The feedforward control strategy exhibits substantial capability and high-precision control for output tracking tasks. However, the feedforward control action obtained through solving the inverse problem is unstable for non-minimum phase systems. In this paper, a novel stable inversion method is presented, termed lifted time stable inversion. Compared to the existing method, the proposed method does not necessitate infinite window to accomplish the tracking tasks. A comprehensive analysis of the developed method is provided, focusing on analysis of finite time stability and input–output finite time stability, aspects that have garnered limited attention in the literature on feedforward control. Furthermore, the relationship with existing stable inversion method is illustrated by constructing a linear transformation of the initial conditions for both inversions. Simulation results substantiate the validity of the finite time bounds and demonstrate the superior tracking advantage of the proposed method relative to the existing method. The performance of the proposed method is further displayed experimentally on a piezoelectric ceramic positioning platform.

中文翻译：

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用于线性非最小相位系统的基于升降时间稳定反相的前馈控制


前馈控制策略对输出跟踪任务表现出强大的能力和高精度的控制。然而，通过求解逆问题获得的前馈控制动作对于非最小相位系统来说是不稳定的。在本文中，提出了一种新的稳定反演方法，称为提升时间稳定反演。与现有方法相比，所提方法不需要无限窗口来完成跟踪任务。对开发的方法进行了全面分析，重点是有限时间稳定性和输入输出有限时间稳定性的分析，这些方面在前馈控制的文献中引起了有限的关注。此外，通过构建两种反演的初始条件的线性变换来说明与现有稳定反演方法的关系。仿真结果证实了有限时间边界的有效性，并证明了所提方法相对于现有方法的卓越跟踪优势。在压电陶瓷定位平台上进一步实验展示了所提方法的性能。