臺灣博碩士論文加值系統

控制系統的性能評估與監控在最近十餘年來吸引了許多學者投入這方
面的研究，主要原因為此技術對改進工業中控制環路之性能有很大的幫助
，但是研究的方向偏重於隨機型性能評估與監控，而本論文則是提出一種
確定型性能評估與監控的方法。首先討論單環路的情況，之後再推廣到多
環路系統中。
在單環路系統中，對於設定點追蹤部分，考慮的控制器包括含積分作
用之一般控制器與PI/PID控制器，分別找出簡單回饋控制系統可達到的極
限最小IAE值與最適上昇時間，以此做為評估之基準，任何系統的性能便
可由其對階梯設定點改變所觀察到的IAE值與上昇時間來評估。假設開環
程序之動態可用FOPDT或SOPDT模式來代表，根據這些模式，計算出最適可
達到IAE值與相對應之上昇時間，同時定義用以評估之定量性能指標。最
適設定點追蹤性能之系統亦具有合理程度的穩定韌性。對於負荷干擾消除
部分，考慮的系統為FOPDT程序以PI/PID控制，此時，系統性能與穩定韌
性存有強烈的衝突，故IAE值之下限與系統的增益邊限有關，定義三個評
估指標用以評估系統的性能與穩定韌性以及兩者間之妥協是否有效運用。
在結合兩控制目的之評估時，計算出最適性能指標曲線以表示系統對兩種
性能之最佳組合情形，然後以系統指標落點偏離最適曲線的程度來評估整
體性能，並討論控制器設計之準則。
至於線上性能監控方面，由PI/PID控制系統對於設定點追蹤之IAE值
與相對應上昇時間所形成的最適軌跡區域，可使評估在程序模式未知的情
況下進行，此外，為了不使系統輸出偏離其正常操作點，引入系統一擾動
輸入可用來估計其對設定點階梯輸入之應答，藉以線上監控性能。為了要
更準確的進行評估或是控制器最適調諧，本文提出利用回饋繼電器測試來
識別程序FOPDT與SOPDT模式之新方法，由識別出之模式不僅可計算系統之
性能下限，更可用來進行控制器的自動調諧，結合此兩者可整合系統性能
之評估與改善。
對於多環路系統之性能評估，藉由對等開環程序(equivalent open-
loop process，EOP)之定義，可將多環路系統分解成數個對等單環路系
統。若程序轉移函數矩陣為未知，EOP之模式除了利用回饋繼電器測試來
識別之外，本文另外提出EOP程序脈衝響應序列模式之閉環路識別法，之
後再將其轉換為低階轉移函數模式，用以計算評估之標準。於是，前述單
環路系統之性能評估與監控方法便可應用至多環路系統中。

Assessment and monitoring of control systems have been an
active area of research for the last decade because these
techniques can be used to improve the loop performance.
However, most research works were focused on stochastic
performance assessment and monitoring. In this thesis, a new
methodology is presented for deterministic performance
assessment and monitoring. This method is first developed for
single-loop systems and then extended to multi-loop systems as
applications.
In the single-loop control system with set-point tracking
as its control task, the controller of general structure having
integral action and of PI/PID structure are studied. The
limiting achievable minimal IAE value and the associated rise
time of a simple feedback system are searched to be the basis
for assessment. Performance of a given system is assessed with
its IAE value and rise time observed from the response of the
system to a step set-point change. Assume that the dynamics of
open-loop processes can be represented by models of FOPDT or
SOPDT. Based on these models, the optimal IAEs and rise times
are computed. An index is thus defined for this quantitative
assessment. The optimal systems for set-point tracking also
have reasonable degree of stability robustness. For the system
to reject the load disturbance, the FOPDT process model
controlled with PI or PID controller is considered. In this
case, the trade-off between performance and robustness is
necessary and, hence, the achievable minimal IAE depends on
gain margin of the system. Three indices are defined to assess
both performance and robustness as well as if the trade-off has
been appropriately made. Furthermore, for combined assessment
of two control objectives, the optimal curve of two performance
indices is computed to characterize the optimal trade-off
between set-point tracking and load disturbance rejection.
The overall performance can be assessed through the deviation
of performance indices from its optimal curve. Besides, the
guidelines on design of controllers are also discussed.
To be free of a process model for assessment, envelopes of
optimal IAE and the rise time are prepared. A method to
estimate the step response for set-point tracking by making use
of the response of the system to dither inputs is presented. By
introduction of dither inputs intermittently to the system, the
performance of the single loop can be monitored on-line. If
more accurate assessment and PI/PID optimal tuning are desired,
a novel method to identify the process model in terms of FOPDT
or SOPDT using relay feedback tests is also proposed. As a
result, the assessment and improvement of performance can be
integrated.
A multi-loop system can be separated into several
equivalent single loops by the definition of equivalent open-
loop process (EOP). The approximation formulas of EOPs are
presented. In the case of open-loop process with unknown
transfer function matrix, the model of EOP can be identified
using relay feedback tests. In addition, the EOP can also be
obtained from proposed closed-loop identification method of
impulse response model. Then, it is converted to reduced low-
order transfer function model to compute the lower bound of
control performance. Therefore, the methodology for single-loop
systems mentioned previously can be directly applied to multi-
loop systems.

誌 謝................................................... I
中文摘要................................................... III
英文摘要................................................... V
目 錄................................................... VII
附圖目錄................................................... XI
附表目錄................................................... XIII
1 緒論 1
1.1 前言.................................................. 1
1.2 文獻回顧.............................................. 2
1.3 研究動機與目的........................................ 10
1.4 章節組織.............................................. 11
2 單環路控制系統之性能評估 - 設定點追蹤 13
2.1 前言.................................................. 13
2.2 單環路控制系統可達到之極限最小IAE值 -- 一般控制器..... 14
2.3 單環路控制系統可達到之極限最小IAE值 -- PI/PID控制器... 28
2.4 控制性能的評估方法.................................... 41
3 單環路控制系統之性能評估 -- 負荷干擾消除 49
3.1 前言.................................................. 49
3.2 控制系統對負荷消除之性能與穩定韌性關係................ 49
3.3 PI/PID控制系統之性能與穩定韌性........................ 53
3.4 控制系統對負荷干擾消除之性能評估...................... 57
3.5 結合設定點追蹤與負荷消除之性能評估.................... 63
4 控制系統之線上性能監控與自動調諧 71
4.1 前言.................................................. 71
4.2 控制性能的線上監控.................................... 71
4.3 線上監控之範例說明.................................... 76
4.4 利用模式識別來進行性能監控與PI/PID自動調諧............ 81
4.5 識別與自動調諧之範例說明.............................. 95
5 多環路控制系統之性能評估 103
5.1 前言..................................................103
5.2 環路配對之可控制性與整體性............................104
5.3 多環路控制系統之對等單環路近似分解....................107
5.4 多環路系統EOPs之標準近似式............................113
5.5 多環路控制系統之性能評估與監控........................117
5.6 程序轉移函數矩陣未知時之性能評估......................124
6 結論與未來展望 135
6.1 結論..................................................135
6.2 未來展望..............................................137
附錄A 最小變異量控制(MVC) 139
附錄B 文中使用到之PI/PID調諧公式 145
附錄C 線性部分轉換(LFT) 149
參考文獻 153
作者簡歷 159
作者著作 161

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