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

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.