漸進式消除定週期或變週期干擾之控制器設計

Abstract

反覆控制(Repetitive Control)能漸進式的追蹤或消除週期性信號。本論文利用近代數學的算子理論(Operator Theory)重新推導反覆控制法則，此推導不但有助於瞭解其學習性控制的機制，更有助於發展出一個設計學習性或適應性演算法的通用方法。反覆控制包含兩個重要的算子（Operator），其中一個算子為受控系統（Plant）的約略倒系統(Rough Inversion)，此算子與反覆控制系統的穩定度與暫態反應速率息息相關。另一算子為延遲算子（Delay Operator），為了完美地漸進消除週期噪音，此延遲算子的延遲時間必須等於噪音的週期。基於這些觀察，本論文設計一個可調的延遲器於一個快速收斂的反覆控制系統中，因而能有效消除變換週期的週期性噪音。與現有方法比較，此方法不但能有減低穩態誤差，亦能保持系統的穩定度與暫態特性。將此方法應用於主動式管路噪音消除，其模擬結果證明此方法的優越性。

Repetitive control, widely used to asymptotically track or reject periodic signals, has conventionally been derived by the internal model principle. However, this dissertation presents a new constructive derivation of repetitive control via iterative operator inversion and the contraction mapping principle. This alternative derivation helps clarify the learning mechanism of repetitive control and also suggests a promising unified method to the design of learning or adaptive algorithms based on the contraction mapping principle. Based on the derivation, a generalized digital repetitive control with adjustable delay FIR filter is presented. The proposed method introduces a delay FIR filter in the repetitive control law, which optimally interpolates the signal between samples and thus effectively reconstructing the signal of the previous period. Accordingly, the proposed repetitive control can reject periodic disturbance whose period is not exactly an integer multiple of the sampling interval. The delay FIR filter is optimally synthesized in a reproducing kernel Hilbert space. The resulting optimal delay filter can be updated easily according to different signal periods. Thus it is specifically suitable for on-line tuning when the signal period is varying. This naturally leads to an alternative adaptive repetitive control algorithm for asymptotic tacking or rejecting periodic signals with varying period. Compared with the available tuning methods, this delay filter tuning method has excellent steady-state performance while maintaining fast transient and system robustness. The simulations on active noise cancellation within a duct confirm the superiority of this tuning method.