數據驅動之迭代學習控制於多變數非線性動態系統之研究

Abstract

在高度重複性運作的精密系統場域中例如：工具機[1]、工業機器人[2]、半導體製程[3]等，迭代學習控制因為其優異的追蹤性能已經被廣泛應用在各種工業量產製程中。迭帶學習控制的效能與收斂性主要建基於系統模型的準確性和有效的學習演算法。對於具有非線性動態的系統，其模型取得不易且成本高昂，設計對應的演算法亦是一個技術挑戰。在先輩的方法中[4]，適應性濾波被巧妙地使用來追蹤單變數非線性系統沿著動態軌跡變化的線性化模型並產生對應的逆動態系統，因此從迭代學習的觀點能夠將輸入輸出視作一線性的非時變系統進行分析和演算法實理。因其數據驅動的特性，減少了建模成本與不確定性造成的影響，並提供了演算法收斂性分析的依據。然而，該方法在具有動態耦合之多變數系統的延伸未有著墨，由於轉移函數矩陣乘法交換律的不成立會對演算法設計與分析帶來更多挑戰。本論文即對此部分提出推廣至多變數的數據驅動迭代學習演算法，提出數種能夠針對加速誤差收斂速度的演算法進行比較，在線性非時變系統與非線性動態系統上進行模擬，並在龍門式x-y平台上實驗驗證。

In highly repetitive operations within precision systems fields, such as machine tools [1], industrial robots [2], and semiconductor manufacturing processes [3], iterative learning control (ILC) has been widely applied in various industrial production processes due to its exceptional tracking performance. The effectiveness and convergence of ILC primarily depend on the accuracy of the system model and the efficiency of the learning algorithms. However, obtaining an accurate model for systems with nonlinear dynamics is a demanding and costly task, presenting a significant technical hurdle. Previous approaches [4] have cleverly employed adaptive filtering to track the linearized model of single-variable nonlinear systems along their dynamic trajectories and generate corresponding inverse dynamic systems. This perspective enables the analysis and algorithm development of the input-output relationship as a linear time-invariant system, providing a data-driven solution that mitigates the impact of modeling costs and uncertainties. Moreover, it offers a foundation for convergence analysis of the algorithms. Nevertheless, extending this method to multivariable systems with dynamic coupling remains unexplored. The non-commutativity of transfer function matrix multiplication introduces additional complexities in algorithm design and analysis. This thesis addresses this gap by proposing an extension of the data-driven iterative learning algorithm to multivariable systems. Several algorithms capable of accelerating error convergence rate are compared, with simulations conducted on both linear time-invariant systems and nonlinear dynamic systems. Experimental verification is performed on a gantry-type x-y platform.