Jie Ling

A Position Domain Cross-Coupled Iteration Learning Control for Contour Tracking in Multi-axis Precision Motion Control Systems

A novel cross-coupled iteration learning controller in position domain is presented to improve contour tracking performance for multi-axis micro systems executing repetitive tasks. The position domain iteration learning control PDILC is combined with position domain cross-coupled control PDCCC to develop a position domain cross-coupled iteration learning control PDCCILC. The stability and performance analysis are given based on lifted system representation in time domain. To illustrate effectiveness and good tracking performance of the proposed control method, simulation studies are conducted based on an identified model of a three dimensional micro-motion stage.

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

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.

A model-data integrated iterative learning controller for flexible tracking with application to a piezo nanopositioner

In precise motion systems, feedforward controller is a key component for significant performance enhancement. However, traditional iterative learning control (ILC) works efficiently under strictly repetitive reference input, and the performance of model-based feedforward controllers is limited by the non-minimum phase zeros and modeling uncertainties during executing tasks. In this paper, a model-data integrated ILC is proposed for flexible tracking, where the stable part of the identified model is utilized to compose the model-based part, and the modeling error and gain mismatch are compensated by the data-driven approach via constructing a parameterized finite impulse response filter. In order to diminish the effect of noise, an instrumental variable method is adopted in the cost criterion. The proposed controller has an analytic solution and retains stability during iterations, which is verified on a piezo nanopositioner. Comparative experimental results indicate that the proposed controller can realize flexible tracking in comparison with norm optimal ILC, and achieve the best performance compared with zero-phase-error tracking controller and polynomial basis functions feedforward controller.

High-bandwidth and flexible tracking control for precision motion with application to a piezo nanopositioner

For precision motion, high-bandwidth and flexible tracking are the two important issues for significant performance improvement. Iterative learning control (ILC) is an effective feedforward control method only for systems that operate strictly repetitively. Although projection ILC can track varying references, the performance is still limited by the fixed-bandwidth Q-filter, especially for triangular waves tracking commonly used in a piezo nanopositioner. In this paper, a wavelet transform-based linear time-varying (LTV) Q-filter design for projection ILC is proposed to compensate high-frequency errors and improve the ability to tracking varying references simultaneously. The LVT Q-filter is designed based on the modulus maximum of wavelet detail coefficients calculated by wavelet transform to determine the high-frequency locations of each iteration with the advantages of avoiding cross-terms and segmenting manually. The proposed approach was verified on a piezo nanopositioner. Experimental results indicate that the proposed approach can locate the high-frequency regions accurately and achieve the best performance under varying references compared with traditional frequency-domain and projection ILC with a fixed-bandwidth Q-filter, which validates that through implementing the LTV filter on projection ILC, high-bandwidth and flexible tracking can be achieved simultaneously by the proposed approach.

Data-based double-feedforward controller design for a coupled parallel piezo nanopositioning stage

Vibrations as well as cross-coupling effects severely hinder fast and accurate tracking for coupled parallel piezo nanopositioning stages. In this article, a data-based double-feedforward controller is proposed to reduce individual-axis repetitive errors and cross-coupling-caused errors simultaneously. The proposed approach utilizes modeling-free inversion-based iterative control to compensate repetitive errors and data-based feedforward decoupling controller to eliminate cross-coupling effect, which has the advantages of no need for accurate identified process and alleviating the difficulty in inversion of non-minimum phase systems. Comparative experiments were performed on a piezo parallel nanopositioning stage to validate the effectiveness of the proposed controller. Experimental results indicate that the cross-coupling errors are compensated significantly and the fast and accurate tracking can be achieved via implementing the proposed controller on planar raster scanning and XY star trajectory with different tracking periods.

Data-Driven Feedforward Decoupling Filter Design for Parallel Nanopositioning Stages

Cross-coupling effect severely hinder fast and accurate tracking for parallel piezo nanopositioning stages. In this paper, a data-driven feedforward decoupling filter (DDFDF) is proposed to reduce the cross-coupling caused errors. Traditional control methods for coupled system could achieve good performance on the premise that the dynamic model is accurate and no non-minimum phase zeros exist. The proposed method is totally data-driven with the advantage of no need for accurate identified model and model structure by Gauss-Newton gradient-based algorithm. The DDFDF for eliminating cross-coupling errors was verified on a 2-DOF coupled nanopositioning stage through simulations. Results show the effectiveness of the proposed controller by comparing with open-loop simulations and the well-designed feedback controller.

Combined Model-Free Decoupling Control and Double Resonant Control in Parallel Nanopositioning Stages for Fast and Precise Raster Scanning

A design of double resonant control combined with a model-free decoupling filter (MFDF) is presented in this paper. The design is demonstrated using the proposed MFDF to decouple a parallel multi-input multi-output (MIMO) system into several single-input single-output systems and applying a double resonant controller for vibration damping and cross coupling reduction in nanopositioners. Raster scan results of simulations based on an identified MIMO transfer function of a nanopositioning stage over an area of 4 μm × 0.4 μm with small RMS errors are demonstrated. Comparisons with using the double resonant controller alone show the effectiveness of the proposed controller.

A position domain iteration learning control for contour tracking with application to a multi-axis motion testbed

To improve contour tracking performance for multi-axis precision motion systems, a position domain iteration learning control (PDILC) is presented in this paper. Traditional control approaches design controllers in time domain individually, thus suffer from poor synchronization of relevant motion axes and result in restriction for contour tracking tasks. Our approach is to combine the positon domain method with the ILC to reduce the contour errors and individual axis simultaneously for repetitive tasks. Stability and convergence analysis of the proposed method are conducted through lifted system representation method. Performance of the PDILC, traditional time domain ILC (TDILC) and feedback control lonely are evaluated and compared through numerical simulations and experimental testing based on a multi-axis precise positioning stage. The proposed method enhances the precision contour tracking performance of the testbed.