Control strategies

In the existing literature, a large number of control strategies have been proposed for developing basic configurations and technology options for active suspension in rail vehicles depending on the design objectives.

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Selamat et al. [67] presented the design of an active suspension control of a two-axle railway vehicle using an optimised linear quadratic regulator (LQR). The control objective was to minimise the yaw angle and lateral displacement of the wheelsets when the vehicle travels on straight and curved tracks with lateral irregularities, where the active yaw damping replaced the longitudinal springs to provide yaw torque.

Li and Hong[24] investigated the trade-off between the maximum deflection of the damper and acceptable levels of ride quality. Different control methods have been applied to the Skyhook active suspension system in order to optimise the trade-off between the random and deterministic track input requirements. Results showed that improvement of around 20% in ride comfort could be achieved with a linear complementary filter and about 50% by using nonlinear Kalman filter strategies.

Moreover, the dynamic movements of railway vehicles are highly interactive, and the DOF order is usually high. Therefore, some form of dynamic simplification can be applied. Mei et al. [68] performed a modal decomposition using the modal controller approach to active steering of the railway vehicle. The development of a modal control approach was applied to a two-axle railway vehicle to decouple body lateral and yaw motions, which enables the development of independent controllers for the two movements. Results showed a significant improvement in vehicle performance on curves and improved the ride quality by around 25% compared to a passive vehicle on a straight track.

Furthermore, the interaction issue between the vehicle body roll and the lateral dynamics substantially influence the tilting system in a high-velocity railway vehicle, which results in a negative impact on ride quality. Therefore, integrating an active secondary suspension system into the tilting control system is one of the solutions to improving the design trade-off between straight truck ride quality and curving performance. In the study, Zhou et al. [69] presented a novel active suspension integration strategy that combines tilting control with active lateral

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secondary suspension, which can enhance tilt control system performance and ride quality. Another study by Zhou et al. [70] investigated H∞ decentralised control compared with a traditional decentralised control for the integrated tilt control with active lateral secondary suspension in high-speed railway vehicles. H∞ decentralised control was used to overcome the control loop interaction in the classical decentralised control and improve the performance of the local integrated suspension control. Zhou et al. [71] applied advanced system state estimation technology, which used the estimated vehicle body lateral acceleration and true cant deficiency to enhance the system performance further.

Further, the hunting phenomenon is a very common instability exhibited by railway vehicles. It is a self-excited lateral oscillation that is produced by the forward speed of the vehicle and wheel-rail interactive force, which results from the conicity of the wheel – railway contours and friction – and the creep characteristic of the wheel – railway geometry.

A theoretical and an experimental study of stabilisation control methods for the hunting problem in a simple wheelset model was proposed by Yabuno et al. [72]. It was concluded that applying a lateral force proportional to yawing motion can increase the critical speed of the railway vehicle. In another study, a controlled electro-mechanical actuator was designed to substitute for a traditional yaw damper that was used to apply a longitudinal force between the vehicle and the bogie. It was concluded that applying longitudinal forces opposite to yawing velocity can maximise the amount of energy dissipation. Mohamadi et al. [73] designed an active control for lateral vibration for a bogie using a variable structure model reference adaptive control. Results showed that using active suspension can be achieved at higher velocities. Pearson et al. [74] presented a comparison of control algorithms for an actively stabilised wheelset on a high-speed railway vehicle; this was applied to yaw torque to provide a bogie which is stable at high speed without the need for a heavy secondary yaw damper.

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Model predictive control based on a mixed H2/H∞ control method has been compared with a classical skyhook controller. This control approach achieved good ride quality while keeping the suspension deflection to its minimum limits, and it is concluded that the proposed controller has the advantage of being multi-objective [75].

3.3

Semi-Active Suspension Systems

Among the many different types of controlled suspensions, semi-active suspension systems have received considerable attention since they achieve the best compromise between cost and performance[15, 40]. The concept of the semi-active suspension system is to apply a controllable device which does not need significant external power to work. The semi-active controllable device is able to respond to feedback control signal from a semi-active control system to control undesired vibrations. The performance of the semi-active suspension system is highly dependent on the selection of an appropriate control strategy and characteristics of the semi-active damper, such as the lower and the upper limits of the damping setting and how fast it can be switched, are particularly important [76].