跳到主要內容

臺灣博碩士論文加值系統

(44.192.67.10) 您好!臺灣時間:2024/11/10 12:13
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:申秉弘
研究生(外文):Bin-Hong Shen
論文名稱:鏈散射描述法求解控制器合成及其於線性伺服系統強健設計之應用
論文名稱(外文):Chain-Scattering Description Approach to Control Synthesis and Its Application to Robust Design of Linear Servo Systems
指導教授:蔡明祺
指導教授(外文):Mi-ching Tsai
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
畢業學年度:95
語文別:英文
論文頁數:141
中文關鍵詞:H∞控制鏈散射式描述動態剛性極點配置線性伺服馬達倒單擺
外文關鍵詞:H∞ controlchain-scattering descriptiondynamic stiffnesspole assignmentlinear servomotorinverted pendulum
相關次數:
  • 被引用被引用:2
  • 點閱點閱:203
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
80年代以來,各種求解H∞控制問題之古典方法常牽涉複雜之高階數學工具,使得僅具工程背景之設計者難以理解H∞控制器合成之精神。本論文基於鏈散射式描述(chain-scattering description, CSD)求解標準H∞控制問題,所提出之方法以兩組耦合之鏈散射矩陣配合其J-lossless性質,求出所有滿足成本函數之控制器集合;由於所提之解題架構僅牽涉代數運算以及Riccati方程式,其解題流程相對簡單許多。爾後進一步將此解題架構延伸至求解所有穩定控制器問題以及H2控制問題,整合提出一可同時處理上述三種控制問題之統一解法。在所提出之解題架構下,上述三種控制問題均可以一致化的數學結構加以描述,並只需視問題種類加以限制各鏈散射矩陣之條件,即可合成出滿足不同目標之控制器集合。

在實務應用之設計考量上,本文提出以高等PDFF控制器完成線性伺服系統之動態剛性設計,並以一線性伺服馬達系統與一雙平行倒單擺同動系統為設計實例,說明高等PDFF控制器所具有之特性與其實務設計流程。本文並利用所提出之鏈散射描述解題方法,求解出高等PDFF控制器之解析式,進而證明利用H∞極點配置對於動態剛性以及閉迴路特性之影響。實驗結果顯示,所提出之高等PDFF控制器設計可有效提升線性伺服馬達之剛性,且可降低雙平行倒單擺系統中極限循環(limit cycle)之振盪效應,驗證了本高等PDFF控制器設計之可行性與實用性。
The classical approaches to solve H∞ problem that involve sophisticated mathematics are often too difficult to be understood by the control designers who have only engineering backgrounds. This research investigates the solution to a standard H∞ control problem based on a coupled chain-scattering description (CSD) framework, in that the H∞ controller generator can be obtained by constructing two CSD matrices and successive J-lossless coprime factorizations. Since the proposed method involves only algebraic operations and Riccati equations, its key concept is relatively simpler and easier to comprehend. Moreover, the proposed framework has been extended to solve the stabilization problem and H2 problem. The proposed procedure to find two successive coprime factorizations is unified for solving the stabilization, H2, and H∞ problem; however the constraint on the CSD matrices of each problem is different from each other. Such an approach is then said to be unified to the controller synthesis problems.

Concerning the practical designs, a dynamic stiffness design scheme based on an Advanced PDFF controller is proposed for linear servo systems. The presented Advanced PDFF control design is applied to a linear servomotor and a parallel dual inverted pendulum system to show the design procedure and benefits. Using the proposed CSD approach, the explicit form of the Advanced PDFF controller can be obtained; furthermore, the design property of the H∞ pole assignment can be investigated. Following that, how the design freedom affects the dynamic stiffness and the closed loop can be manifested. The experimental results show that the advanced PDFF controller effectively enhances the dynamic stiffness of the linear servomotor and reduces the limit cycle in the PDIPS.
1. Introduction ............................................. 1
1.1 Background review........................................... 4
1.1.1 Solution for H∞ control problem ......................... 5
1.1.2 Dynamic stiffness design.................................. 7
1.2 Contribution and organization of this dissertation.......... 8

2. Chain scattering description and its application to network analysis 11
2.1 Preliminaries................................................. 11
2.1.1 Coprime factorization....................................... 11
2.1.2 Normalized coprime factorization............................. 12
2.1.3 Algebraic Riccati equations and Hamiltonian matrix........... 14
2.2 Chain scattering description .................................. 15
2.2.1 Definitions and operations................................... 15
2.2.2 A coupled CSD framework...................................... 16
2.2.3 J-lossless systems........................................... 20
2.2.4 J-lossless coprime factorization............................. 21
2.2.5 Star connection.............................................. 23
2.3 The application to network analysis............................ 24

3. A unified approach to control synthesis.......................... 36
3.1 Stabilization problem.......................................... 36
3.1.1 Method I: using a right CSD coupled with a left CSD.......... 37
3.1.2 Method II: using a left CSD coupled with a right CSD......... 41
3.2 H2 control problem............................................. 44
3.3 General H∞ control problem..................................... 46
3.4 Specific H∞ design problems.................................... 50
3.4.1 Robust stabilization problem of left coprime factor plant description system............................................................. 50
3.4.2 Robust stabilization problem of right coprime factor plant description system............................................................. 57
3.4.3 Weighted mixed sensitivity problem (WMS)..................... 63
3.4.4 WMS problem with constant weights............................ 69
3.5 Summary........................................................ 71

4. Advanced PDFF controller design................................. 72
4.1 Advanced PDFF controller........................................ 72
4.2 Problem formulation of the Advanced PDFF control design......... 74
4.3 Properties of the Advanced PDFF control design.................. 79
4.4 Summary ........................................................ 86

5. Dynamic stiffness design of a linear servomotor system.......... 87
5.1 Problem statement.............................................. 87
5.2 Design procedure .............................................. 88
5.3 Performance evaluations........................................ 93
5.4 Summary....................................................... 97

6. Parallel dual inverted pendulum system.......................... 98
6.1 Motivation and problem statement .............................. 98
6.2 System configuration........................................... 100
6.2.1 Setup and implementation..................................... 100
6.2.2 Single axis modeling......................................... 102
6.3 Single-axis control design..................................... 104
6.3.1 Inner loop controller design................................. 105
6.3.2 Outer position control loop design........................... 108
6.3.3 Design procedure............................................. 109
6.4 Dual-axes synchronization control design....................... 110
6.4.1 Classical master-slave control............................... 110
6.4.2 Proposed synchronization control scheme...................... 111
6.4.3 Stability analysis of proposed compensator................... 113
6.5 Experimental results............................................ 114
6.5.1 Limit cycle reduction and single axis tracking................ 114
6.5.2 Dual axes synchronization control............................ 115
6.6 Summary......................................................... 119

7. Conclusions...................................................... 121
7.1 Summary......................................................... 121
7.2 Suggestions for further research................................ 122

Appendix A. State-space formulae of H2 optimal controller........... 124
Appendix B. State-space formulae of H∞ sub-optimal controller...... 128
Reference ........................................................... 136
[1]Allen, J.C.: H�V Engineering and Amplifier Optimization, Birkhauser, Boston, 2004.
[2]Alter, D. M., and Tsao, T. C.: ‘Control of linear motors for machine tool feed drives: design and implementation of H�V optimal feedback control.’ ASME J. of Dynamic Systems, Measurement, and Control, 1996, 118, pp. 649-656.
[3]Balabanian, N., and Bickart, T.A.: Linear Network Theory: Analysis, Properties, Design and Synthesis, Matrix Publishers, Inc., Beaverton, 1982.
[4]Bombois, X., and Anderson, B.D.O.: ‘On the influence of weight function modification in H∞ control design,’ in Proceedings of the 41st IEEE Conference on Decision and Control, Les Vegas, U.S.A., 2002, pp. 1958-1963.
[5]Cho, J.U., and Jeon, J.W.: ‘A motion-control chip to generate velocity profiles of desired characteristics,’ ETRI Journal, 2005, 27, (5), pp. 563-568.
[6]Doyle, J.C., Glover, K., Khargonekar, P. P., and Francis, B.A.: ‘State-space solutions to standard H2 and H∞ control problems,’ IEEE Trans. AC, 1989, 34, (8), pp. 831-847.
[7]Ellis, G.: ‘PDFF: an evaluation of a velocity loop control method.’ in Conf. Rec. PCIM, Nuremburg, Germany, 1999, pp. 49-54.
[8]Fang, L., Chen, W.J., and Cheang, S.U.: ‘Friction compensation for a Double Inverted Pendulum,’ in Proc. IEEE Int. Conf. on Control Applications, Mexico city, Mexico, 2001, pp.908-913.
[9]Glover, K., and Doyle, J. C.: ‘State-space formulae for all stabilizing controllers that satisfy an H∞-norm bounded and relations to risk sensitivity,’ Systems Control Letter, 1988, 11, pp. 167-172.
[10]Glover, K., and McFarlane, D.: ‘Robust stabilization of normalized coprime factor plant description with H∞-bounded uncertainty,’ IEEE Trans. AC, 1989, 34, (8), pp. 821-830.
[11]Glover, K., Limebeer, D.J.N., Doyle J.C., Kasenally, E.M., and Safonov, M.G.: ‘A characterization of all the solutions to the four block general distance problem,’ SIAM Journal of Control and Optimization, 1991, 29, (2), pp. 283-324.
[12]Graser, F., D’Arrigo, A., Colombi, S., and Rufer, A.C.: ‘JOE: a mobile, inverted pendulum,’ IEEE Trans. Industrial Electronics, 2002, 49, (1), pp.107-114.
[13]Green, M., Glover, K., Limebeer, D.J.N., and Doyle J.C.: ‘A J-spectral factorization approach to H∞ control,’ SIAM Journal of Control and Optimization, 1990, 28, (6), pp. 1350-1371.
[14]Green, M.: ‘H∞ controller synthesis by J-lossless coprime factorization,’ in Proceedings of the 29th Conference on Decision and Control, Hawaii, U.S.A., 1990, pp. 2437-2438.
[15]Green, M.: ‘H∞ controller synthesis by J-lossless coprime factorization,’ SIAM Journal of Control and Optimization, 1992, 30, (3), pp. 522-547.
[16]Groß, H., Hamann, J., and Wiegärtner, G.: Electrical feed drives in automation, Publicis MCD Corporate Publishing, Munich, 2001.
[17]Hong, J.L.: ‘A chain scattering-matrix approach to the H∞ output feedback control for the state-delayed systems,’ International Journal of Control, 2004, 77, (16), pp. 1373-1381.
[18]Hong, J.L., and Teng, C.C.: ‘H∞ control for nonlinear affine systems: a chain scattering-matrix description approach,’ International Journal of Robust and Nonlinear Control, 2001, 11, pp. 315-333.
[19]Hyde, R. A., and Glover, K.: ‘The application of scheduled H∞ controllers to a VSTOL aircraft,’ IEEE Trans. AC, 1993, 38, pp. 1021-1039.
[20]Kautsky, J., Nichols, N. K., and Van Dooren, P.: ‘Robust pole assignment in linear state feedback,’ Int. J. of Control, 1985, 41, pp. 1129-1155.
[21]Kim, B.K., Chung, W.K., and Suh, I.H.: ‘Robust synchronizing motion control of twin-servo systems based on network modeling,’ Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 1019-1024.
[22]Kim T. Y., and Kim J.: ‘Adaptive cutting force control for a machining center by using indirect cutting force measurements,’ Int. J. Machine Tools & Manufacture, 1996, 36, 925-937.
[23]Kimura, H.: ‘(J,J’)-lossless factorization based on conjugation,’ Systems and Control Letters, 1992, 19, pp. 95-109.
[24]Kimura, H.: ‘Chain-scattering representation, J-lossless factorization and H∞ control,’ Journal of Math. Systems, Estimation and Control, 1995, 5, pp. 203-255.
[25]Kimura, H.: Chain-Scattering Approach to H∞ Control, Birkhauser, Boston, 1997.
[26]Koren, Y.: ‘Cross-coupled biaxial computer control for manufacturing systems,’ Journal of Dynamic Systems, Measurement, and Control, 1980, 102, pp.265-272.
[27]Lanzon, A., Anderson, B.D.O., and Bombois, X.: ‘Selection of a single uniquely specifiable H∞ controller in the chain-scattering framework,’ Automatica, 2004, 40, pp. 985-994.
[28]Lee, P. H., and Soh, Y. C.: ‘Synthesis of simultaneous stabilizing H∞ controller,’ International Journal of Control, 2005, 78, (18), pp.1437-1446.
[29]Loffler, K., Gienger, M., Pfeiffer, F., and Ulbrich, H.: ‘Sensors and control concept of a biped robot,’ IEEE Trans. Industrial Electronics, 2004, 51, (5), pp.972-980.
[30]Lorenz, R.D., and Schmidt, P.B.: ‘Synchronized motion control for process automation,’ in Conf. Record of IEEE, IAS Annual Meeting, San Diego, U.S.A., 1989, pp. 1693-1698.
[31]Lorenz, R.D.: ‘Robotics and automation applications of drives and converters,’ in Proceedings of the IEEE, 2001, 89, (6), pp. 951-962.
[32]Malasse, O., Zasadzinski, M., Iung, C., Hayar, M., and Darouach, M.: ‘H∞ design using normalized coprime factors: an application to an electromechanical actuator,’ in Proceedings of the Third IEEE Conference on Control Applications, Orlando, U.S.A., 1994, pp. 983-988.
[33]McFarlane, D., and Glover, K.: ‘A loop shaping design procedure using H∞ synthesis,’ IEEE Trans. AC, 1992, 37, (6), pp. 759-769.
[34]Mihelj, M., and Munih, M.: ‘Double inverted pendulum optimal control- basis for unsupported standing in paraplegia,’ in Proc. AMC, Maribor, Slovenia, 2002, pp. 121-126.
[35]Payette, K.: ‘Synchronized motion control with the virtual shaft control algorithm and acceleration feedback,’ in Proc. of the American Control Conference, San Diego, U.S.A., 1999, pp. 2102-2106.
[36]Petty, R.D.: ‘Transportation technologies for community policing: a comparison,’ in Proc. ISTAS/CPTED, Amsterdam, Netherlands, 2003, pp. 33-38.
[37]Postlethwaite, I., O'Young, S.D., Gu, D.W., and Hope, J.: ‘H∞ control system design: A critical assessment based on industrial applications,’ in Proc. of the 10th IFAC World Congress, Munich, Germany, 1987, pp. 328-333.
[38]Pugh, A.C., and Tan, L.: ‘A generalized chain-scattering representation and its algebraic system properties,’ IEEE Trans. AC, 2002, 45, (5), pp. 1002-1007.
[39]Sampei, M., Mita, T., Chida, Y., and Nakamichi, M.: ‘A direct approach to H∞ control problems using bounded real lemma,’ in Proc. of 28th Conference on Decision and Control, Tampa, U.S.A., 1989, pp. 1494-1499.
[40]Schierling, H.: ‘Fast and reliable commissioning of AC variable speed drives by self-commissioning,’ in Proc. of IEEE IAS Annual Meeting, Pittsburg, U.S.A., 1988, pp. 489-492.
[41]Shiroma, N., Matsumoto, O., Kajita, S., and Tani, K.: ‘Cooperative behavior of a wheeled inverted pendulum for object transportation,’ in Proc. IROS, Osaka, Japan, 1996, pp. 396-401.
[42]Skogestad, S., and Postlethwaite, I.: Multivariable Feedback Control- Analysis and Design, John Wiley & Sons, Inc., 1996.
[43]Tan, K.K., Lim, S.Y., Huang, S., Dou, H.F., and Giam, T.S.: ‘Coordinated motion control of moving gantry stages for precision applications based on observer-augmented composite controller,’ IEEE Trans. Control System Technology, 2004, 12, (6), pp.984-991.
[44]Tsai, M.C., and Postlethwaite, I.: ‘On J-lossless coprime factorization approach to H∞ control,’ International Journal of Robust and Nonlinear Control, 1991, 1, pp. 47-68.
[45]Tsai, M.C., and Tsai, C.S.: ‘A chain scattering-matrix description approach to H∞ control,’ IEEE Trans. AC, 1993, 38, (6), pp. 1416-1421.
[46]Tsai, M.C., and Tsai, C.S., and Sun, Y.Y.: ‘On discrete-time H∞ control: a J-lossless coprime factorization approach,’ IEEE Trans. AC, 1993, 38, (7), pp. 1143-1147.
[47]Tsai, M.C., Chuang, H.S., and Lee, M.Y.: ‘Biaxial contouring control using H∞ pole placement design,’ International J. of JSME, Series C, 1998, 41, pp. 413-420.
[48]Whidborne, J., Postlethwaite, I., and Gu, D.W.: ‘Robust controller design using H�V loop-shaping and the method of inequalities,’ in Proc. of Conference on Decision and Control, San Antonio, U.S.A., 1993, pp. 2163-2168.
[49]Yang, J.X., Tsai, M.C., and Hsieh, M.F.: ‘Identification and control of a linear servo system,’ in Proceedings of the 4th International Symposium on Linear Drives for Industry Applications, LDIA 2003, Birmingham, UK, 2003, pp. 351-354.
[50]Yeh, S.S., and Hsu, P.L.: ‘Analysis and design of the integrated controller for precise motion systems,’ IEEE Trans. Control system Technology, 1999, 7, (6), pp.706-717.
[51]Younkin, G.W., McGlasson, W.D., and Lorenz, R.D.: ‘Considerations for low-inertia AC drives in machine tool axis servo,’ IEEE Trans. Industry Applications, 1991, 27, pp. 262-267.
[52]Yu, D., Guo, Q., and Hu, Q.: ‘Study on synchronous drive technique of biaxial linear servo motor based on decoupling control and internal model control with two-degree-of-freedom,’ Proceedings of the 6th International Conference on ICEMS, Beijing, China, 2003, pp. 541-543.
[53]Zames, G.: ‘Feedback and optimal sensitivity: model reference transformation, multiplicative seminorms, and approximated inverse,’ IEEE Trans. AC, 1981, 26, pp. 301-320.
[54]Zhu, C., and Kawamura, A.: ‘Walking principle analysis for biped robot with ZMP concept, friction constraint, and inverted pendulum model,’ in Proc. International Conference on Intelligent Robots and Systems, Les Vegas, U.S.A., 2003, pp. 364-369.
[55]Zhou, K., Doyle, J.C., and Glover, K.: Robust and optimal control, Prentice-Hall Inc., New Jersey, 1996.
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top