Non-linear contour tracking using feedback PID and feedforward position domain cross-coupled iterative learning control

Abstract

In this paper, a position domain cross-coupled iterative learning controller combining proportional–integral–derivative (PID)-type iterative learning control (ILC) and proportional–derivative (PD)-type cross-coupling control (CCC) is presented aiming at non-linear contour tracking in multi-axis motion systems. Traditional individual control methods in the time domain suffer from poor synchronization of relevant motion axes. The complicated computation of coupling gains in CCC and cross-coupled ILC (CCILC) restricts their applications for non-linear contour. The proposed position domain CCILC (PDCCILC) approach introduces a position domain design concept into CCILC to improve synchronization and performance for non-linear contour tracking and it relies less on the accuracy of coupling gains than conventional CCILC. The stability and performance analysis are conducted using a lifted system representation. The contour error vector method is applied to estimate the coupling gains in simulations and experiments. Simulation and experimental results of three typical non-linear contour tracking cases (i.e. semi-circle, parabola and spiral) based on a two-axis micro-motion stage demonstrate superiority and efficacy of the proposed feedback PID and feedforward PDCCILC compared with existing ILC and CCILC in the time domain.