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Piezoelectric actuators (PEAs) are widely applied in various nanopositioning equipment. However, the strong hysteresis nonlinearity compromises the positioning accuracy. In this work, a novel modified Bouc-Wen (MBW) model with a polynomial function of the differential of the input is established for modelling the hysteresis nonlinearity of the PEA-actuated nanopositioning stages. The particle swarm optimisation algorithm is adopted to identify the parameters of the MBW model with a set of input-output experimental data. The obtained model with the corresponding identification parameters matches well the experimental data with 0.31% relative error. A feedforward compensator based on the obtained model is also applied to compensate the hysteresis nonlinearity. Experiments are conducted to validate the effectiveness of this approach, and the results show the great improvement of positioning accuracy of the stage.

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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.