臺灣博碩士論文加值系統

本文中在利用強韌D分割技術來討論參數未確定系統的穩定性分析，
在參數空間法中，D分割技術是一種可應用在系統穩定性分析的方法，
許多學者在傳統D分割技術的領域中，提出了相當多的理論。
D分割技術利用系統的特徵多項式來將控制器參數劃分為數個區域，
每個區域所包含的特徵多項式的根的種類皆不相同，稱為D分割區域，
劃分區域的線段稱為D分割邊界。
若系統的參數當中包含有未確定性存在時，會造成D分割邊界的擴張，
形成帶狀的區域稱為D分割界限(border)，
而定出此帶狀區域的邊界的過程則成為分析參數未確定系統穩定性的關鍵。
D分割界限的邊界的形成，也受制於系統的特徵多項式，
於論文中將推導出強韌D分割的形式。
如何快速的找出D分割的邊界是相當重要的，由D分割決定出了邊界的多項式後，
利用軌跡追蹤的方法，可以準確地定出D分割的邊界，
但因為此類的方法在追蹤前必須先選擇一起始點，若邊界並不經過此起始點時，
便無法找出此邊界，故無法確保在指定的參數範圍中找出所有的邊界。
為了確保所有的邊界被定出，因而使用了Branch and Bound的觀念，
將指定的參數範圍分割成數個小區域，再一一檢驗每個小區域是否包含了邊界，
如此一直重覆分割區域，直到最後剩下的區域的大小，在可容許的誤差範圍內，
而這些小區域所組合構成的區域即為D分割的邊界。
為了快速的檢驗每個區域是否包含了邊界，因而使用了函數值域的估算法，
本論文中主要以Bernstein Expansion為主，此類方法選定了一組特定的基底函數，
接著將要估算的函數作變換，形成以基底函數為主的形式，進而因基底函數而產生特定的性質，
這些特定的性質會有助於函數值域的估算。
最後將強韌D分割的原理和技術連貫，針對一般性的參數未確定的系統進行實作，
以驗證強韌D分割技術的實用性和可行性。

In this session, we discuss the stability analisys of systems with
parametric uncertainty by using robust D-partition.
Among several parametric space methods, D-partition is an applicable method
in the analysis of system stability.
Many people proposed some theorem in the domain of D-partition.
With the characteristic polynomial of systems,
D-partition subdivides controller parametric space into several subdomain.
Each subdomain includes the difference kind of poles, called D-partition areas.
The lines which subdivide the subdomains was called D-partition boundary.
If the system has uncertain parameters, D-partition boundary will expanse to band.
It is called D-partition border. To locate the boundary of the border is the key
to analyze the stability of systems. The formation of the boundary of the D-partition border
is enslaved to the characteristic polynomial of system. In this paper,
we will derive the form of robust D-partition.
It is important that how to locate the D-partition boundary rapidly.
After deciding the polynomial of the boundary by using D-partition method,
it could be located precisely with locus tracking methods.
The kind of methods must make a choose on a starting point before tracking.
If the boundary does not lap over the starting point, it can not be found.
Therefore, the locus tracking method can not provide a guarantee of locating all boundary
in the parametric space. To be sure that, we quote the concept of branch and bound.
The concept is that the controller parametric space is subdivided into several subdomain,
and exclude the subdomain which does not include the boundary.
The remain subdomain repeat the procedure until the subdomain is small enough.
Finally, the remain subdomain is the set of D-partition boundary.
For checking whether the boundary is included in subdomain rapidly,
we will use the Bernstein expansion.
This kind of method specified a set of base function
to make a transformation with the object function.
Because of the properties of the base function, it help us to evaluate the value of object function.
At last, we link up the theorem and technology of D-partition
for the application of parametric uncertainty of general systems,
and prove the D-partition is applicable and realizable.

1. 緒論 1
2. 參數未確定性系統之穩定性分析 6
3. 多項式函數值域估算 18
4. 範例 37
5. 結論及未來展望 51
6. 參考文獻 53

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