Self-tuning cross-coupled two degree-of-freedom PID control for position synchronization of dual linear motors

Syuan Yi Chen*, Chin Sheng Chen, Zhen Wei Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


The objective of this study is to propose a self-tuning cross-coupled two degree-of-freedom (DOF) proportional-integral-derivative (PID) control strategy for position synchronization of a dual linear motors (DLMs) driven stage. First, independent one DOF PID (I1PID) control and cross-coupled 1PID (C1PID) control are designed to control the DLMs. Subsequently, independent two DOF PID (I2PID) control and cross-coupled 2PID control (C2PID) are built to further examine the enhanced control performances of the two DOF control systems; the structure of the C2PID control provides improvement over the C1PID in control performance. Nevertheless, it is arduous to tune three main parameters including the proportional gain, the integral time, and the derivative time as well as two compensation parameters including the proportional and the derivative constants. In this regard, a self-tuning C2PID (SC2PID) control is developed in which all the control parameters are dynamically and concurrently optimized through an improved artificial bee colony algorithm. Numerical simulations and experimental results indicate that the proposed SC2PID control exhibits optimal tracking performance with lowest synchronous error when compared with other control schemes.

Original languageEnglish
Pages (from-to)214-234
Number of pages21
JournalApplied Mathematical Modelling
Publication statusPublished - 2018 Dec


  • Artificial bee colony (ABC) algorithm
  • Cross-coupled control
  • Dual linear motors (DLMs)
  • Synchronous control
  • Two degree-of-freedom (DOF) proportional-integral-derivative (PID) control

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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