ex. 5, active) 2 1 1 s(A) s(A) F (Ex. 5, passive) F (Ex. 5, active) 2 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -5 -15 -25 Time (s) (a) d(A) d(A) d(A) F (Ex. 4, passive) F (Ex. 4, active) F (Ex. 4, passive) 1 1 2 d(A) d(A) d(A) F (Ex. 4, active) F (Ex. 5, passive) F (Ex. 5, active) 2 2 1 d(A) d(A) F (Ex. 5, passive) F (Ex. 5, active) 2 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -5 -10 -15 -20 Time (s) (b) sAðÞ sAðÞ Fig. 10 Response action of the passive and active vibration damping systems: a coupler spring forces F and F vs. time; b coupler 1 2 dAðÞ dAðÞ damping forces F and F vs. time 1 2 A A A disturbances on the MUT with only passive vibration action of tractive forces F , F , and F during active 1 2 3 damping, the coupler forces’ values are significant con- vibration damping. cerning those shown in Fig. 11 (and unnoticed in Fig. 10), For active vibration damping, the feedback action which express the effective response action of the active introduced in slave control systems makes the response of vibration damping systems from Fig. 8. these systems relatively insensitive to external distur- For the MUTs with all self-propelled 10 ? carriages, bances, as shown in Figs. 10 and 11. Figure 10 shows the computer simulations of the action effectiveness for active passive vibration damping system cannot so effectively vibration damping systems have also been carried out. The reduce external disturbances. During the impact of these Rail. Eng. Science (2021) 29(2):163–182 Spring forces (kN) Damping forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 175 s(A) s(A) F (Ex. 4, active) F (Ex. 4, active) 1 2 s(A) s(A) F (Ex. 5, active) F (Ex. 5, active) 1 2 3.0 2.0 1.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -1.0 -2.0 -3.0 Time (s) (a) d(A) d(A) F (Ex. 4, active) F (Ex. 4, active) 1 2 d(A) d(A) F (Ex. 5, active) F (Ex. 5, active) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 Time (s) (b) sAðÞ sAðÞ Fig. 11 Response action of the active vibration damping systems: a coupler spring forces F and F vs. time; b coupler damping forces 1 2 dAðÞ dAðÞ F and F vs. time 1 2 5.3 MUT operating in the push–pull configuration simulation results have shown that the values of the cou- plers forces are included in the following ranges: sAðÞ dAðÞ EMU configurations can include various combinations of 3N\F \3 N and 80 N\F \80 N. It should be i i power carriages. The push–pull MUT (represented by emphasized that the use of systems for active vibration model A of Fig. 3a) has the first and the third (in this case damping allows substantially to eliminate the risk of such the last) motored vehicles. It means that the traction forces events as pitches of rail vehicle bodies and bogies due to A A A are as follows: F 6¼ 0, F ¼ 0, and F 6¼ 0. Figure 12a coupler impact forces. 1 2 3 shows a course of velocity change over time of the MUT Rail. Eng. Science (2021) 29(2):163–182 Spring forces (N) Damping forces (N) 176 J. Jackiewicz c (A) Speed command v Output speed v (Ex. 6) (A) (A) Output speed v (Ex. 7) Output speed v (Ex. 8) 1 1 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -10.0 Time (s) (a) A A A F (Ex. 6) F (Ex. 6) F (Ex. 6) 1 2 3 A A A F (Ex. 7) F (Ex. 7) F (Ex. 7) 1 2 3 A A A F (Ex. 8) F (Ex. 8) F (Ex. 8) 1 2 3 0 25 50 75 100 125 150 175 200 225 250 275 300 -100 -200 -300 -400 Time (s) (b) Fig. 12 Simulation results based on the LTD for model A of the push–pull MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 6, passive vibration damping is only used) for the following successive stages: the acceleration to the systems based on the feedback compensation have been set velocity of 50 m/s, the cruising at the constant speed, employed to achieve this goal. Note that the loop of the then the deceleration during braking. The simulation results negative-feedback slave control system shown in Fig. 14 is for the push–pull MUT are summarized in Figs. 12 and 13. based on differently defined inputs of reference signal than During these simulations, both active and passive vibration in the case of active vibration damping systems for all damping systems are used. motored carriages of the MUT (as depicted in Fig. 8). It is In Fig. 12 and 13, the outcomes are marked by Ex. 6 caused by that the coupler between the 1st and 2nd car- when the passive vibration damping is only used. An riages is stretched. In turn, the coupler between the 2nd and attempt has been made to reduce the forces in the railway 3rd carriages is compressed. In such a case, only the couplers using active vibration damping. The slave control respective equalization of the absolute values of the com- Rail. Eng. Science (2021) 29(2):163–182 Speed (m/s) Tractive forces (kN) Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 177 s(A) s(A) F (Ex. 6) F (Ex. 6) 1 2 s(A) s(A) F (Ex. 7) F (Ex. 7) 1 2 s(A) s(A) F (Ex. 8) F (Ex. 8) 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 -100 -120 Time (s) (a) d(A) d(A) d(A) F (Ex. 6) F (Ex. 6) F (Ex. 7) 1 2 1 d(A) d(A) d(A) F (Ex. 7) F (Ex. 8) F (Ex. 8) 2 1 2 0 25 50 75 100 125 150 175 200 225 250 275 300 -20 -40 -60 -80 -100 Time (s) (b) sAðÞ sAðÞ Fig. 13 Simulation results based on the LTD for model A of the push–pull MUT: a coupler spring forces F and F vs. time; b coupler 1 2 dAðÞ dAðÞ damping forces F and F vs. time (in Ex. 6, passive vibration damping is only used) 1 2 pressive and tensile forces is possible. And, this goal has Due to the established limits, the hierarchical control sys- been achieved according to results labeled by Ex. 7 of tem, which consists of two control levels, has reduced the Fig. 13. tractive force, F (produced by the leader drive unit). The However, the values of the forces in the railway cou- ability of MUT to accelerate and decelerate has also plers remain too large. Therefore, for both tractive and decreased. The outcomes labeled by Ex. 8 of such control braking forces, the allowable value set is limited by are illustrated in Figs. 12 and 13. sAðÞ dAðÞ 42:5kNF 42:5kN and 42:5kNF 42:5kN. i i Rail. Eng. Science (2021) 29(2):163–182 Damping forces (kN) Spring forces (kN) 178 J. Jackiewicz Disturbance A . A 3 x , x 3 3 3 s d F, F , F 3rd vehicle d(A) F m s(A) LTDM + SCSs x − x 1 2 + Expression: + ∑ 1/s x − x + ∑ 3 2 − K ·∫(x − x )dτ + I(A) 1 3 ∑ + . . K ·(x − x )+ P(A) 1 3 x − x 1 2 Saturation . ∑ K ·(x − x ) Saturation D(A) 1 3 x − x 3 2 Fig. 14 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the push–pull MUT 5.4 Test simulations for the MUT with Jacobs’ vibration damping method only slightly improves the bogies used as connections between carriages’ evenness of the distribution of forces transmitted by springs bodies and dampers of the bogies’ second suspensions compared to the passive vibration damping method. The active Let us consider a train shown in Fig. 3b (model B), which vibration damping method might be a bit more effective has two standard bogies situated on both its ends, of which during acting external disturbances on the MUT (such, for only the first is with an electrically powered traction motor. instance, as combined excitations or wind gusts). In this The other two Jacobs’ bogies of the train connect the three case, the employed active vibration damping method is B B B carriage bodies. Therefore, F 6¼ 0, F ¼ 0, F ¼ 0, and also based on slave control systems with the feedback 1 2 3 compensation configuration (Figs. 15, 16). F ¼ 0. Train model parameters are also selected based on The loops of the negative-feedback slave control sys- data from [23]. This example is labeled by Ex. 9, kept the tems, shown in Fig. 17, are tailored to vibration damping in same as the simulation scenario of the ride by the MUT the MUT with Jacobs’ bogies used as connections between (see Fig. 12a), for which Figs. 12 and 13 show the sum- carriages’ bodies. This adaptation consists of choosing the mary results of numerical calculations The label Ex. 10 is appropriate reference input signals. The assumption is assigned to such simulations, during which all MUT bogies B B B made that the coordinates, q (see Fig. 17), have zero initial are self-propelled (i.e., F 6¼ 0, F 6¼ 0, F 6¼ 0, and 1 2 3 values. The springs of the second suspensions are non- F 6¼ 0), and simultaneously the method of passive vibra- deformed at the initial time, typically denoted t ¼ 0. This tion damping is solely applied. When besides the passive assumption allows keeping the desired initial distances vibration damping method, the active vibration damping between the bogies with uniform deformation of the method is employed, the simulation outcomes are desig- springs during the simulation ride. nated by the label Ex. 11. It can be noticed that the active Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 179 c (B) Speed command v Output speed v (Ex. 9) 1 1 (B) (B) Speed v (Ex. 10) Output speed v (Ex. 11) 1 1 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0 25 50 75 100 125 150 175 200 225 250 275 300 -10.0 Time (s) (a) (b) Fig. 15 Simulation results based on the LTD for model B of the MUT: a train speed x_ vs. time; b tractive forces F vs. time (in Ex. 9 and 10, passive vibration damping is only used; in Ex. 11 both passive and active vibration damping are used) but, most of all, properties of the distributed traction sys- 6 Conclusions tems themselves. Nevertheless, by applying the original method for coupler force reduction in the MUTs composed The paper examines an original method for coupler force reduction in both distributed and concentrated traction of separate self-propelled carriages with couplers used as connections between carriage bodies, an even better result systems [24]. The results show that the most efficient way for reducing coupler forces is the method based on active is achieved. Namely, the values of dynamic forces carried through railway couplings are closely reduced to zero. vibration damping applied in the distributed traction sys- However, for load-bearing structures of the MUTs sup- tems. The obtained substantial reduction of coupler forces, ported on all motored Jacobs’ bogies, the method of active wherein, is not solely caused by active vibration damping Rail. Eng. Science (2021) 29(2):163–182 Speed (m/s) 180 J. Jackiewicz (a) (b) sBðÞ sBðÞ Fig. 16 Simulation results based on the LTD for model A of the MUT: a secondary suspension spring forces F and F vs. time; 1 2 dBðÞ dBðÞ b secondary suspension damping forces F and F vs. time (in Ex. 9 and 10, passive vibration damping is only used; in Ex. 11 both passive 1 2 and active vibration damping are used) vibration damping is not so very effective. As the traction The innovative two-level control system is applied to and braking forces transmitted by Jacobs’ bogies are only reduce vibration amplitudes of dynamic forces in couplers slightly more evenly distributed. Therefore, their load- of the MUTs. This developed control system consists of the bearing structures can carry only slightly smaller stresses, master control level, which performs like standard cruise which are a little more uniformly distributed in the longi- control, and the secondary control level implemented to tudinal direction. reduce the dynamic vibrations in couplers. Between the Rail. Eng. Science (2021) 29(2):163–182 Coupler force reduction method for multiple-unit-trains using a new hierarchical control system 181 Disturbance s d Vehicle j F, F , F d(B) d(B) F F j m j j + 1 s(B) s(B) 1 F + 1 q q j + 1 j LTDM + SCSs m Q j + 1 B B F F j + 1 ∑ 1/s Expression: q + K ·(q − q )dτ + I(A) 1 j + + ∑ F K ·(q − q )+ . P(A) 1 j + . . K ·(q − q ) ∑ D(A) 1 j Saturation . Saturation j − (avg) n = #vehicle j − 1 N = #bogies Expression: ∑ 1/s j = 1, ..., N j − (avg) K ·∫(x − q )dτ + I(A) j − 1 j (avg) No x = x (avg) j j K ·∫(x − q )dτ + j < n .. (avg) P(A) j − 1 j (avg) x = x j j x + j − 1 . . Yes (avg) . ∑ Saturation K ·∫(x − q ) D(A) j − 1 j (avg) j − x = 1/2(x + x ) j j j+1 .. . (avg) x = 1/2(x + x ) j j j+1 Fig. 17 Essential part of the block diagram of the slave control systems enabling the realization of the active vibration damping in the MUT with Jacobs’ bogies (all MUT bogies are self-propelled) Acknowledgements The author would like to express his gratitude to higher and lower control levels of this system, there are no the editorial committee of Railway Engineering Science for help. I noticeable adverse couplings. would especially like to thank Professor Wanming Zhai (editor-in- The correctness of the new hierarchical control system chief). has been successfully validated for LTD problems of the Open Access This article is licensed under a Creative Commons MUT. This system has a simple structure that can be Attribution 4.0 International License, which permits use, sharing, modified. Besides, this system allows considering combi- adaptation, distribution and reproduction in any medium or format, as nations of diverse traction control models for the MUTs long as you give appropriate credit to the original author(s) and the using computationally efficient numerical methods. These source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this models are essential for the prevention of wheels from article are included in the article’s Creative Commons licence, unless excessive slip (for traction) or sliding (for braking) indicated otherwise in a credit line to the material. If material is not [25, 26]. included in the article’s Creative Commons licence and your intended This system makes it possible to find compromise use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright solutions for control issues, which represent, for instance, holder. To view a copy of this licence, visit http://creativecommons. setting the compromise between the possibility of obtain- org/licenses/by/4.0/. ing simultaneously the low overshoot and the close to zero value of the steady-state error. Most of all, it is also sus- ceptible to modifications, which lead to the much better performance obtained with the adopted additional nonlin- References ear feedforward action or by the possibility of self-tuning implementation [27]. The developed method of active 1. Allenbach JM, Chapas P, Comte M, Kaller R (2008) Electric traction. 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Journal

Railway Engineering Science – Springer Journals

Published: Jun 23, 2021

Keywords: Longitudinal train dynamics; Control system; Multiple-unit train; Railway coupler

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