Feng Zhao, Ling Jie, Ming Min, Xiao Xiao-Hui
Hubei Key Laboratory of Waterjet Theory and New Technology, Wuhan University, Wuhan 430072, China.
Rev Sci Instrum. 2017 Aug;88(8):085107. doi: 10.1063/1.4998303.
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.
对于精密运动而言，高带宽和灵活跟踪是显著提升性能的两个重要问题。迭代学习控制（ILC）是一种仅适用于严格重复运行系统的有效前馈控制方法。尽管投影迭代学习控制能够跟踪变化的参考信号，但其性能仍受限于固定带宽的Q滤波器，特别是对于压电纳米定位器中常用的三角波跟踪。本文提出一种基于小波变换的线性时变（LTV）Q滤波器设计用于投影迭代学习控制，以补偿高频误差并同时提高跟踪变化参考信号的能力。线性时变Q滤波器基于小波变换计算的小波细节系数的模极大值来设计，以确定每次迭代的高频位置，具有避免交叉项和无需手动分段的优点。所提方法在压电纳米定位器上得到验证。实验结果表明，与传统频域和具有固定带宽Q滤波器的投影迭代学习控制相比，所提方法能够准确地定位高频区域并在变化参考信号下实现最佳性能，这证实了通过在投影迭代学习控制上实现线性时变滤波器，所提方法能够同时实现高带宽和灵活跟踪。
