发表机构
Institute of Control Systems, Johannes Kepler University Linz（林茨约翰·开普勒大学控制系统研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对后向平坦非线性离散时间系统，提出一种基于平坦性的跟踪控制器设计方法，通过隐式欧拉离散化构造后向平坦离散系统，采用含平坦输出后向移位的线性化反馈降低误差动力学阶数，并以二维龙门起重机验证了方法有效性。
AI 中文摘要
本文针对后向平坦非线性离散时间系统，研究基于平坦性的跟踪控制器设计问题。首先，通过对结构平坦的三角表示应用隐式欧拉离散化，可从微分平坦连续时间系统构造性地得到后向平坦离散时间系统。随后，考虑后向平坦系统的两种精确线性化方法：除了基于预延拓的动态反馈外，还可采用包含平坦输出低阶后向移位的线性化反馈，无需显式实现对应的动态扩展，这能降低所得跟踪误差动力学的阶数，仅需存储过去系统轨迹的值。基于所得线性输入输出表示，推导了基于平坦性的跟踪控制律，并以二维龙门起重机为例，对所提离散化方法和控制器设计进行了验证。
英文摘要
This paper addresses the design of flatness-based tracking controllers for backward-flat nonlinear discrete-time systems. First, we show that backward-flat discrete-time systems can be constructively obtained from differentially flat continuous-time systems by applying an implicit Euler discretization to a structurally flat triangular representation. Subsequently, two approaches for the exact linearization of backward-flat systems are considered. Besides a dynamic feedback based on prelongations, we show that a linearizing feedback involving lower-order backward-shifts of the flat output can be employed without explicitly implementing the corresponding dynamic extension. This allows the order of the resulting tracking error dynamics to be reduced while requiring only stored values of past system trajectories. Based on the resulting linear input-output representation, flatness-based tracking control laws are derived. The proposed discretization and controller design are illustrated for a 2D gantry crane.
