具大參數變化之多變數控制系統的定量回授設計

Abstract

在本論文中吾人提出數種"定量回授設計" 方法，來解決有關「具大 參數變化之多變數線性非時變控制系統」之設計問題。在兩自由度控制系 統之架構下，設計之主要任務在尋找適當之強健性補償器，以便達成下列 兩點目標: (1)頻道間之相互影響力應降至一可接受之準位，(2)系統頻率 響應需在所容許之範圍內。根據本文所提供之方法，一個n階多變數控制 系統之設計問題被轉換成n個單輸入-單輸出控制系統之設計問題，因此 SISO-QFT之方法可直接應用於設計工作中。在Schauder's fixed-point 定理之保證下，吾人導出兩個充分條件，使得系統各頻道間相互影響之限 制規格得以確保。此外，吾人亦提出兩種全新之量測指標，即相對誤差量 和絕對誤差量，可用來評估已完成設計之系統各頻道間耦合量之大小。為 使頻率響應能落在所容許之範圍內，本論文提供兩種處理方式。第一種方 式是發展出一套可快速分配原先給定之"性能容許範圍"之法則，使得設計 工作得以系統化進行。第二種方式是利用相對誤差量或絕對誤差量兩種指 標，先行評估系統各頻道間相互影響之程度，在允許一微小的耦合量之條 件下，每一主頻道之頻響能以一種近似法則處理。值得一提的是在第一種 方法中，它提供了各頻道性能規格值相互調整之權衡能力，此舉可讓各頻 道之"回授成本"作最佳調配。吾人最後亦提出了一種有效的解耦合設計架 構，該架構因另外使用了一全階非對角補償器，可額外提供n x (n-1)個 自由設計參數，來降低系統因使用僅具對角元素之補償器所帶來之過量設 計。透過不同例子之分析與說明，驗證了論文中所提各種設計方法之實際 性與有效性。 In this thesis, several quantitative feedback design schemes are provided for designing the linear time-invariant multivariable feedback control system with large plant uncertainty. Each element of the plant transfer function matrix is described with a bounded parameter range. The objective is to find proper robust compensators, embedded in a two-degree-of-freedom structure, such that not only is the channel interaction suppressed to an acceptable level, but the system frequency response should lie within the prescribed main channel performance boundaries. Under the proposed design framework, the synthesis of an n x n MIMO control system is replaced by n single-input single-output(SISO) design problems, so that the SISO-QFT method can be directly invoked for designing. Based on Schauder's fixed-point theorem, two sufficient conditions have been derived for assuring the achievement of the noninteracting performance, or alternatively, the off-diagonal performance. Two new interaction indexes, the relative error and the absolute error, are derived to serve as a practical measure for assessing the achieved noninteraction of the system. The use of these indexes as noninteraction measure is shown to be very simple even for the system of large dimension. On the other hand, the division of the given main channel performance tolerance is either re-allocated in a systematical basis or omitted completely by using the concept of the relative error and the absolute error, which forms a foundation for achieving the prescribed main channel performance. Remarkably, the proposed approach is with the capability to trade off the performance bound between the loops, so that the cost of feedback in each loop can be compromised. Finally, we give a practical decoupling mechanism, using a full-order compensator, to reduce the inherent overdesign limited by using a diagonal compensator.