A Novel Iterative Learning Approach for Tracking Control of High-Speed Trains Subject to Unknown Time-Varying Delay

Abstract

In this article, a novel iterative learning control scheme is proposed for high-speed trains, aiming to track the desired reference displacement and velocity, where the Krasovskii function is constructed to compensate for the negative influence of unknown time-varying speed delays. The main feature of the proposed approach is that the hyperbolic tangent function and the command filter are integrated into the learning controller to overcome the singularity problem that may occur during the control process and relax the requirement for the derivability of the desired velocity. The stability of control system is strictly proved through establishing the composite energy function, and the effectiveness is confirmed via numerical simulations. Compared with the existing works, the merits of the proposed control scheme lie in that more general nonlinear uncertainties are imposed on the dynamic model of train instead of the Lipschitz condition, and the reference acceleration assigned by the railway department is not required. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —High-speed train always runs periodically on the same railway, e.g., the same tunnels, slopes, and bridges, according to the scheduling plans developed by the railway department. Due to the repetitive operation pattern, the iterative learning control has the prospect of becoming an inherent method for devising the tracking controller of trains. Nevertheless, the unknown speed delays, which are inevitable due to the damping effect of wheel rails, couplers, and so on as well as the disturbance of external environments, may degrade the performance of control system and even cause instability in severe cases. As a result, this article exploits a compensation method to eliminate the effects of unknown delay under the iterative learning control framework, thus guaranteeing the safety of train operation and the comfort of passengers. To enhance the practicability, the hyperbolic tangent function is introduced to keep the continuity of control signal, and the command filter is synthesized to reduce the complexity of controller implementation. Although the stability analysis and numerical simulations have confirmed the feasibility and effectiveness of the proposed scheme, it is still expected to be verified by experiments in the future.