Active suspension in railway vehicles: a literature survey

There are different approaches to classifying the various active suspension technologies. A natural way is to categorize the technologies into two types according to their location:

An active primary suspension is meant to improve the stability, guidance and curve-negotiation behaviour for solid-axle wheelsets (SW) or independently rotating wheels (IRW). An active secondary suspension is aimed at improving the ride quality and controlling the quasi-static motion of car-body, for example with a Hold-Off-Device (HOD). Tilting trains tilt the car-body to a desired rolling angle in curves so that the lateral acceleration perceived by the passengers will be reduced, allowing higher curve-negotiation speed. Tilting trains theoretically belong to active secondary suspension and can integrate other active schemes like HOD, but as a distinctive and well-developed technology, it is reasonable to split it from active secondary suspension as is introduced separately in Sect. 3.

Semi-active and fully active controls are two categories from the perspective of the degree of control. A clear distinction between the two can be seen in Fig. 2. The fully active control requires a power supply to produce the desired force so that the motion of the mechanical structure can be controlled. In contrast with neither power supply nor actuation system, the controllable variables in semi-active suspension are those parameters of passive suspension: adjustable stiffness spring [6], adjustable inerter [7] and adjustable damper [8]. Most studies focus on the last one. In semi-active suspension, as the damping force generated is still dependent upon the speed of the damper, the improvement of vehicle dynamics is naturally constrained. For instance, semi-active control cannot create the desired force for low-frequency vibrations or in quasi-static conditions. However, the simplicity of semi-active damper makes it easier to implement so it can serve as a trade-off solution between passive suspension and fully active suspension.

Another kind of classification for active suspension is based on the purpose of the active control [1]. Four types are categorized as follows:

Since the purpose of active suspension decides control targets and the interesting frequency range, the active control schemes consisting of controllers, sensors and actuators will vary accordingly. Therefore, this classification helps the organization of the description of control strategies and other parts. In this state-of-the-art review work, the idea of this classification is applied within each subsection. For instance, when it comes to the active primary suspension system, the control strategies are introduced based on the functions of ‘steering’ and ‘stability’ separately.

High-bandwidth control deals with stochastic vibration excited from track irregularities to improve passenger ride comfort. Before the introduction to the control strategies, it is worth mentioning different methods to evaluate the ride comfort. The method prescribed in EN 12299 [28], or the Ride Index \(W_{Z}\) [29] is usually used which takes into consideration the RMS value of frequency-weighted accelerations on the car-body floor. The weighting functions are used to reflect the human interpretation of ride comfort. The human body is most sensitive in the range between 0.5 and 10 Hz. The weighting functions vary depending on methods and directions.

Rigid car-body modes are generally in a frequency range around 1 Hz while modes involving car-body deformability relevant to ride comfort fall between 8 and 15 Hz [30]. Bogie rigid modes are often in the range of 5 to 10 Hz. Thus, it is important to properly design the secondary suspension system to avoid unacceptable levels of ride quality due to poor separation between different resonance frequencies. Moreover, the general demand of higher speeds in rail vehicles requires lighter car-bodies resulting in lower structural stiffness, which eventually results in lower natural frequencies. This effect tends to worsen ride comfort. Once a passive system is optimized, a good way to improve passenger comfort is the usage of an active (or semi-active) suspension system to suppress undesired vibrations coming from the track.

In the literature, different control approaches are used like Modal control, LQG and \(H_{\infty }\), but these concepts may not be adopted independently. Therefore, in Fig. 8 their relationship is organized in substructures. Other concepts exist but they are not considered here. One main distinction can be found between model-based and non-model-based controllers. Model-based controls including \(H_{\infty }\) and LQG can produce better performances but at the same time they can suffer from unmodeled behaviours and parameter uncertainties. The dashed line in Fig. 8 indicates that a model-based approach may be used but it is not necessary to design a sky-hook or fuzzy controller. The second distinction can be found in the application of a modal separation approach. This approach goes by the name of modal control and will be explained next. In the following, six categories are introduced and their applications in fully active control in high bandwidth are shown. The control concepts are as follows: (a) modal control (b) sky-hook damping control, (c) linear quadratic Gaussian (LQG) control, (d) \(H_{\infty }\) control and (e) fuzzy control. A separate mention will be given to (f) inter-vehicle actuator control.

To help the understanding of the concept of modal control, the so-called local control, shown in Fig. 9, is introduced first. In this approach, the global system is not directly considered. Benefits on the system come from separate localized actions. In this approach, each sensor-controller-actuator triplet creates a separate subsystem that has no direct communications with the others.

In contrast, the target of modal control is to attenuate different motions efficiently using one common control strategy. The modal decomposition is achieved by processing the acceleration measured at different locations in the car-body. Then, to suppress each single mode, the desired actuation forces will be calculated separately, and these forces will be superimposed so that finally the different vibration modes can be damped at the same time. An example of modal control is given in Fig. 10 in which the modal separation is applied to bounce, pitch and roll motions of the car-body.

Orvnäs applied this idea to design control schemes for lateral, yaw and roll motions control [31] as well as for bounce, pitch and roll motions control [32]. The control scheme proposed and applied in [31] is shown in Fig. 11. In this scheme, sensors mounted on front and rear position of the car-body will measure lateral accelerations. Then, the sum and difference of the two signals are processed to reflect the lateral oscillation and yaw motion separately. Then, forces aimed at controlling the motions will be generated according to sky-hook or \(H_{\infty }\) control. Moreover, the lateral acceleration of the bogie is low-pass filtered and half the bogie mass is used as gain to form the force reference for HOD function. The idea of modal control is also applied in the studies by Hammood and Mei [33], Sugahara et al. [34], Yusof et al. [35], and Qazizadeh et al. [36, 37].

Sky-hook damping control, also known as absolute damping, was introduced by Karnopp [38], and is one of the simplest and most effective control techniques for vibration isolation. The basic idea on sky-hook control relies on the concept shown in Fig. 12 centre. To solve the trade-off problem of passive suspensions between resonance frequency amplitude attenuation and higher frequencies amplitude magnification, the damper is moved from the original position of Fig. 12 left to be connected to a virtual constraint called ‘sky’. In practice, the damper still has to be mounted between the car-body and the bogie. Thus, a control force is introduced to produce the same effect of the desired ‘sky’ configuration. This concept is illustrated in Fig. 12 right.

Ideally, the sky-hook force applied on the car-body can be calculated according to Eq. (1).where \(F_{\text{sky}}\) is the desired force acting on car-body, \(C_{p}\) is controllable damping and \(\dot{x}_{2}\) is the velocity of the car-body in the lateral or vertical direction.

The ride quality on tangent track can be significantly improved by applying a sky-hook damper, but the deflection of the suspension is enlarged on deterministic track segments like curves and gradients. In a real implementation, the car-body and bogie velocities are produced by integration of acceleration. Consequently, the integration of quasi-static acceleration as the lateral acceleration in curves must be avoided. The velocities are therefore high-pass filtered after the integration. This solution will also mitigate any thermal drift in the sensors. Figure 13 gives the workflow for sky-hook damping.

Thanks to the simplicity of sky-hook control, it is the one that finds application in full-size vehicle tests (Qazizadeh et al. [36, 37] and Sugahara et al. [39, 40]). In scientific studies, the sky-hook control is also used as reference to prove the effectiveness of other refined control techniques by Gopala Rao et al. [41], Sugahara et al. [39], [40], Pacchioni et al. [42] and Orukpe et al. [43].

The damping factor (gain) for sky-hook control can be set as critical damping, but this is not necessarily the best choice. Efforts are made to improve the performances of sky-hook control and a few examples are given here. Linear and nonlinear approaches were explored with different filtering techniques to improve ride comfort and minimize suspension deflection [44]. Turnip et al. [45] introduced a sensitivity approach to improve sky-hook performances at high frequencies. Hammood and Mei [33] used a gain-scheduling approach based on the difference between car-body and bogie speeds to improve the performances while Yusof et al. [35] used non-dominated sort genetic algorithm II (NSGA II) to optimize control gain and actuator stiffness. With a careful choice of the control parameters, sky-hook performances can match the performances of a linear quadratic regulator (LQR) [41].LQG control is a combination of LQR and a Kalman filter to create a model-based control. The LQG controller is aimed at optimizing the performances based on specific penalty values assigned to the state vector \(x\) and the input vector \(u\). It must be mentioned that in many implementations, the Kalman–Bucy filter or its digital equivalent is used rather than the more general form of Kalman filter. A graphical representation of this control is given in Fig. 14.

A successful implementation of LQG was described by Gong et al. [46], where it was combined with preview control. It is shown that LQG control is effective in control of both rigid and elastic modes together over a wide frequency range. An interesting application was studied by Leblebici and Türkay [47]. Here, a lumped track model was introduced, and it was proven through simulations that the LQG control can effectively counteract bounce and pitch motions of the car-body. A quarter car model with nonlinear suspensions was studied by Nagarkar et al. [48] where NSGA II was used to optimize PID and LQR control parameters with a multiple objective problem compromising ride comfort, suspension space and control force. Sugahara et al. [40] compared sky-hook damping and LQG control both by simulation and test on a full-scale model. It is shown that LQG control works better when the natural frequency of the first bending mode of the car-body is far from the bogie one while the sky-hook damping improves the response when these two are close to each other. A similar approach was applied by Pacchioni et al. [42]. Here, it is shown that with a careful choice of the gains similar effects can be produced by sky-hook and LQG. Nevertheless, as discussed by Sugahara et al. [39], LQG control can be a precise control but it can suffer from unmodeled uncertainty or even dynamics that can cause a drastic decrease in the controller performances.\(H_{\infty }\) control is a robust model-based control technique using measurement feedback to produce a stable controller that handles unmodeled dynamics of the plant and model uncertainties. A graphical representation of this control is given in Fig. 15.

\(H_{\infty }\) was introduced into control theory in the late 1970s. One of the first applications of \(H_{\infty }\) control to the control of vehicle modes was carried out by Hirata et al. [49, 50] where lateral roll and yaw motions were successfully attenuated in the low-frequency region. This type of control was extensively used by Kamada et al. [51‐53]. Here, the effectiveness of the control strategy is shown both with simulations and experimental tests on a 1:6 scale model of Shinkansen vehicle. The usage of the \(H_{\infty }\) control is especially useful for piezoelectric actuators. The robust \(H_{\infty }\) control overcomes the problem of unmodeled behaviours and uncertainty on parameters of the piezoelectric actuators [51]. A \(H_{\infty }\)-sky-hook control was developed by Leblebici and Türkay [54] showing the possibility of achieving good amplitude reduction near the resonance frequencies of the car-body. The development of a \(H_{\infty }\)-sky-hook control is possible due to the measurement feedback approach. A comparison in performance evaluation was carried out between sky-hook control and model predictive control (MPC) based on mixed \(H_{2} /H_{\infty }\) using linear matrix inequality (LMI) by Orukpe et al. [43]. It is shown through simulations that MPC better suppresses the bounce motion of the vehicle than the classical sky-hook control while keeping the suspension deflection within a similar range and producing comparable forces.Fuzzy logics come from the definition of fuzzy sets which was first introduced by Zadeh [55] in 1965. By definition, a fuzzy set is a set to which a variable may belong partially. This gives the possibility to the fuzzy logic to decide accordingly to a defined linguistic rule which output (control input) to choose depending on the combination of the inputs it takes (error between reference signal and system output or measurements). A graphic representation of a fuzzy logic implementation is given in Fig. 16.

Fuzzy logic control was successfully applied by Guclu and Metin [56] on a tram with a three-bogie configuration. Good results were presented in time and frequency domain with simulation results. In a subsequent work Metin and Guclu [57] compared the results obtained with a PID control with fuzzy logic control. Both controls are tuned with the use of genetic algorithms (GAs). It is shown by simulations that the fuzzy one improves the performances. A self-tuning fuzzy logic approach was implemented by Sezer and Atalay [58] achieving good results in terms of acceleration reduction and proving the robustness of the implemented approach against car-body mass variation. The simulation results were shown in terms of time and frequency domain analysis showing that low-frequency amplitude was properly attenuated.Since the inter-vehicle actuation system has a special arrangement as shown in Fig. 7, the proposed control strategy is unique. When actuators connect the adjacent car-bodies, the motions of the car-bodies are coupled so that the whole train set should be considered as a complete system. As each car-body is equally important, control objectives are multiplied with increasing number of interconnected car-bodies. The complexity of the system makes model-based control strategies too complicated to implement, while multi-objective GAs are introduced and turn out to be effective [25]. In this work, a three-car-body train set is studied, where the objective function J is created considering RMS values of acceleration measured from the front, middle and rear positions for each car-body.

Each desired actuator force is optimized through GAs to minimize the objective function. Constraint function could also be introduced to limit the deflection of suspension in low bandwidth. In this way, the knowledge of the vehicle dynamic model is not required. Instead, the control is purely based on an optimal mathematic model. This control idea can be applied for other multi-objective control targets, as is shown in Eq. (2) [59].where \(a_{\text{b}} ,x_{\text{d}}\) and \(F_{\text{a}}\) are body acceleration, suspension deflection and actuator force, respectively, and the coefficients in front of each index are their weighting factors. So, through the definition of objective function \(J\), different control targets can be considered in one scheme.

Hold-off-device, as a typical application of active control in low bandwidth, was first proposed by Allen [60]. The target of this application is to generate a force in the lateral direction to counteract the movement of the car-body with respect to the bogie in curves so that the car-body will hold off the stiff bump stop. Consequently, the ride comfort will be improved, and bump stop clearance can be reduced to increase the width of the car-body. Alternatively, with the suspension deflection unchanged, the HOD allows for softer lateral secondary springs which means a better ride comfort can be achieved. Besides, the instability and risk of overturning in strong crosswind can be reduced since the car-body centre of mass position displacement will be restricted by the reduced bump stop gap.

For the control strategy, the low-pass filters are used to process the lateral acceleration of bogie or car-body so that the track layout information will be extracted. Orvnäs calculated the reference actuation force for centring the car-body as product of car-body mass and bogie lateral acceleration [31]. A recent work considered the allowed small deflection of secondary suspension [61]. When lateral displacement exceeds the limit value \(d_{\text{l}}\), the HOD will be activated and provide the actuation force according to Eq. (3) [62].where \(M_{\text{c}} a_{\text{c}}\) is the product of car-body mass and lateral acceleration; \(K_{\text{l}}\) represents the sum of lateral stiffness in secondary passive suspension.

For the control of semi-active suspension, the above-introduced full-active control strategies can be referred. The idea of modal separation, sky-hook control, \(H_{\infty }\) control, LQG control, etc., can also be applied in a semi-active suspension. In the design of control schemes, the features of a variable damper must be considered. They can be divided into two types according to the degree of control: two-state/on–off variable damper and continuously variable damper. The former damper works either with maximum or minimum damping rate. The control strategy for this simple damper is decision-making between the two states, which can be achieved by high-level and low-level voltage or current signals. In contrast, the continuously variable damper requires a more complicated control, but it has the potential to provide better performance. Sky-hook control is used here as example to further illustrate their features.

Two-state sky-hook control is the most frequently used control strategy. The high damping state \(C_{\hbox{max} }\) and low damping state \(C_{\hbox{min} }\) are determined by the sign of directions of car-body velocities (\(\dot{x}_{2}\)) and relative velocity between car-body and bogie \(\left( {\dot{x}_{2} - \dot{x}_{1} } \right)\),

However, Eq. (5) shows a damping force applied on the car-body which does not fit the definition of sky-hook control in Eq. (1), since the dampers connect bogie and car-body and therefore the bogie velocity is involved.

This problem can be solved by implementing continuous sky-hook control shown in Eq. (6), where not only the sign but also the magnitude of the bogie and car-body velocities decides the reference damping.

This control law can produce the ideal sky-hook damping force, but it means a higher demand for adjustable damping technology and an additional controller for the damper to generate the desired force. For instance, a magneto-rheological (MR) damper is a promising technology, but it has strong nonlinear dynamic behaviour. The input current or voltage is not proportional to the damping force generated. Therefore, in order to obtain the reference damping force, the command signals for the damper need to be pre-calculated [62].

Sky-hook control for semi-active suspension has relatively poor performance in the high-frequency range, so various improvements of this classic control law have been proposed. Savaresi introduced acceleration-driven-damper (ADD) where the acceleration of the car-body was used to calculate the reference damping [63]. The results validate the improved attenuating effect in high-frequency vibration but also confirm the poor performance of this control scheme in the low-frequency range. Therefore, a mixed sky-hook and ADD control strategy was proposed to take advantages of the two controls and provide good results over a wider frequency range [64].

A bogie-based sky-hook control was compared with the classic car-body-based sky-hook by Hudha [65]. The simulation results of a 17 DOF dynamic model show that the bogie-based control can better attenuate the vibration in terms of lateral, roll and yaw motions.

Advanced controls are investigated through simulation to achieve more complicated control targets. A LQG control law was applied by Wang [66, 67] where a MR damper was applied to reduce the vibration in lateral, yaw and roll directions. Three working modes of semi-active control (passive-off, passive on and semi-active) were compared. Zong investigated \(H_{\infty }\) and the use of adaptive neuro-fuzzy interference system (ANFIS) for the control of MR damper. The lateral, yaw and roll acceleration can be reduced by 30% according to the simulation results [62].

A control strategy for an adjustable damper in primary vertical suspension was explored for suppressing high-frequent first bending mode of the car-body vibration [39, 68]. Through the idea of modal separation, both bounce and pitch motions of the bogie are controlled according to the sky-hook control. Although any measurement of car-body vibration is not required in this control, its vertical acceleration between 5 and 10 Hz can be suppressed. Then, LQG control with tuned weighting function turns out to be more effective for attenuating the first bending motion at 8.5 Hz than sky-hook control. In addition to this semi-active damper dealing with car-body flexible modes, the air spring with controllable orifice valve is applied simultaneously to cope with rigid motions at low frequency.

In the late 1970s and early 1980s, British Railways Technical Centre in the UK carried out a series of theoretical and experimental studies on active suspension [69]. The assessment methods for ride comfort and the limitations of passive suspensions were thoroughly analysed. Experimental tests for both vertical and lateral active suspension were undertaken considering different actuator technologies. In the vertical direction, electromagnetic actuators were mounted on a Mark III coach with BT10 bogies in parallel with the air springs. An alternative solution was also explored where an air pump actuator can vary the pressure and volume of air spring by an electric motor. According to the measured acceleration, around 50% vibration reduction can be achieved at 1–2 Hz. For the lateral active control, servo-hydraulic actuators were placed in parallel with air spring, and the vibration between 0.5 and 2 Hz was significantly reduced. A specially designed electro-mechanical actuator was involved in the field test for lateral active suspension and proved fail-safe when a failure of the control system occurred.

In the 1990s, Fiat Pendolino implemented a HOD function through pneumatic actuators in addition to tilting technology in operation. In a later stage, the centring function was integrated with the tilting devices [4].

In the mid of the 1990s, Siemens in Austria performed field tests on a prototype vehicle where tilting, lateral centring, and lateral and vertical semi-active technologies were put together [70‐72]. The integrated active control strategy improved the overall dynamic performance.

KTH and Bombardier Transportation in Sweden have explored and developed active suspension in the program Green Train since 2005 [73]. Active lateral suspension and active vertical suspension were implemented on Regina 250 trains and tested in the line from 2007 to 2013 [31, 37, 74]. The HOD function was incorporated in the suspension to centre the car-body above the bogies in curves. The field tests were performed in curves with radii changing from 300 m to 3200 m showing that the maximum lateral displacement of the car-body could be reduced from 50 mm to 25 mm, and significant improvement of ride comfort was observed as the contact of bump stop could be avoided. An active lateral suspension similar to the one tested in the Green Train project is now in use in the ETR1000 high-speed trains in Italy.

In recent years, Korea Railroad Research Institute carried out roller rig tests and field tests for active lateral suspension [75]. Electromagnetic actuators were implemented, and sky-hook control was applied in these experiments. Both urban vehicles and intercity vehicles were tested on a roller rig at 70 km/h and 100 km/h, respectively. The lateral accelerations were reduced by 7 dB for both types of vehicle. The intercity vehicle was then tested on track at speeds of 90–100 km/h, showing a good agreement with measured results on rig tests. A fail-safe control scheme was proposed and examined in the field test. When the vehicle speed and actuator temperature signals exceeded beyond the ‘yellow’ or ‘red’ threshold, the control commands for active suspension were reduced (60%) or deactivated. Redundant sensors were also implemented to achieve the fail-safe target as presented in Fig. 17.

Japan started the research for active suspension in the 1980s and has launched the first commercial train with fully active suspension in early 2000.

In the beginning of the 1980s, the old Japanese National Railways (JNR) tested lateral active suspension with pneumatic actuators which halved the vibration at 120 km/h [76]. After the privatization of JNR, the JR-East in 1991 made field tests on Series 400 EC train where pneumatic actuators and \(H_{\infty }\) control were implemented for full-active suspension in lateral direction at maximum test speeds up to 240 km/h. In 1993, a new field test on Star 21 with a maximum speed 425 km/h was carried out. Both tests showed that 50% or more lateral vibration can be suppressed by active suspension. At the same time, JR West installed lateral pneumatic actuators in the test train WIN 350 and prototype of Series 500 EC [77]. Hitachi tested an active suspension with hydraulic actuators on WIN 350. Kawasaki Heavy Industries made field tests on the test Train 300X also with hydraulic active suspension based on the \(H_{\infty }\) control law. These activities were the major field tests before the real implementation of active suspension. Research about rig tests and investigations of \(H_{\infty }\) control in the same period can be found in [50, 78].

In 2001, the commercial operation of Series E2 and E3 Shinkansen trains started using fully active lateral suspension. In these vehicles, pneumatic actuators are implemented on the end cars and the green car (first class car). Semi-active suspensions have been installed in all cars [79]. \(H_{\infty }\) control is adopted to eliminate the yaw and roll car-body vibrations. After that, the fully active suspension was further explored and developed in the project Fastech 360, aimed at developing higher speed trains. The test trains 360S and 360Z had electromagnetic actuators with high bandwidth installed [80], while electro-mechanical actuators are applied in Series E5 and E6 in 2011 and 2013 [81].

Regarding the active suspension in the vertical direction, extensive tests on a 1:6 scaled Shinkansen vehicle were performed by Kamada et al. [51‐53]. In their studies, the control strategy applied was a robust \(H_{\infty }\) modal control. The 1:6 scaled experimental set-up is shown in Fig. 18.

Firstly, five modes were considered: two rigid modes and three elastic modes [51]. A weighting function for disturbance suppression (\(W_{s}\)) was chosen separately for each considered mode. A combination of linear and 20 stack piezoelectric actuators was used. The tasks were split between the two different actuators types. Linear actuators were used to control the two rigid modes while the piezoelectric ones were used to suppress the three elastic modes. Subsequently, the usage of pneumatic actuators in parallel with the air spring was considered [52]. Despite rigid body modes were effectively suppressed, the control performance became worse near the elastic vibration modes due to the nonlinearity of the electric-pneumatic valve. Lastly, air suspensions were directly used to control the first and second rigid modes and the first bending mode [53]. The air spring was controlled by adjusting the air pressure, and accelerometers were placed at the edges and the centre of the 1:6 scaled vehicle. Satisfactory results were obtained for the 1:6 scaled vehicle and for a simulated full-size vehicle. Here, a careful model of the pressure valve should be considered.

On-track tests of a vehicle with active vertical secondary suspensions were reported by Qazizadeh et al. [36, 37]. Here, secondary lateral and vertical dampers were replaced by electro-hydraulic actuators on the high-speed train Regina 250. A view of the actuator installation is given in Fig. 19.

A modal sky-hook approach was used on a two car-body train in which one car was equipped with conventional suspension and the other with the active devices. Accelerations were measured on the car-bodies above the secondary suspensions. The measurements were performed at speeds up to 200 km/h, showing 44% reduction of weighted vertical acceleration compared to the passive reference car.

In the early 1990s, UK started an initial exploration of semi-active suspension on a test rig in GEC-Alstom Engineering Research Centre [82], with the purpose of studying the potential of semi-active damper in secondary lateral position. In the experimental work, a simplified scaled test rig was applied where an electro-hydraulic actuator produced excitation to simulate the bogie vibration. A two-state damper was realized by external pipework and solenoid valve enabling high and low damping. An interesting control strategy was proposed based on one single lateral velocity of the car-body. A threshold value was to switch between high and low damping rate. This switch damper scheme was shown to produce more than 25% improvement of the lateral ride index.

In the middle of the 1990s, on-track tests of secondary lateral semi-active suspension on a X2000 train set were carried out in Sweden [83]. A control strategy based on sky-hook law was applied to attenuate the lateral and yaw motions of the car-body. A mixed hydraulic and electromagnetic actuator was created to enable continuously variable damping rates. In the field test, semi-active devices were mounted on the driving trailer at the end of the train set. The RMS values of lateral acceleration decreased by 30% from 0.8 to 2 Hz but increased below 0.8 Hz.

At around the same time, Austria Siemens carried out field tests for semi-active suspension [70‐72]. Two lateral and two vertical hydraulic dampers with continuously adjustable damping valves were mounted on the vehicle in addition to the electro-mechanical tilting and pneumatic lateral positioning devices on the prototype bogie SF 600. The ideal damping force was calculated based on sky-hook control, and a lookup-table method was used to produce demand current signals. Field measurements showed that the ride quality improvements in the range of 15% in terms of RMS acceleration.

In Korea, studies for semi-active suspensions through rig tests and field tests in the last decade were carried out in the last decade [84‐88]. Shin et al. [84‐86] carried out 1:5 scaled (Fig. 20) and full-scale [86] roller rig tests to study the effects of semi-active lateral suspension with MR dampers at different speeds. The classic sky-hook control and later \(H_{\infty }\) control were applied to suppress the vibration. After that, a field test to evaluate ride quality was carried out [88]. The semi-active MR damper with sky-hook control scheme could provide more than 29% improvement of weighted acceleration compared to the passive system.

Japanese researchers started to explore semi-active suspension technologies in the early 1990s and the technologies have been applied in commercial use since the end of the 1990s [77].

In 1994, JR-West used the test train WIN350 to explore the performance of semi-active suspension where 6-level variable dampers were implemented. The control was based on the sky-hook control law, showing 30% vibration reduction at a speed of 300 km/h with no influence on safety. Later, this system was implemented on Series 500 Shinkansen EC trains.

JR-Central installed semi-active suspension on Series 300 EC in 1994 for field tests, with similar variable dampers similar to the ones of JR-West. An improvement was achieved by introducing delay compensation and a bandpass filter to achieve a larger controllable frequency range. Series 700 Shinkansen EC trains have this system installed and are in operation since 1999.

To explore the concept of semi-active control for primary vertical damping introduced in Sect. 4.2.3, a Shinkansen vehicle was tested recently on a roller rig and in the line. Field tests were carried out on a line having a relatively poor track quality, to verify the effectiveness of the scheme [27, 39, 89]. The semi-active primary suspension can selectively reduce the vibration of the first bending mode of the car-body, and with tuned LQG controller, the rigid car-body motions can also be attenuated to some degree. The roller rig test and installation of semi-active damper are shown in Fig. 21.

For solid-axle wheelsets, ASW is the most extensively studied configuration where either yaw torque or lateral force is applied directly to the wheelset to control the yaw and lateral motions so that curve negotiation and stability will be improved [3]. This principle can be realized by three general mechanical arrangements. Yaw torque could be applied directly by one yaw actuator mounted between bogie and wheelset as shown in Fig. 22a or in a more practical way utilizing two actuators in the longitudinal direction at the ends of the wheelset, as indicated in Fig. 22b. Since wheelset yaw motion and lateral motion are coupled, implementing lateral actuators (see Fig. 22c) is another way to achieve the motion control of the wheelset. However, a study [92] based on a simplified two-axle vehicle model concluded that the lateral actuation requires a larger force to achieve the same stability of the vehicle than the yaw actuator. Moreover, when this scheme is used, a deterioration of the ride quality can be expected and the installation space for lateral actuators would be an issue.

Among the three schemes, arrangement (b) is the most favourable idea from which some new specific schemes have been proposed as shown in Fig. 23.

In the left scheme shown in Fig. 23, introduced by Park et al. [93], each wheelset has one longitudinal actuator. The mechanical linkages are designed to transfer the mutually opposite actuation force on the left and right ends of each wheelset. Therefore, there is only one actuator implemented for each wheelset. In the right scheme, introduced by Umehara et al. [94], a more elaborately designed set of connecting rods couples the front and rear wheelset motion so that only one actuator is required for each bogie to achieve the steering effect. Reducing the number of actuators by introducing articulated mechanical linkages can save installation space and cost for actuation system. However, implementing fewer actuators means higher performance requirements for each actuator, such as higher maximum force and maximum pressure, but it still has potential to improve the reliability of the whole system. When the number of actuator is reduced, the installation space and cost can be saved for fault-tolerant actuators with redundant structures. This is an important aspect in the practical design process [95].

In the concept of ‘yaw relaxation’ [96], as shown in Fig. 24, a spring is arranged in series with a longitudinal actuator connecting the axle to the bogie frame. On tangent track, the stability is ensured by the passive spring and high stiffness of the actuation system working in low bandwidth frequency range or passive mode. In curves, the actuation works in active mode and can steer the wheelset with low force.

If the primary spring remains in parallel with yaw actuators in the longitudinal direction to ensure the stability of the vehicle, a higher actuation force is required to cancel out the action of the passive spring in curves. However, having a passive suspension in parallel to the actuator is an efficient approach to guarantee fault tolerance of the active suspension, which is crucial for the implementation of ASW [95]. In real design of a primary suspension, longitudinal stiffness of the passive spring is difficult to be completely removed, because of the existence of either coil spring or rubber spring required to bear the vertical load. Nevertheless, reducing conventional longitudinal stiffness is instrumental to achieve lower actuation force as shown in [97, 98].

Secondary yaw control was firstly proposed by Diana et al. in order to improve stability in tangent track and curving performance of a tilting train [99, 100]. Yaw torque from car-body to bogie is produced by two longitudinal electro-mechanical actuators in the position where the original passive yaw damper is mounted. This scheme is also called active yaw damper (ADD, in German: ‘aktiver Drehdämpfer’). A schematic of this concept is shown in Fig. 25. The concept SYC can enhance the vehicle critical speed and reduce track shift forces. Since the motion of the wheelset is uncontrolled, the steering effect is not as effective as ASW, but the improved stability can allow lower primary yaw stiffness and consequently lead to an improvement of the curving performance. Although it is reasonable as well to classify the SYC into active secondary suspension, the target of SYC is to improve stability and reduce track shift forces in curves rather than improving ride quality. Therefore, this control scheme is closer to the nature of active primary suspension.

Sharing the similar idea of SYC, a new active control for a bogie is proposed to improve the stability as is introduced in [101]. In this work, two inertial actuators are applied in lateral direction on the front and rear beam of the bogie frame. Simulation results proved the enhancement of stability and recently a scaled roller rig test demonstrated a reduced lateral displacement of the bogie [102].Based on SYC, a new active suspension AY-FS was proposed by Simson for heavy hauling locomotives [103‐105]. In this concept, force steering linkage is implemented with SYC. It can be seen as a combination of SYC and passive steering linkages through which wheelsets can be forced into an ideal position according to the kinematic relationship between bogie and car-body, as presented in Fig. 26. This concept can significantly improve the curving behaviour of locomotives with high tractive effort.

The control strategy varies according to the control targets, from which different strategies are classified into two main categories: (a) control strategies for steering and (b) control strategies for hunting stability.The fundamental objective of implementing an active primary suspension is often to improve the curving behaviour. Wear number/wear index and equality of track shift force among different wheelsets are often used to assess the vehicle’s curving behaviour. Different principles of steering introduced in literature are summarized below: (a.1) Radial control, (a.2) Perfect control, (a.3) Steering control in locomotives, and (a.4) Other controlsThe idea of radial control is to steer each wheelset to achieve a radial position in curves. In other words, the attack angle of wheelset should be as small as possible. Based on this idea, some schemes of steering bogies by means of passive linkages or coupling of wheelsets have been proposed. Well established is for example the design of Talgo [106]. However, theoretically this control concept produces perfect curving behaviour only when cant deficiency is zero which seldom is the case in real operation. An appropriate small angle of attack is needed to produce lateral creep force that can balance the un-compensated lateral force in normal cases. Despite its simplicity, this control scheme has been shown to provide significant improvement for curving behaviour [107].The perfect steering defined by Goodall and Mei [59] points out that the longitudinal creep forces on wheels on the same axle should be equal to zero if no traction or braking force is applied. Meanwhile, the equal lateral creep force on each wheelset should be achieved. However, in operation, direct measurements of creep forces are very difficult. Therefore, some equivalent indicators that can be formulated for perfect steering conditions are proposed and summarized as below.Zero longitudinal force (without traction and braking force) and equal lateral forces mean pure rolling of each wheel. To achieve the pure rolling, a yaw torque can be applied to control the lateral position of the wheelset [108, 109].

Under the assumption that the wheel is a straight cone [93], the needed lateral displacement of the wheelset can be calculated according to Eq. (7):

where \(e\) is the half track clearance; \(r_{0}\) represents the rolling radius; \(\lambda\) refers to the wheel conicity, and \(R\) is the curve radius. In this control, wheel conicity and lateral displacements of the wheelset may be difficult to measure or estimate. The approach was used for a two-axle vehicle where a scaling procedure based on vehicle speed and estimated curvature was applied to improve the stability of a PID controller in different running conditions [110].This control strategy was first proposed in the previously mentioned yaw relaxation method by Shen and Goodall [96] and some following studies were carried out by Perez and Shen, respectively [108, 109].

The force applied on the wheelset can be divided into two parts: the force from the wheel–rail contact, and the force transmitted from the bogie through the primary suspension. The two creep forces pointing in opposite direction on the two wheels exert a yaw torque but in the ideal steering condition this torque should be zero. If the inertia force of the wheelset is neglected, the yaw torque generated by the primary suspension should be reduced to zero. In other words, to make the wheelset take the pure rolling position, the yaw motion of wheelset is set to free. Therefore, this control is also known as yaw relaxation. The measurement of this yaw torque can be realized by calculating the longitudinal forces applied on the axle box. The actuation force could be measured from the actuation system, and the spring force could be obtained by measuring the deflection of the springs and the knowledge of the stiffness characteristics. A measurement error could be introduced because stiffness varies at different load levels.Equal ideal angle of attack for each wheelset is another indicator for equal lateral contact force on both wheelsets in a bogie [109]. The ideal angle for each wheelset is determined by track data (curvature and super-elevation), cant deficiency (vehicle speed) and creep coefficient. Feedforward control could be implemented to simplify the control design and avoid instability of the system. However, many inaccurate measurements of these parameters and uncertainty of primary suspension stiffness can cause ineffectiveness of the control. Therefore, the application of feedback control will improve the effectiveness of steering.In this control strategy, neither ideal angle of attack nor ideal lateral displacement is required. Instead, zero difference of the angle of attack and lateral displacement between the wheelsets is prescribed as the control target. The force or deflection of the primary suspension in lateral and longitudinal direction can be measured as alternative solution to eliminate the difference of wheelsets motions.

In summary, the above-mentioned four strategies are all based on the same principle about creep forces. In the ideal condition that all the parameters can be accurately measured, all four control strategies can provide perfect steering effect. If sensing issues and uncertainty of measurement are considered, the steering effect of these control strategies could be deteriorated and present different characteristics. Table 2 compares the above control schemes.

The above four control strategies are proposed because of the difficulty to measure creep forces. With some specific filtering methods being proposed for estimation of creep forces [111], the estimated creep forces can be directly considered as a control target to achieve the perfect steering control [98].Even though perfect steering in (a.2) can be applied in a abroad range of railway vehicles, it may not be suited well for hauling locomotives. Because of the significant tractive effects in longitudinal directions, heavy haul trains in curves have longitudinal and lateral forces on couplers which will generate a yaw moment [103]. However, this moment cannot be balanced in the concept of perfect steering where equal longitudinal and lateral creep forces are required.

Given that, Simson et al. proposed two steering principles for locomotives. ‘Modified perfect locomotive steering’ was firstly proposed as modification of perfect steering. It requires equal longitudinal creep force at each wheel and equal lateral creep force for the wheelsets in the same bogie. In other words, it allows different lateral forces generated from front and rear bogies so that the yaw moment can be balanced. However, the equality of longitudinal force will limit the utilization of adhesion, as the vertical load of each wheel varies in many operations.

To solve this problem, ‘Ideal locomotive steering’ was proposed where the requirement for equality of longitudinal creep forces is released but its direction should be kept the same as the traction force. This strategy allows more flexible positions of the wheelset and can minimize the creep forces. Moreover, flange contact can be avoided effectively even in tight curves and the risk of derailment is said to be reduced [103].For the scheme SYC, reducing/equalizing track shift forces of the two axles on the same bogie is the major control target. When the vehicle passes a specific curve radius with a particular non-compensated acceleration, the reference actuation force will be obtained from a lookup table derived from a large number of simulations considering different operational scenarios [100].

Regarding the scheme AY-FS, a reference yaw angle of the bogie can be calculated according to the position of the bogie in the curve. A PID controller is introduced to achieve the target angle. The control idea based on sensing longitudinal forces can be found in [104, 105].The self-excited oscillation of solid-axle wheelset introduces hunting instability of the vehicle system. Achieving stabilization is the primary interest of active primary suspension apart from steering. The yaw angle, lateral velocity and yaw angular velocity of the wheelset are three indicators for wheelset instability. Three corresponding control strategies are proposed to stabilize the kinematic modes of the wheelset.

Active lateral damping and active yaw damping are two similar control strategies. The former one applies a lateral force that is proportional to the yaw velocity of the wheelset, while the latter one introduces yaw torque proportional to the lateral velocity of the wheelset. The stabilization effects of these two control strategies are theoretically verified in [3] based on a model of a two-axle vehicle. The active yaw damping is preferable to active lateral damping as it requires lower actuation force and can produce better ride quality [92]. The active yaw damping effect was also validated with tests by Pearson et al. [112].

The third stability control strategy named ‘Sky-hook spring’ (also known as ‘Absolute yaw stiffness’) is inspired by the ineffectiveness of passive yaw stiffness [44, 113]. In a passive primary suspension, springs produce yaw force that is proportional to the relative rotation between bogie and wheelset, but an ideal yaw force should be proportional to the absolute yaw motion of wheelset. Increasing stiffness of the spring can enhance the effect of yaw force and thereby the stability will be improved, but the effect will still be deteriorated by the motion of the bogie. In order to solve this issue, ‘Sky-hook spring’ was proposed [113]. The yaw force acting on the wheelset is proportional to the measured absolute yaw angle of the wheelset with a high-pass filter to remove the low-frequency signal from curving. Table 3 presents the above three control strategies.

In SYC, the stabilization of the vehicle is achieved by two longitudinal actuators used to mimic secondary yaw dampers. The reference forces of actuators can be calculated according to Eq. (8):

where \(v_{\text{rel}}\) is relative velocity between bogie and car-body and \(c_{\text{v}}\) is a gain like viscous damping. The delays from sensors and action of the actuator are compensated by introducing term \(m_{\text{v}} a_{{x}}\) [100].

The control principles for stability and steering are separately summarized above, while the control of actuator behaviour can also be realized by adopting a controller like \(H_{\infty }\). The efficiency of \(H_{\infty }\) has been investigated for a conventional bogie vehicle (Mousavi et al. [114]) and two-axle vehicle (Qazizadeh et al. [115]), where the improvement of curving performance can be achieved with reduced actuation force.

Except for the concept of SYC, there is no commercial application of active primary suspension, but significant new progress has been made since the last review work in 2007 [4].

SYC has been tested on a full-scale roller rig and track [99, 100, 116] in the early 2000’s. Reduced wheelset guiding force and improved vehicle stability were confirmed in the tests. Siemens has implemented active yaw damper (ADD) into electric locomotives (types ES64F4 and ES64U2 [117]) and intends to use this system for the new locomotive generation ‘Vectron’.

In recent years, the concept of ASW received more attention. In the following, roller rig tests and field tests carried out in different countries are described.

Umehara et al. [94] developed a steering truck based on the scheme shown in Fig. 23 right. For each bogie, there is only one electro-hydrostatic actuator (EHA) which is designed through special circuit and valves to rule out any risk of inverse control of actuators [118]. If inverse steering occurs, the actuator will produce no force, i.e. the actuation system is fail-safe. A test was carried out at 10 km/h on tangent track to validate the fail-safe function of the EHA actuator, showing no increase in wheelset guiding force in case of inverse steering control.

At around 2010, the Korea Railroad Research Institute carried out an experiment on a 1:5 scaled roller rig test based on the mechanical arrangement shown in Fig. 23 left [93]. A perfect steering control based on ideal lateral displacement of the wheelset was implemented, with the assumption of perfectly coned wheels. Electromagnetic linear actuators are applied in this experiment. The test demonstrated improvement in terms of wheelset lateral displacement and guiding force.

After this work, a series of studies focusing on a new steering arrangement were performed ranging from simulations to on-track tests. The control strategy is based on the radial position of wheelset in curves as introduced in Sect. 5.2.2 (a.1). A real-time curve radius estimation method is proposed where the only measurement is relative displacement between two points from car-body and bogie, respectively [97]. A special electro-mechanical actuator was created in which the rotation of a drive motor is used together with linkages to achieve the linear motion of rods at both ends, as shown in Fig. 27 (left), different from a conventional linear actuator. By doing so, there is only one actuator device at each side of the bogie. Additionally, a primary rubber spring is redesigned to achieve lower longitudinal stiffness. Figure 27 (right) presents the prototype of the steering bogie, which was firstly put on track for a stationary experiment to examine the movement of the actuation system [119]. The curvature signal measured in advance was sent to the control system to simulate the real track information, and then, measurements were carried out for yaw angle of wheelset and actuation force. Considering maintenance and cost of the yaw angle measurement system, a feedforward control is adopted for controlling the displacement of the actuator. Therefore, the measurement of the wheelset yaw angle is only to assess the wheelset movement. The maximum error between reference steering angle and the measured one is 8%. Moreover, the controller has a self-diagnosis function. When an error signal is identified, the actuation system will switch into passive bogie mode.

A recent publication [107] presents experimental results carried out on a commercial line. The curvature estimation and steering angle are satisfactory with a maximum error of 2.4% and 4.9%, respectively. The wheel lateral force is significantly reduced, and a total of 1000 km test runs showed negligible flange wear on the wheels.

In China, CRRC has presented a prototype of the next generation of metro vehicle ‘Cetrovo’ which is equipped with an active steering system [120]. Dr. Wang Xu, a senior engineer in R&D Center, CRRC Qingdao Sifang Co. Ltd. presents us the recent progress. The steering system adopts hydraulic servo actuators. The reference displacement of the actuator is computed according to the track curvature that is obtained through the utilization of track curvature database and geo-localization technology. Initial field tests have been finished recently, showing significant improvement in terms of wheelset guiding force and noise from the wheel–rail contact.

Bombardier has developed a double-deck train called TWINDEXX [121] where active steering is implemented. However, no further technical information has been published so far and the current development status is unknown.

It should be noted that when approaching the final implementation of active primary suspension, a serious look at fault tolerance of active suspension systems should be taken. While beneficial effects have been confirmed, safety critical issue must be dealt with properly at the same time. Some fail-safe designs have been made in the above-mentioned works. In the future, continuous attention should be put on fault-tolerant design of actuation system.

The concept of AIRWs (Fig. 29) is based on the possibility of controlling the yaw and lateral displacement of the common axle on which the independently rotating wheels are mounted with an external actuator. This can be done either by the direct application of a torque to the axle (Goodall et al. [122, 134, 135] and Mei et al. [136]), or use of a linear actuator (Pérez et al. [123, 137]). The example of Fig. 29 shows this last possibility. The possibility of using a semi-active approach was shown by Mei et al. [8] where MR dampers are considered. Using a two-axle linear model, it was proved by Mei and Goodall [92] that the torque required to steer the AIRW is lower than the one required by a solid-axle vehicle due to the early zero longitudinal creep forces. A combination of AIRW and DIRW was though presented by Perez et al. [137].

The concept of DIRWs (Fig. 30) is based on the possibility of controlling the speed of the two wheels of one axle autonomously. This was done firstly by applying a differential torque provided by electric servomotors through a gearbox connecting the two wheels by Gretzschel et al. [128, 138]. More recently, thanks to the advances in asynchronous induction motor control methods, an AC motor is assigned to each wheel. These are then used to provide traction, wheel guidance and stability control. The motors can be externally mounted and connected to the wheelset through a gearbox (Pérez et al. [137], Liang et al. [139, 140], Ahn et al. [141], Lu et al. [142] and Farhat et al. [98, 143]) as shown in Fig. 30 or embedded inside the wheels (Mei et al. [144], Ji et al. [145] and in the ‘Next Generation Train’ project in [124], [146‐149]). The absence of additional actuators leads to a reduction in the space required by the wheelset frame, and to the possibility to provide both traction and control within the same system reducing cost and improving reliability. The DIRW solution is therefore an attractive solution and has been the subject of extensive studies in recent years.

The concept of DSW (Fig. 31) involves the removal of the common axle between the wheels which is replaced by a frame on which the two wheels connected by a track rod are mounted. In this way, the two wheels can be directly steered. An actuation can be provided applying a displacement to the steering rod (Aknin et al. [130] and Wickens in [150], [151]) as shown in Fig. 31 or by applying a differential torque through hub-mounted traction motors (Powell in [152]). A configuration of DSW having self-steering capability was presented by Michitsuji et al. [153‐155]. It was also shown by Wickens in [151] that the stability issue achieved through active control is less affected by friction and traction than with other types of active control. Nevertheless, this idea is one of the less studied.

In this section, the control strategies proposed to solve the stability and guidance problems are discussed in the perspective of: (a) stability control and (b) guidance and steering Control.Stability control is aimed at increasing the running speed of the vehicle by reducing unstable wheelset motion that may occur. When necessary, in IRW, stability control needs to be applied in conjunction with guidance control. In fact, as mentioned above, the lack of the self-centring mechanism in IRWs makes the presence of active guidance control strongly recommended when passive solutions are missing. The stability problem is particularly evident when the longitudinal suspensions are removed. Although both AIRW and DIRW can share some control strategies, this is not generally valid for the DSW due to its peculiarity.The yaw speed difference approach to IRW stabilization concerns the actuated type (AIRW). Nevertheless, it is possible to apply it on different types of IRW. This approach was introduced by Goodall and Mei [122]. Here, yaw damping for each wheelset is actively introduced in the system through the feedback of the difference between the wheelset and bogie/car-body yaw velocity. This choice is done to simplify sensing issues in the implementation of the concept. Moreover, in his studies Goodall proposed the adaptation of the control effort based on the train speed [122], [135]. Subsequently, Mei and Goodall in [134] developed an \(H_{\infty }\) control using μ-synthesis based on the same concept as described above. This is to overcome the problem of parameter variation, non-modelled actuator dynamics and the necessity of a simple model to describe the complexity of a real train. The concept was further investigated by Mei et al. [8]. A semi-active approach using MR dampers is used observing that the required control effort is much lower than what is needed for a solid axle with the same control objective. Moreover, only the feedback signals that are in phase with the control force can be considered [135]. The stability problem was less crucial in the work by Perez et al. [123, 137] because of the consideration of a conventional bogie vehicle with longitudinal suspension.Absolute yaw rate feedback provides stability to DIRW by controlling the rotational speed of the two wheels through a common gearbox or the differential torques provided by independent wheel motors. The first approach was introduced by Gretzschel et al. [128, 138]. In this work, stability and guidance are considered at the same time. The yaw velocity of the leading axle together with the front and rear axle lateral displacements are fed back into a common PID controller that sets the direction and the amount of torque to be produced by the steering motor through a gearbox that connects the two wheels on the same axle. The same approach was studied by Liu et al. [156], where cascade PID controllers are used instead of the common PID approach. Here, each wheelset is controlled by a separate cascade control scheme and differential torque control is applied instead of a common gearbox.Absolute yaw stiffness is aimed at increasing the stability of the IRW by actively introducing yaw stiffness through the feedback of the yaw angle. This approach relies on the possibility to measure the yaw angle which might not be feasible in real applications. Absolute yaw stiffness for DIRW was introduced by Mei et al. [144] where wheel embedded permanent magnet synchronous motors are used. The desired yaw stiffness is achieved through the differential torque generated by the two motors. The yaw angle measurement is high-pass filtered to influence only kinematic behaviours and not interfere with the quasi-static ones, such as guidance and curving action. Based on the same principle, the stability action for this control was tested in a test rig and compared with simulation results by Liang and Iwnicki [139, 140].Concerning the DSW configuration, stabilization is achieved by simply applying guidance control with a large stability margin with respect to the speed as shown by Wickens in [150, 151]. In [151], Wickens compared stability limits of conventional passive vehicle, yaw relaxation control, ASW and DSW showing that only for the DSW configuration no stability limits exist for speed and equivalent conicity variation.

The comparison among above-mentioned schemes for stability control is summarized in Table 4.Guidance control is necessary when high-speed applications of IRW with absence of otherwise passive solutions are considered, especially considering AIRW and DIRW. As mentioned before, guidance control is aimed at actively restoring the self-steering mechanism and provides steering capability. Often, guidance control is applied together with stability control. As mentioned in the stability control section, the DSW configuration relies on different approaches with respect to the other two configurations. In fact, mechanical configurations are generally preferred for DSW to restore the self-centring capability.Controlling the two wheels to have the same speed will mimic the behaviour of a wheelset with solid axle. In this way, guidance and self-centring mechanism are restored leading though to the possibility of facing the same problems affecting a solid wheelset. This approach was proposed by Goodall et al. [122, 135] for AIRW. The external actuator will steer the IRW wheelset such that the speed difference of the two wheels is set to zero. The problem of adaptation was introduced too. As mentioned for the stability part, an \(H_{\infty }\) control using μ-synthesis was subsequently developed in [134]. Concerning DIRW, the same approach can be used where the wheel speed difference is controlled directly through the wheel motors. Ji et al. [145] studied the dependency between the synchronous motors control accuracy and the rail-wheel clearance, proposing an optimized tread profile to reduce this dependency. A model of the synchronous motors is introduced where torque ripples generated by non-uniform magnetic field and stator high harmonics currents are considered. Liu et al. [156] combined absolute yaw rate feedback (1.b) with the equal wheels speed control in a cascade PID control. Enhancement of the vehicle’s running behaviour is found when the cascade control is applied with respect to the application of the equal wheels speed control alone.Concerning AIRW, an approach to restore guidance was proposed by Pérez et al. [123, 137]. To avoid flange contact lateral clearance is set to zero. Because of the impracticality of measuring the lateral displacement of the wheelset with respect to the track centre line, a reference signal for the wheel speed difference based on the curvature of the track and the velocity of the train is derived. The reference value is obtained from the dynamic equations that describe the system. The wheels speed difference is found to be related to the rest of the variables by a first-order transfer function with low time constant that allows to neglect this contribution in the frequency range of the guidance control. The relation is then further simplified by considering the quasi-static condition during curving. The simplifications done eventually lead to an error of the obtained lateral displacement with respect to the centre line.An alternative approach to the nonzero lateral clearance is often applied. Here, the IRW is controlled to be at the centre line and thus having a zero lateral clearance. This kind of approach involves the necessity of measuring the lateral displacement of the wheelset or the usage of estimation procedures. This approach is generally applied to DIRW where additional feedback variables may be introduced. Within the ‘Next Generation Train’ project, a PD control was used by Kurzeck et al. [146] to implement the zero lateral clearance approach. In his study, Kurzeck focused on the peak torque and power required due to track irregularities. Here, a torque limiter is introduced, and a pattern search optimization is used to tune the controller with the objective of reducing the wear in curved track with irregularities. Using the same control approach but focusing on the synchronous motor control, Ahn et al. [141] successfully showed the effectiveness of this control scheme on a 1:5 scaled test rig. A feedforward action was introduced by Grether in [147] to compensate the gyroscopic moment introduced into the system in transition curves. This concept was then used by Heckmann et al. [148] in combination with a feedback control on lateral displacement, yaw angle and yaw velocity of the wheelset. In his work Heckmann also introduced a gain-scheduling approach based on the vehicle velocity to avoid possible control instability caused by speed variation. A preceding control was then implemented to improve the performance of the rear wheelset by Grether et al. [149]. The information of the leading bogie is used for an advanced control of the trailing one, leading to a further improvement in terms of wear number.

Using the lateral displacement and the yaw angle of the IRW wheelset as feedback, Lu et al. [142] developed a robust torque control using μ-synthesis. To reduce the complexity of the model, the control is based only on the model of the IRW wheelset using the bogie force and torque as external inputs. The simulation results are then experimentally validated on a 1:5 scaled test rig.

A comparison of the control performances between ASW, SYC and DRIW controlled with zero lateral clearance was proposed by Farhat et al. in [98]. Simulations are performed showing that for the cases studied DIRW performs better than other solutions. In particular, SYC is the least advantageous method. Nevertheless, Farhat et al. [143] showed that degraded performances can be seen in the diverging route of switches with respect to standard solid wheelsets, especially for high-speed switches. This does not apply to the through route though.By a combination of AIRW and DIRW concepts, Pérez et al. [137] provided steering with the AIRW concept and guidance with the DIRW concept. To facilitate the task of the steering procedure of the AIRW part, the torque on the two wheels is controlled to be equal with the DIRW part. In this way, the contact forces on the left and right wheel are virtually kept equal. In [137], the dynamic model of the synchronous motor was introduced. The separation method of field and armature winding equations is used, and the control is designed considering the field current constant.On DSW, a first approach for guidance was proposed by Wickens in [150] where the wheels are steered by an angle proportional to the tracking error. The tracking error is here defined as the error of the vehicle position with respect to the track centreline. Subsequently, a passive bogie with self-steering capability was introduced by Michitsuji and Suda in [153]. Here, a feedforward action is introduced to improve the vehicle behaviour during curve transition by compensating the disturbances that emerge from the time variation of the track curvature. The effectiveness of the solution is shown by simulation results and experimental ones carried out on a 1:10 scaled test rig.

Table 5 compares the features of different guidance controls.

Controlled independently rotating wheels are an interesting concept, having potential advantages over actively controlled solid wheelsets. Nevertheless, known implementations consist of scaled models, with exception described in [157].

The first application of a DIRW concept was developed by DLR in 1999 by Gretzschel and Bose [128] and was further developed in [138]. In the 1:5 scaled test rig of Fig. 32, the differential control is provided by an external servomotor mounted directly between the two wheels through a gearbox. The applied scaling procedure together with the obtained results is given in [158].

A 1:5 scaled wheelset was developed and tested by Liang et al. [139], [140]. Both DC and AC motors were considered. Only AC motors were tested. Equal wheel speeds and absolute yaw velocity feedback controls were applied. Good agreement of results between simulations and experiments are found. Additionally, the behaviour of the test wheelset with and without absolute yaw velocity feedback control are reported to show significant improvements when the control is applied. Another 1:5 scaled test rig was implemented by Ahn et al. [141] representing a high-depth subway system where a linear scaling was applied. Surface permanent magnet synchronous motors are used, and zero lateral clearance strategy is applied with the usage of a saturated PI controller. In Fig. 33, the above-mentioned test rig is shown.

A robust control approach was successfully applied on a 1:5 test rig by Lu et al. [142]. The scaled vehicle runs on a real track with reduced gauge differently from most of the applications that involve tests on experimental IRW vehicles. A zero lateral clearance control is applied where eddy current displacement sensors are used on both left and right wheels. The two signals are then used to estimate the wheel–rail lateral displacement and the yaw angle. In Fig. 34, the experimental vehicle is shown.

A different approach was chosen by Oh et al. [159]. Instead of developing a scaled model of the vehicle, a hardware-in-the-loop (HIL) approach is used to study the real-time behaviour of a full-scale wheel motor. A linear vehicle model is used to simulate the vehicle behaviour in which the longitudinal dynamics is considered too. Simulations and wheel motor are coupled by a load motor. The use of a linear model is justified by the need to run the model in real-time, while a more complex, nonlinear model might cause time lag in the computation of the vehicle dynamics, eventually hindering the implementation HIL. The vehicle is controlled using the zero lateral clearance strategy. The experimental set-up is shown in Fig. 35. The same authors designed the wheel motor armature windings to improve the motor performance [160, 161].

An application of DSW was proposed by Michitsuji et al. [153] on a 1:10 scaled model for the EEF bogie (Fig. 36). The vehicle was tested on a 25 m track with a curve of 3.3 m radius that corresponds to a very narrow curve of 33 m in real-scale track. The steering capability of the vehicle is improved with a feedforward control that assists the self-steering capability of the proposed design during transition curves. The vehicle is not actively steered during the circular part of the curve. A satisfactory agreement between simulation and experimental results is reported.