臺灣博碩士論文加值系統

儘管PID控制演算法是一門老舊的學問，但它仍廣泛的使用在多變的控制系統中。PID控制能長久被使用是在於它PID演算法本身的原理是易懂的且其控制行為在各種程序上都是令人滿意的。此外，能簡單的實行也是為何PID控制器在工業程序能長久最受大眾化應用的理由之一。數位計算器和/或微處理器。PID控制演算的執行和調節變得可調性。
本論文中吾人考慮的問題在定義PID控制器增益的集合是其能夠使n階的離散時間系統穩定化。分析並推導在控制器增益空間中穩定區域邊界的特徵式。此一方法的基本構想是來自已參數化法計算離散系統的均方差(mean-squired-error)。此步驟比Xu等學者簡化利用了Hermite-Biehler theorem 的連續時間的觀點時間來做雙線性轉換。並且為了得證此一步驟並舉一數值範例說明之。

Although the PID control algorithm is old, it is still widely used in a variety of industrial control systems. The longstanding use of PID controllers lies in the facts that the principle of PID algorithm is easy to understand and the control performance is satisfactory for a wide class of processes. Moreover, simplicity of implementation is also one of the reasons why PID controller remains the most popular approach for industrial process control despite continual advances in control theory. This is particularly true after the advent of digital computers and/or microprocessors. With the availability of low-cost programmable microprocessors, the implementation and tuning of PID control algorithm becomes advantageously flexible.
This paper is concerned with the problem of determining the set of PID controller gains that can stabilize a given nth-order discrete-time plant. An analytic characterization of the stability-domain boundary in the controller gain space is derived. The idea for this stability-domain boundary characterization is taken from the field of parametric evaluation of mean-squared-errors for discrete-time systems. The proposed approach is simpler than that recently proposed by Xu et al., which utilizes a
continuous-time version of Hermite-Biehler theorem along with the bilinear transformation. To illustrate the proposed approach, a numerical example is provided.

目 錄
中文摘要........................................................... Ⅰ
英文摘要...........................................................Ⅱ
圖表目錄...........................................................Ⅲ
第一章 緒論........................................................1
1.1 研究動機................................................... 1
1.2 文獻探討................................................... 2
1.3 章節與組織.................................................3
第二章 線性系統穩定區域之判斷......................................4
2.1 介紹.......................................................4
2.2 計算複變積分的展開式.......................................4
2.3 數位PID控制器穩定化的特徵.................................8
第三章 解析表示式.................................................15
3.1 積化合差展開式............................................15
第四章 範例.......................................................19
4.1 範例......................................................19
4.2 結論......................................................21
第五章 總結與未來的展望...........................................24
5.1 總結......................................................24
5.2 未來的展望................................................24
參考文獻...........................................................26
附錄A.............................................................28

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