Cascade Modular Path Following Control Strategy for Gantry Virtual Track Train: Time-Delay Stability and Forward Predictive Model

Abstract

The virtual track train (VTT) is a new type of urban transit system with all-wheel active steering technology utilized to make the long combination vehicle run along the planned route (virtual track) like railway vehicles along physical track. This paper proposed a scalable cascade modular path following control strategy for the newly designed gantry virtual track train (G-VTT) based on preview & tracking controller, focusing on the lateral control for low-speed turning manoeuvre. The mathematical characteristics of the 2-norm was utilized to establish a local tracking objective function (LTOF) to find the optimal lateral acceleration (OLA) of the tracking point in the preview window and calculate the optimal wheel steering angle (WSA) to achieve the optimal local trajectory. Considering the lag time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , the yaw stability and path following ability of the vehicle are contradictory in some cases, so the damping adjustment factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> was proposed to optimize the damping characteristics and the time-delay stability factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ξ</i> was proposed to evaluate the time-delay stability. The influence of the key parameters, preview time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ξ</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> , on the stability and following ability were analyzed by frequency domain analysis method, and the optimal region of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ξ</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> was obtained to instruct the configuration of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> . Finally, steady-state and dynamic forward predictive models were proposed to compensate for the oscillation caused by the lag time. The effectiveness of the proposed control strategy, forward predictive models and the configuration method of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> were verified by theoretical analysis and numerical simulation.