(18.207.129.82) 您好!臺灣時間:2021/04/19 20:12
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:黃立方
研究生(外文):Li-fong Hwang
論文名稱:參數未確定系統之強韌D分割分析
論文名稱(外文):Robust D-partition analysis for parametric uncertain systems
指導教授:黃奇黃奇引用關係
指導教授(外文):Chyi Hwang
學位類別:碩士
校院名稱:國立中正大學
系所名稱:化學工程研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:60
中文關鍵詞:強韌D分割強韌控制D分割參數未確定性
外文關鍵詞:Robust D-partitionRobust controlD-partitionParametric uncertaintyBernstein
相關次數:
  • 被引用被引用:0
  • 點閱點閱:167
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
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

\item{Ackermann, J. (1980).
Parameter space design of robust control systems.
{\it IEEE Transactions on Automatic Control,} {\it 25}(6), 1058-1072.}
\item{Ackermann, J. (1993).
{\it Robust control: Systems with uncertain physical parameters.} London: Springer-Verlag.}
\item{Barmish, B. R. (1994)
{\it New tools for robustness of linear systems.} New York: Macmillan.}
\item{Besson, V., \& Shenton, A. T. (1997).
Interactive control system design by a mixed $H\sp \infty$-parameter space method.
{\it IEEE Transactions on Automatic Control,} {\it 42}(7), 946-955.}
\item{Bhattacharyya, S. P., Chapellat, H., \& Keel, L. H. (1995).
{\it Robust control, The parametric approach.}
New Jersy: Prentice Hall PTR.}
\item{ }{Bimbirekov, B. L. (1993).
Determination of the parameters of a controller for a linear system from frequency criteria.
{\it Automation and Remote Control,} {\it 54}(5), part 1, 699-706.}
\item{Boese, F. G. (1994).
An auxiliary theorem for stability analysis in the presence of interval-valued parameters.
{\it Multidimensional Systems and Signal Processing,} {\it 5}(4), 419-440.}
\item{Bradshaw, A., \& Porter, B. (1974).
Stabilizability of linear discrete-time dynamical systems with retarded control.
{\it International Journal of Systems Science,}
{\it 5}(2), 137-144.}
\item{Chang, C. H., \& Han, K. W. (1990).
Gain margins and phase margins for control systems with adjustable parameters.
{\it Journal of Guidance, Control, and Dynamics,}
{\it 13}(3), 404-408.}
\item{Chen, J. J., \& Hwang, C. (1998).
Value sets of polynomial families with coefficients depending nonlinearly on perturbed parameters.
{\it IEE Proceedings-Control Theory and Applications,}
{\it 145}(1), 73-82.}
\item{Cheng, S. L., \& Hwang, C. (1999).
On stabilization of time-delay unstable systems using PID controllers.
{\it Journal of the Chinese Institute of Chemical Engineers,}
{\it 30}(2), 123-140.}
\item{Cook, R. P. (1966).
Gain and phase boundary routine for two-loop feedback systems.
{\it IEEE Transactions on Automatic Control,}
{\it 11}(3), 573-577.}
\item{Fam, A. T., \& Meditch, J. S. (1978).
A canonical parameter space for linear systems design.
{\it IEEE Transactions on Automatic Control,}
{\it 23}(3), 454-458.}
\item{Fil\'ts, R. V., Tymoshuk, V. V., \& Koziy, B. I. (1971).
Calculation of $D$-partition boundary in the plane of two parameters that occur nonlinearly
in the coefficients of the characteristic equation.
{\it Soviet Automatic Control,} {\it 4}(2), 61-63.}
\item{Fruchter, G., Srebro, U., \& Zeheb, E. (1987).
On several variable zero sets and application to MIMO robust feedback stabilization.
{\it IEEE Transactions on Circuits and Systems,}
{\it 34}(10), 1208-1220.}
\item{Fruchter, G., Srebro, U., \& Zeheb, E. (1991a).
Conditions on the boundary of the zero set and application to stabilization of systems with uncertainty.
{\it Journal of Mathematical Analysis and Applications,}
{\it 161}(1), 148-175.}
\item{Fruchter, G., Srebro, U., \& Zeheb, E. (1991b).
On possibilities of utilizing various conditions to determine a zero set.
{\it Journal of Mathematical Analysis and Applications,}
{\it 161}(2), 361-366.}
\item{Gantmacher, F. R. (1959).
{\it The theory of matrices.} Vol. 2, New York: Chelsea Publishing Co.}
\item{G\"uvenc, L., \& Ackermann, J. (2001).
Links between the parameter space and frequency domain methods of robust control.
{\it International Journal of Robust and Nonlinear Control,}
{\it 11}(15), 1435-1453.}
\item{Han, K. W., \& Thaler, G. J. (1966).
Control system analysis and design using a parameter space method.
{\it IEEE Transactions on Automatic Control,} {\it 11}, 560-563.}
\item{Hollot, C. V., Looze, D. P., \& Bartlett, A. C. (1990).
Parametric uncertainty and unmodeled dynamics: Analysis via parameter
space.
{\it Automatica,} {\it 26}(2), 269-282.}
\item{Hwang, C., \& Hsiao, C. Y. (2002).
Solution of a non-convex optimization arising in PI/PID control design.
{\it Automatica,} {\it 38}(11), 1895-1904.}
\item{Kharitonov, V. L. (1979).
Asymptotic stability of an equilibrium position of a family of systems of
linear differential equations.
{\it Differential Equations,} {\it 14}(11), 1483-1485.}
\item{Kiselev, O. N., Le, H. L., \& Polyak, B. T. (1997).
Frequency responses under parametric uncertainty.
{\it Automation and Remote Control,}
{\it 58}(4), part 2, 645-661.}
\item{Kogan, J. (1995).
{\it Robust stability and convexity.}
London: Springer-Verlag.}
\item{Lanzkron, R. W., \& Higgins, T. J. (1959).
$D$-decomposition analysis of automatic control systems.
{\it IRE Transactions on Automatic Control,}
{\it 4}(3), 150-171.}
\item{Lawrenson, P. J., \& Bowes, S. R. (1969.)
Generalization of $D$ decomposition techniques.
{\it Proceedings of the Institution of Electrical Engineers,}
{\it 116}, 1463-1470.}
\item{McKay, J. (1970).
The D-partition method applied to systems with dead time and distributed lag.
{\it Measurement and Control,} {\it 3}(10), 293-294.}
\item{Munro, N. (1999).
{\it Symbolic methods in control system analysis and design.}
IEE Control Engineering Series, 56. Institution of Electrical Engineers (IEE), London.}
\item{Neimark, Yu. I. (1948a).
On the determination of the values of the parameters for which a system of automatic regulation is stable.
(in Russian) {\it Avtomatika i Telemehanika,} {\it 9}, pp. 190-203.}
\item{Neimark, Yu. I. (1948b).
The structure of the $D$-decomposition of a space of polynomials and the diagrams of Vy\v snegradski\u\i and Nyquist.
(in Russian) {\it Doklady Akad. Nauk SSSR (N.S.),}
{\it 59}, 853-856.}
\item{Neimark, Yu. I. (1948c).
The structure of the $D$-decomposition of the space of quasipolynomials and the diagrams of Vy\v snegradski\u\i and Nyquist.( in Russian) {\it Doklady Akad. Nauk SSSR (N.S.),}
{\it 60}, 1503-1506.}
\item{Neimark, Yu. I. (1949).
$D$-decomposition of the space of quasipolynomials. (On the stability of linearized distributive systems).
(in Russian)
{\it Akad. Nauk SSSR. Prikl. Mat. Meh.,} {\it 13}, 349-380.}
\item{Neimark, Ju. I. (1973).
$D$-decomposition of the space of quasi-polynomials (on the stability of linearized distributive systems).
American Mathematical Society Translations, Series 2. Vol. 102: Ten papers in analysis.
American Mathematical Society, Providence, R.I., pp. 95-131.}
\item{Neimark, Yu. I. (1991).
Robust stability of linear systems.
{\it Soviet Physics Doklady,}
{\it 36}(7), 506-509.}
\item{Neimark, Yu. I. (1992a).
Robust stability and D-partition.
{\it Automation and Remote Control,}
{\it 53}(7), part 1, 957-965.}
\item{Neimark, Y. I. (1992b).
Robust stability for periodic perturbations.
{\it Automation and Remote Control,}
{\it 53}(12), part 1, 1863-1865.}
\item{ }{Neimark, Yu. I. (1992c).
A measure of robust stability and modality of linear systems.
{\it Soviet Physics Doklady,}
{\it 37}(7), 321-322.}
\item{Neimark, Yu. I. (1992d).
Robust stability region and robustness with respect to nonlinear parameters.
{\it Soviet Physics Doklady,}
{\it 37}(7), 323-324.}
\item{Neimark, Yu. I. (1992e).
Robust stability with respect to nonlinear parameters.
{\it Differential Equations,}
{\it 28}(12), 1829-1831.}
\item{Neimark, Y. I. (1993).
Measures of robust stability of linear systems.
{\it Automation and Remote Control,}
{\it 54}(1), part 2, 100-103.}
\item{ }{Neimark, Yu. I. (1994a).
Robust interval matrix stability.
{\it Automation and Remote Control,}
{\it 55}(7), part 2, 1037-1041.}
\item{Neimark, Yu. I. (1994b).
Robust modality and aperiodicity.
{\it Journal of Computer and Systems Sciences,}
{\it 32}(4), 102-107.}
\item{Neimark, Yu. I. (1998).
$D$-partition and robust stability.
{\it Computational Mathematics and Modeling,}
{\it 9}(2), 160-166.}
\item{Nikolaev, Yu. P. (2000).
Phase margin and the parameter space of continuous linear systems.
{\it Automation and Remote Control,}
{\it 61}(3), part 2, 451-462.}
\item{Petrov, N. P. \& Polyak, B. T. (1991).
Robust D-partition.
{\it Automation and Remote Control,}
{\it 52}(11), part 1, 1513-1523.}
\item{Polyak, B. T., \& Kogan, J. (1995).
Necessary and sufficient conditions for robust stability of linear
systems with multiaffine uncertainty structure.
{\it IEEE Transactions on Automatic Control,}
{\it 40}(7), 1255-1260.}
\item{Porter, B. (1968).
{\it Stability criteria for linear dynamical systems.}
New York: Academic Press.}
\item{Porter, B., \& Bradshaw, A. (1974).
Effect of integral action on the stabilizability of continuous-time linear
dynamical systems with retarded control.
{\it International Journal of Systems Science,}
{\it 5}(9), 807-815.}
\item{Putz, P., \& Wozny, M. J. (1987).
A new computer graphics approach to parameter space design of control systems.
{\it IEEE Transactions on Automatic Control,} {\it 32}(4), 294-302.}
\item{Siljak, D. D. (1969).
{\it Nonlinear systems: The parameter analysis and design,}
New York: Wiley.}
\item{Siljak, D. D. (1989).
Parameter space methods for robust control design: a guided tour.
{\it IEEE Transactions on Automatic Control,} {\it 34}(7), 674-688.}
\item{Spal, J. (1979).
Generalization of the method of $D$-decomposition.
{\it Kybernetika,} {\it 15}(6), 429-455.}
\item{Stenton, A. T., \& Shafiel, Z. (1994).
Relative stability for control systems with adjustable parameters.
{\it Journal of Guidance, Control, and Dynamics,}
{\it 17}(2), 304-310.}
\item{Walach, E., \& Zeheb, E. (1982).
Generalized zero sets of multiparameter polynomials and feedback stabilization.
{\it IEEE Transactions on Circuits and Systems,}
{\it 29}(1), 15-23.}
\item{Zeheb, E. (1990).
Necessary and sufficient conditions for robust stability of a continuous system---the continuous dependency case illustrated via multilinear dependency.
{\it IEEE Transactions on Circuits and Systems,} {\it 37}(1), 47-53.}
\item{Zeheb, E. (1997).
Zero sets analysis of systems with uncertainties.
{\it Uncertainty: models and measures.} pp. 217-230, Math. Res., 99, Berlin: Akademie Verlag.}
\item{Zeheb, E., \& Walach, E. (1981).
Zero sets of multiparameter functions and stability of multidimensional systems.
{\it IEEE Transactions on Acoustics, Speech and Signal Processing,}
{\it 29}(2), 197-206.}

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔