A Control Model for Metro Train Movements: The Piecewise Nonlinear Time-domain Model

Abstract

Metros have been becoming a mainstream means of transportation in China. The research of various aspects of metro transportation has developed rapidly. However, how to construct a practical control model has always been a research hotspot. In this paper, we propose a piecewise nonlinear time-domain model (PNTM). This model describes a piecewise control process of the train driving in each section. The most notable feature of PNTM is that according to the electromagnetic principle of the motor, the acceleration process of the train is divided into three phases: constant torque, constant power, and natural characteristic. In each operation phase, speed, position, and instantaneous power are chosen to describe driving states of the train. Moreover, functional expressions instead of differential equation sets are used to formulate the driving states. Finally, the model is validated by numerical examples for comparison with the linear model and the measured data in real cases in Shanghai Metro Line 1 (SML1). The experimental results indicate that the correlation coefficients between PNTM and the measured data in terms of speed and power are 0.9874 and 0.9999, respectively, which are much higher than the 0.9251 and 0.9996 of the linear model.