Modelling and Control of Active Suspension System for Railway Vehicle

Abstract

A high-speed railway system is one of the sustainable alternatives to other modes of transportation and may connect the most congested urban cities with minimum carbon emissions. However, the vibration intensity also increases as the train's operating speed increases, leading to a decline in both ride comfort and stability. Both passenger ride comfort and vehicle stability are the essential aspect of performance evaluation in high speed railway vehicles, which can be accomplished by employing effective vibration control techniques. Previously, different control strategies have been adopted in this context; however, a completely effective method has not yet been revealed. Hence, the prime focus of this work is to investigate a thirty-eight-degree-of-freedom (38-DOF) dynamic model of a full-scale railway vehicle integrated with effective control strategies to reduce the railway vehicle vibrations using active suspension system. The dynamic models of the system are developed by considering the translational and rotational motion of the car body, bogies, and wheelsets. The wheel-rail contact model and the rail irregularities model are also incorporated in the analytical model. The developed dynamic model has been translated into the two-dimensional state-space model to evaluate the effect of different track irregularities on the human ride comfort. The railway vehicle's vibration analysis is conducted at different speeds for the vertical, lateral and longitudinal directions and the critical velocity of the vehicle is evaluated. The spectral analysis techniques have been employed to analyze the output frequency response of the railway vehicle's motion. The outputs are defined in three-dimensional Power Spectral Densities under three random track irregularities: vertical profile, lateral alignment, and cross-level. Furthermore, the Sperling's method has been used to evaluate the human comfort index. For the case study, a Linke-Hofmann-Busch coach based model has been employed, and the results are validated with the experimental data of ride comfort reported by the Research Design and Standard Organization (RDSO). The simulated results of the proposed model demonstrate a remarkable alignment with the experimental data, exhibiting a small error ranging from 2.36 8.81% for vertical motion and 5.84 8.30% for lateral motion, respectively. Such promising results offer valuable insight for the design of future coaches, ensuring enhanced ride comfort even at high speeds. However, controlling different motions during vibration control is also an imperative criterion to achieve the desired passenger ride comfort and stability. Hence, a decentralized control structure has been developed, which performs the controlling action with five optimized Fractional Order Proportional Integral Derivative controllers that suppress the vehicle body's vertical, lateral, pitch, roll, and yaw motions. To obtain tight controller tuning parameters of the FOPID, a novel metaheuristic optimization technique named hybrid Particle Swarm Optimization-Gray Wolf Optimization has been proposed. The simulated results are compared with the passive system as well as other conventional (Z-N) and two metaheuristic optimization tuning techniques named as PSO and GWO. Moreover, the performance of the proposed control strategy is evaluated in the time and frequency domain under random track irregularities, and the results are characterized in terms of power spectral densities. The simulated results show that the hybrid metaheuristic algorithm outperforms with a significant reduction in vehicle vibration compared to other tuning methods. The percentage reduction of the vertical, lateral, pitch, rolls, and yaw accelerations is 34.83%, 29.27%, 39.17%, 24.99%, and 33.45%, respectively, ensuring enhanced vehicle ride comfort. To better control action further, a sophisticated control strategy with the combination of an adaptive neuro-fuzzy inference system and a linear quadratic Gaussian controller tuned with equilibrium optimization has been analyzed. The effectiveness of the suggested control technique is assessed in the time and frequency domain under random track excitations. Moreover, the ride comfort enhancement capability of the proposed with passive systems and the classical tuning methods. The findings suggest that the EO-LQG controller offers a promising solution for enhancing ride comfort as the percentage reduction in RMS values for the vertical, lateral, pitch, roll, and yaw acceleration are 35.62%, 24.98%, 38.77%, 27.98%, and 35.68%, respectively. On the other hand, the active suspension system tuned with classical methods shows lower reduction capability as compared to proposed technique. Also, the ride comfort indices for vertical motion using EO algorithms are found to be 2.482, and for lateral motion, the indices were 2.528, representing a superior level of comfort compared to that of passive and other tuning algorithms. Eventually, despite having sound suspension systems and efficient control algorithms, the suspension system performance deteriorates with time. Hence, this work proposes a robust active vibration control system with two different robust control techniques, and -synthesis, integrated with the Kalman estimator. For analysis, a 27-degree of freedom model consisting of structured and unstructured uncertainties has been considered. The robust stability and the robust performance of the proposed control strategies have been evaluated using the structured singular values. The time and frequency domains of the closed loop perturbed responses to random track disturbances are shown. The root mean square values of the accelerations of the car bodies are used to compare the suggested control schemes to the passive system. The primary focus of this study is to examine the level of ride comfort provided by the railway vehicle in the uncertain environment. To achieve this, simulated findings are compared and verified against experimental data collected and reported by the RDSO. The observational data demonstrates that the results obtained from the suggested control methods are in close agreement with the experimental findings, with a minimal disparity ranging from 2.36% to 8.81% for lateral motion and 2.84% to 6.30% for vertical motion. Also, the percentage improvement of RMS values with -synthesis controller confirms the enhancement of the ride comfort as compared to other techniques. Some directions for the future extension of the current research work have also been identified and discussed.