跳到主要內容

臺灣博碩士論文加值系統

(44.222.218.145) 您好!臺灣時間:2024/02/26 23:01
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

: 
twitterline
研究生:李紹鈺
研究生(外文):Shao-Yu Lee
論文名稱:多參數規劃方法之約束系統的模式預測控制
論文名稱(外文):Model Predictive Control for Constrained System based on Multi-Parametric Programming
指導教授:練光佑
指導教授(外文):Kuang-Yow Lian
學位類別:碩士
校院名稱:中原大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
論文頁數:53
中文關鍵詞:對照表成本函數多參數規劃最佳控制模式預測控制線性規劃
外文關鍵詞:look-upLinear ProgrammingOptimal controlMulti-Parametric ProgrammingCost functionModel Predictive control
相關次數:
  • 被引用被引用:0
  • 點閱點閱:176
  • 評分評分:
  • 下載下載:2
  • 收藏至我的研究室書目清單書目收藏:0
隨著預測控制在工程、科學及經濟等領域中的廣泛應用,近年來,預測控制理論研究也有相當的進展。然而,預測控制利用線性模型進行線上多步預測設計,由於線上預測需要龐大計算量,此計算時間取決於系統維度與預測步數的大小而異,使得線上預測控制的應用範圍局限在小型或反應慢速的系統中,因此本文將針對此一問題進行改善。近幾年來,由於半導體製程技術的發展迅速,同時帶動控制系統相當大的影響,使得微處理器在功能與實用上有著顯著的躍進,因此由數位控制器所取代傳統類比控制器之嵌入式系統也是現今熱門的研究方向,於是控制理論在於探討數位控制與連續時間系統之間連結的相關研究也引起許多學者投入,本論文中所採用之MLD(Mixed Logic Dynamical)建模方法也有敘述這層關係。
在本論文中,為求減輕計算負荷,在控制架構中我們利用多參數規劃方法的模式預測控制(Model Predictive Control based on Multi-Parametric Programming),將所有系統狀態視為參數變數,透過線性規劃技巧事先計算出對應狀態空間之成本函數(Cost Function)得到最佳控制增益,將其計算結果儲存在對照表(Look-Up Table)中,便可使上述線上計算負荷簡化成線性函數查表,也就是以離線方式進行控制策略之應用,此法可應用範圍也隨之更加廣闊。在章節中,我們對閉迴路系統的穩定性分析加以敘述。最後,將此方法應用在三個系統上並呈現模擬結果,以證實其控制效果。

關鍵字:模式預測控制、成本函數、多參數規劃、線性規劃、最佳控制、對照表。
In the past few years, many researchers have been devoted to the optimal control
and stabilization of hybrid systems and piece-wise affine (PWA) systems. Particu-
larly, PWA framework can specify a broad class of hybrid models. After obtaining
the mathematical model of plant, a control scheme based on optimal feedback con-
trol of the system is presented. We discuss the optimal control problem and model
predictive control (MPC) for discrete time systems in this thesis. Especially, we
consider the optimal control problem with constraints on states and inputs.
MPC utilizes an internal model of controller system to predict the future evo-
lution of the system dynamic behavior over a finite horizon. A cost function is
minimized to obtain the optimal control input sequence, which is applied to the
plant by means of a receding horizon policy. MPC can be applied off-line by com-
puting the feedback solution after solving a multi-parametric programming. The
state-space is treated as a parameter, can be used to derive the PWA state feedback
control law. The resulting control law is a PWA state feedback control law defined
over a polyhedral partition of the state-space, which can be stored in a look-up ta-
ble. Thus, the on-line computing of the resultant MPC controller can be simplified
to a linear function evaluation of a look-up table.
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Organization of This Thesis . . . . . . . . . . . . . . . . . . . . . . . 3
2 Hybrid Dynamical Systems 5
2.1 Mixed Logical Dynamical Systems . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Logic Propositions . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Structure of Mixed Logic Dynamical Systems . . . . . . . . . 8
2.2 Piece-Wise Affine Systems . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Model Predictive Control 14
3.1 Basic Terminology and Definitions . . . . . . . . . . . . . . . . . . . . 14
3.2 Polytopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Constrained Optimal Control . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 On-Line Computation of Control Input . . . . . . . . . . . . . 18
3.3.2 Off-Line Computation of State-Feedback Control Law . . . . . 23
i
3.3.3 Continuity and Convexity Properties . . . . . . . . . . . . . . 30
4 Application Examples 34
4.1 Double integrator plant . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 DC-DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Inverted pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 Conclusion and Outlook 48
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
References 50
ii
List of Figures
1.1 Hybrid system: Microprocessors and continuous dynamics interact
through A/D and D/A interfaces. . . . . . . . . . . . . . . . . . . . . 2
1.2 Scheme of Model Predictive Control . . . . . . . . . . . . . . . . . . . 4
3.1 On-line computation Scheme of Model Predictive Control . . . . . . . 21
3.2 Critical regions, CR0 and CRrest . . . . . . . . . . . . . . . . . . . . 28
3.3 Partition of CRrest step 1 . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Partition of CRrest step 2 . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Final partition of CRrest . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Off-line computation Scheme of Model Predictive Control . . . . . . . 33
4.1 States and control response of double integrator . . . . . . . . . . . . 36
4.2 Partition of the state space and closed-loop trajectory for initial con-
dition x0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 The explicit state-feedback control law for the double integrator . . . 37
4.4 State space partition of value function for the double integrator . . . 37
4.5 Equivalent circuit of synchronous buck converter . . . . . . . . . . . . 38
iii
4.6 Equivalent circuit of synchronous buck converter while power MOS-
FET M1 is turned on, and M2 is turned off . . . . . . . . . . . . . . . 39
4.7 Equivalent circuit of synchronous buck converter while power MOS-
FET M1 is turned off, and M2 is turned on . . . . . . . . . . . . . . . 39
4.8 Closed-loop simulation of the converter during start-up . . . . . . . . 41
4.9 Sketch : Inverted Pendulum . . . . . . . . . . . . . . . . . . . . . . . 42
4.10 Structure of multiple model predictive control . . . . . . . . . . . . . 46
4.11 States responses of local linear model 1 . . . . . . . . . . . . . . . . . 47
4.12 States responses of local linear model 2 . . . . . . . . . . . . . . . . . 47
iv
List of Tables
2.1 Conversion of basic logic relations into integer inequalities . . . . . . 7
3.1 Definition of the partition of CRrest . . . . . . . . . . . . . . . . . . . 27
v
References
[1] H. P. Williams, Model building in mathematical programming, 3rd edn., John
Wiley and Sons, 1993.
[2] E. F. Camacho and C. Bordons, Model Predictive Control, Springer-Verlag,
London, 1999.
[3] P.J. Antsaklis, "A brief introduction to the theory and applications of hybrid
systems," in Proc. IEEE Special Issue on Hybrid Systems: Theory and Appli-
cations, vol.88, no.7, pp. 879-887, July 2000.
[4] M. S. Branicky, V. S. Borkar, and S. K. Mitter, "A unified framework for hybrid
control: model and optimal control theory, " IEEE Trans. Automat. Control,
vol .43, no.1, pp. 31-45, 1998.
[5] E. D. Sontag, "Interconnected automata and linear systems: A theoretical
framework in discrete-time," in Hybrid Systems III: Verification and Control
(R. Alur, T. Henzinger, and E.D. Sontag, eds.), vol. 1066, LNCS, pp. 436-448,
Springer-Verlag, 1996.
[6] A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics,
and constraints," Automatica, vol. 35, no. 3, pp. 407-427, Mar., 1999.
[7] E.D. Sontag, "Nonlinear regulation: The piecewise linear approach," IEEE
Trans. Automat. Contr., vol. 26, no. 2, pp. 346-358, April 1981.
[8] F.D. Torrisi and A. Bemporad, "HYSDEL - A Tool for Generating Compu-
tational Hybrid Models for Analysis and Synthesis Problems," IEEE Trans.
Contr. Syst. Technol., vol. 12, no. 2, pp. 235-249, 2004.
[9] W.P.M.H. Heemels, B. De Schutter, and A. Bemporad, "On the equivalence
of classes of hybrid dynamical models," in Proc. 40th IEEE Conference on
Decision and Control, Orlando, Florida, pp. 364-369, Dec. 2001.
[10] R. DeCarlo, M. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and
results on the stability and stabilizability of hybrid systems", in Proc. IEEE,
vol. 88, no. 7, pp. 1069-1082, 2000.
[11] M. Johannson and A. Rantzer, "Computation of piece-wise quadratic Lyapunov
functions for hybrid systems," IEEE Trans. Automat. Contr., vol. 43, no. 4, pp.
555-559, 1998.
[12] D. Q. Mayne and S. Rakovi c, "Model predictive control of constrained piecewise
affine discrete-time systems," Int. Journal on Robust and Nonlinear Control,
vol. 13, no. 3-4, pp. 261-279, 2003.
[13] J. Lygeros, C. Tomlin ,and S. Sastry, "Controllers for reachability speci cations
for hybrid systems," Automatica, vol. 35, no.3, pp. 349-370, 1999.
[14] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University
Press, 2004. http://www.stanford.edu/class/ee364/.
[15] K. Fukuda, Polyhedral computetion FAQ, 2000.
http://www.ifor.math.ethz.ch/sta /fukuda.
[16] J.B. Rawlings and K.R. Muske, "The stability of constrained receding-horizon
control," IEEE Trans. Automat. Control, vol. 38, pp. 1512-1516, 1993.
[17] D. Chmielewski and V. Manousiouthakis, "On constrained in nite-time linear
quadratic optimal control," System and Contrl Letters, vol. 29, no. 3, pp. 121-
130, 1996.
[18] S. S. Keerthi and E. G. Gilbert, "Optimal in nite-horizon feedback control laws
for a general class of constrained discretetime systems: stability and moving-
horizon approximations," J. Opt. Theory and Applications, vol. 57, pp. 265-293,
1988.
[19] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained
model predictive control: Stability and optimality," Automatica, vol. 36, no. 6,
pp. 789-814, June, 2000.
[20] M. Lazar, W. P. M. H. Heemels, S. Weiland, and A. Bemporad, "On the sta-
bility of Quadratic forms based model predictive control of constrained PWA
systems," In Proc. American Contr. Conf., pp. 575-580, 2005.
[21] A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos, "The explicit solu-
tion of model predictive control via multiparametric quadratic programming,"
In Proc. American Contr. Conf., vol. 2, pp. 872-876, June, 2000.
[22] M.S. Bazaraa, H.D. Sherali, and C.M., Nonlinear Programming - Theory and
Algorithms, JohnWiley & Sons, Inc., New York, 2nd ed.,1993.
[23] V. Dua and E.N. Pistikopoulos, "An algorithm for the solution of multipara-
metric mixed integer linear programming problems," Annals of Operations Re-
search, vol. 99, no. 1-4, pp. 123-139, 2000.
[24] W. W. Hogan, "Point-to-set maps in mathematical programming," SIAM
Reveiw, vol. 15, no. 3, pp. 591{603, July, 1973.
[25] J. Mahdavi, A. Emadi, and H. A. Toliyat, "Application of state space averaging
method to sliding mode control of PWM DC/DC converters," In Proc. IEEE
IAS'97, vol. 2, pp. 820-827, 1997.
[26] T. Geyer, G. Papafotiou, and M. Morari, "On the optimal control of switch-
mode DC-DC converters," In Proc. Hybrid Systems: Computation and Control,
vol. 2993, pp. 342-356, Springer-Verlag, 2004.
[27] R. H. Cannon, Dynamics of physical systems, New York, McGraw-Hill, 1967.
[28] S. H. _ Zak, Systems and Control, Oxford University Press, Oxford, 2003.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top