# Optimized Model Predictive Controller Using Multi-Objective Whale Optimization Algorithm for Urban Rail Train Tracking Control

## TL;DR

This paper introduces an improved control system for urban trains that reduces energy use and improves performance using an optimized algorithm.

## Contribution

A novel MPC-MOWOA control strategy with enhanced convergence and adaptability for urban rail train tracking.

## Key findings

- The proposed control strategy reduces energy consumption by nearly 5.9% compared to Fuzzy-PID.
- Integral of time-weighted absolute error is reduced by nearly 39.6% with the new method.
- Punctuality, stopping accuracy, and comfort improve by 33.2%, 12.4%, and 7.1%, respectively.

## Abstract

With the rapid development of urban rail transit, train operation control is required to meet increasingly stringent demands in terms of energy consumption, comfort, punctuality, and precise stopping. The optimization and tracking control of speed profiles are two critical issues in ensuring the performance of automatic train operation systems. However, conventional model predictive control (MPC) methods are highly dependent on parameter settings and show limited adaptability, while heuristic optimization approaches such as the whale optimization algorithm (WOA) often suffer from premature convergence and insufficient robustness. To overcome these limitations, this study proposes an optimized model predictive controller using the multi-objective whale optimization algorithm (MPC-MOWOA) for urban rail train tracking control. In the improved optimization algorithm, a nonlinear convergence mechanism and the Tchebycheff decomposition method are introduced to enhance convergence accuracy and population diversity, which enables effective optimization of the initial parameters of the MPC. During real-time operation, the MPC is further enhanced by integrating a fuzzy satisfaction function that adaptively adjusts the softening factor. In addition, the control coefficients are corrected online according to the speed error and its rate of change, thereby improving adaptability of the control system. Taking the section from Lvshun New Port to Tieshan Town on Dalian Metro Line 12 as the study case, the proposed control algorithm was deployed on a TMS320F28335 embedded processor platform, and hardware-in-the-loop simulation experiments (HILSEs) were conducted under the same simulation environment, a unified train dynamic model, consistent operating conditions, and an identical evaluation index system. The results indicate that, compared with the Fuzzy-PID control method, the proposed control strategy reduces the integral of time-weighted absolute error nearly by 39.6% and decreases energy consumption nearly by 5.9%, while punctuality, stopping accuracy, and comfort are improved nearly by 33.2%, 12.4%, and 7.1%, respectively. These results not only verify the superior performance of the proposed MPC-MOWOA, but also demonstrate its capability for real-time implementation on embedded processors, thereby overcoming the limitations of purely MATLAB-based offline simulations and exhibiting strong potential for practical engineering applications in urban rail transit.