离散系统变结构控制理论及其在电力电子装置中的应用
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摘要
本文探讨了离散系统的变结构控制及其在电力电子装置中的应用。论文首先简要地回顾了连续系统的变结构控制，然后分析了将连续系统的变结构控制离散化后应用在离散系统时采样时间选取的问题；论述了直接针对离散系统的变结构控制的一些常用的方法，改进了离散变结构控制的等式到达条件；在此基础上，提出了一类新的离散系统的趋近律方法——衰减变速趋近律，并从理论上证明了它是一种无抖振的趋近律，通过仿真验证理论的正确性。同时，阐述了离散系统变结构无抖振控制的设计方法。论文重点讨论了离散系统鲁棒变结构控制方法，特别是应用离散衰减变速趋近律实现的鲁棒控制策略。最后讨论了离散变结构控制在电力电子装置中的应用实例及对离散变结构控制的发展方向作了展望。
Variable structure control of discrete-time systems and its applications in power electronic apparatus are discussed in this paper. At first, variable structure control of continuous-time systems is reviewed briefly. After that, the problem of choosing sample time in the discretized variable structure control of continuous-time systems is analyzed. Some common methods of variable structure control for the discrete-time system are dissertated, and the discrete equation reaching conditions are improved . A new reaching law based on attenuating variable rate control which is verified as a chattering-free reaching law in theory is presented and its' correctness is validated by simulation. Meanwhile, design methods of chattering-free in the discrete-time systems are expounded and the strategies of robust control for the discrete-time variable structure control systems are discussed in emphasize, especially the robust discrete-time variable structure control strategy with the reaching law based on discrete attenua
ting rate control . In the end, some applications in the power electronic apparatus with the discrete-time variable structure control are introduced. The future development for the discrete-time variable structure control systems is also provided.
Variable structure control of discrete-time systems and its applications in power electronic apparatus are discussed in this paper. At first, variable structure control of continuous-time systems is reviewed briefly. After that, the problem of choosing sample time in the discretized variable structure control of continuous-time systems is analyzed. Some common methods of variable structure control for the discrete-time system are dissertated, and the discrete equation reaching conditions are improved . A new reaching law based on attenuating variable rate control which is verified as a chattering-free reaching law in theory is presented and its' correctness is validated by simulation. Meanwhile, design methods of chattering-free in the discrete-time systems are expounded and the strategies of robust control for the discrete-time variable structure control systems are discussed in emphasize, especially the robust discrete-time variable structure control strategy with the reaching law based on discrete attenua
ting rate control . In the end, some applications in the power electronic apparatus with the discrete-time variable structure control are introduced. The future development for the discrete-time variable structure control systems is also provided.
引文
1. Xinghou Yu. Discrete variable structure control systems. Int. J.Systems. Sci., 1993, Vol.24,No.2:273～386.
2. Furuta K. Sliding mode control of a discrete system. System &Control Letters, 1990. Vol.14:145～152.
3. Wang W J, Wu G H, Yang D C. Variable structure control design for uncertain discrete time systems. IEEE AC., 1994,Vol.39.No.1: 99～102.
4. S. K. Spurgeon. Hyperplane design techniques for discrete time variable structure control systems. Int J. Control, 1992,Vol.66,No.2: 445～456.
5. Engin Yaz, Xiaoru Niu. Stability robustness of linear discrete time systems in the presence of uncertaInty. Int. J. Control, 1989, Vol.50, No.1: 173～182.
6. Weibing Gao, Yufu Wang, Abdollah Homaifa. Discrete time variable structure control systems. IEEE. Trans. on IE., 1995, Vol.42,No.2:117～122.
7. F. Yu, Z. X. Chang, and Y. W. Shi. Variable structure control of discrete time systems and their quality. Proc. ICIT'96,1996: 816～820.
8．翟长连，吴智铭．不确定时间系统离散变结构控制设计．自动化学报，2000．Vol．26，No．2：184-191
9. A. Balestrino,A. Landi, Intelligent variable structure control in electrical drive. IEEE Int. WIM. 1990:333～338
10. K. Furuta, K. Kosuge and H. Kobayasshi. Selftuming sliding mode and adaptive control for direct drive motor. IEEE Int. EC., 1985. Vol.32,No.3:238～244.
11．彭永进著．变结构控制的基础与理论讲义．湖南大学
12．高为炳著．变结构控制基础，科学出版社，1989．
13．高为炳著．变结构控制的理论及设计方法．北京：科学出版社，1996．
14．姚琼荟，黄继起，吴汉松编著．变结构控制系统．重庆：重庆大学出版社，1997．
15．李涛，冯勇，安澄全．变加权系数减小变结构系统抖振的设计方法．控制与决策．2000．Vol．15，No．6：645～648．
16．李涛，冯勇，安澄全．变边界饱和特性减小抖振的设计方法．自动化学报．2000．Vol．26，No．1：90～93．
17．叶涛．变结构控制的抖动抑制及其在伺服系统中的应用．湖南大学硕士学位论文．1999
18. M.Letizia Corradini and Giuseppe Orlando. Variable structure control of discretized continuous time systems. IEEE Trans on AC.,1998. Vol.43, No.9:1329～1333.
19. Addisu Tesfaye, Masayoshi Tomizuka. Robust control of discretized continuous systems using the theory of sliding modes. Int. J. Control, 1995,Vol.62,No.1: 209～226.
20. XinKai Chen, Toshio Fukuda. Computer controlled continuous time variable structure systems with sliding modes. Int. J. Control,1997,Vol.(67), No.4:619～639.
21. K.David Young, Vadim I.Utkin. A control engineer's guide to sliding mode control.IEEE Trans on CS.,1999, Vol.7,No.3:328～341.
22. Choon Yik Tang, Eduardo A. Mosawa. Discrete variable structure control for linear Multivariable Systems. ASME.,2000,Vol. 122,No. 10: 783～791.
23. Jung-ho Kim Seung-Hyun Oh,J.Karl Hedrick. Robust discrete time variable structure control Methods. ASME., 2000, Vol. 122 ,No. 10: 766～775.
24. Sami Z. Sarpturk, Yorgo Istefanopulos,Okyay Kaynak. On the stability of discrete time sliding mode control systems.. IEEE. Trans.on AC., 1987, Vol.32, No.10:930～932.
25. Xinghuo Yu, Renfrey B. Protts. Analysis of discrete variable structure systems with pseudo-sliding modes.Int. J.Systems Sci.,1992, Vol. 23, No.4,503～516.
26. Wen-June Wang, Rong-Chyang Lee, Dah-ching Yang. Sliding mode control design in multi-input perturbed discrete time systems. ASME.,1996, Vol. 118, No.6: 322～327.
27. A.Jafafi Koshkouei,A.S.I.Zinober. Sliding mode control of discrete time systems. Trans of the ASME., 2000, Vol. 122,No. 10:793～801.
28. Hebertt Sira-Ramirez. Non-linear discrete variable structure systems in quasi-sliding mode. Int. J. Control, 1991, Vol.54,No.5:1171～1187.
29．高为炳．离散系统的变结构控制．自动化学报：1995，Vol．21，No．2：154～161．
30．姚琼荟，宋立忠，温洪．离散变结构控制系统的比例-等速-变速控制．控制与决策．2000．Vol．15，No．3：329～332．
31．周靖林，肖雁鸿等．离散变结构系统的衰减变速控制．基础自动化，2001，Vol．8，No．5：16～18．
32. Xiao Yanhong.Zhou Jinglin. The reaching law for variable structure control of discrete Time system based on attenuation control. 控制理论与应用．已录用．
33. Xinghuo Yu, Shuanghe Yu. Discrete sliding mode control design with invariant sliding sectors. Trans. of the ASME., 2000, Vol. 122,No. 10:776～781.
34. Hsu L. Smooth sliding control of uncertain systems based on a prediction error, Int J of
Robust and Nonlinear Control..l997,Vol.7No.4:353-372．
35． Shengyuan Xu ,Chengwu Yang . Yuang Niu . Robust stabilization for uncertain discrete singular systems . Automatica, 2001． Vol.37: 769-774．
36． Pan Y,Furuta K. Discrete time VSS controller design. Int.J. of Robust and Nonlinear Control,1997,Vol.7,No.4:373~386．
37． Yongsoon Eun,Dong-Il Dan Cho . Robustness of multivariable discrete time variable structure control. Int.J. Control,1999, Vol.72． No.12 : 1106-1115．
38． Yongsoon Eun,June-Ho Kim.Kwangsoo Kim, Dong-II Cho, Discrete time variable structure controller with a decoupled disturbance compensator and its application to a CNC servomechanism . IEEE Trans on CS.,1999, Vol.7, No.4:414-423．
39． Mooncheol, Won, J.K.Hedrick . Disturbance adaptive discrete time sliding control with application to engine speed control. ASME.,2001, Vol.123 , No.3:1~9．
40． Feng-Hsiag Hsiao, Shing-Tai Pan, Jiing-Dong Hwang . D-stabilization control for discrete time two-time-scale systems . IEEE. Control Systems Magazine ,2000, No.2 : 56-66．
41． Xinkai Chen . Toshio Fukuda . Variable structure system theory based disturbance identification and its application.Int.J.Control,1997, Vol.68, No.2: 373-384．
42． XinKai Chen , Toslu'o Fukuda . Adaptive quasi-sliding mode control for discrete time multivariable systems . Int. J. Control. 1999 Vol. 72, No.2: 133-140．
43． Xiaoqiu Li , Stephen Yurkovich . Neural network based , discrete adaptive sliding mode control for idle speed regulation in IC engines.ASME.,2000, Vol. 122, No.6 :269~278．
44． C.Y.Chan . Discrete time adaptive sliding mode control of a linear system in state space form. Int. J. Control ,1997,Vol. 67, No.6: 859-868．
45． C.Y.Chan .Discrete adaptive quasi-sliding mode control. Int.J. Control,1999, Vol.72, No.4: 365-373．
46． Feng Zhao,Vadim I Utkin . Adaptive simulation and control of variable structure systems in sliding regimes . Automatica ,1996;VoI.32,No.7:1037-1042．
47． 马勇,计晓鸣，李辉．基于模糊逻辑系统的变结构控制．电气自动化，2000,No．1：4-6
48． Steven Ching-Yei Chung . The frequency domain analysis of discrete variable structure control and chattering-free criteria. IJ. of Sys. Sci., 2000,Vol. 31, No.12: 1619-1626．
49． D.Q.Zhang , S.K-Panda . Chattering-free and fast response sliding mode controller . IEE. Proc.-Control Theory Appl. ,1999, Vol.146 e No. 2 :171~177．
50． 于双和,强文义,傅佩琛．无抖振离散准滑模控制．控制与决策 2001．
Vol.16,No.3:380～382.
51. E.A. Misawa. Discrete time sliding mode control: The linear case.ASME., 1997, Vol. 119,No. 12:819～821.
52. Chung. S.C.,Lin C.I. A transformed Lure′ problem for sliding mode control and chattering reduction.IEEE. Trans. on AC.,1999, Vol.44,No.3:563～568.
53. Chung. S.C.,Lin C.I. A general class of sliding surface for the sliding mode control.IEEE. Trans. on AC. ,1998,Vol.43,No.6:1509～1512..
54. Hebrett Sira-Ramirez. Sliding mode controlled relaxation oscillations. IEEE. Trans. on CS.,1990, Vol.37,No.4: 540～543.
55. Jessen Chen, Pei-Chong Tang. Sliding mode current control scheme for DC motor drives. IEEE. Trans. on PE., 1999,Vol.14,No.3:5541～551.
56. Cem Unsal,Pushkin Kachroo. Sliding mode measurement feedback control for antilock braking systems. IEEE Trans. on CS., 1999 ,Vol.7,No.2:271～280.
57. Masahiro Nishimoto, Juan W. Dixon Ashok etc. An Integrate controller current PWM rectifier chopper link for sliding mode position control. IEEE. Trans. on IA.,1987,Vol.23,No.5:894~899.
58．李辉，谢剑英，高卫华．感应电机调速系统的变结构控制．电气自动化，2000，No．4：10～13．
59．吴捷，钱来，杨金明．感应电机锁相及模糊滑动模控制．控制理论与应用，2000，Vol．17，No．2：198～203．
60．夏超英著．交直流传动系统的自适应控制．北京．机械工业出版社，1998：116～159．
61．胡寿松编．自动控制原理．北京．国防工业出版社，1994：518～541．
62．李辉，谢剑英．基于一种新的变结构控制思想的开关型正弦电压源．电气传动，2000，No．5：61～64．
63．何希才编著．新型开关电源设计与应用．北京．科学出版社，2001：37～51．
64．王聪编著．软开关功率变换器及其应用．北京．科学出版社，2000：172～178．
2. Furuta K. Sliding mode control of a discrete system. System &Control Letters, 1990. Vol.14:145～152.
3. Wang W J, Wu G H, Yang D C. Variable structure control design for uncertain discrete time systems. IEEE AC., 1994,Vol.39.No.1: 99～102.
4. S. K. Spurgeon. Hyperplane design techniques for discrete time variable structure control systems. Int J. Control, 1992,Vol.66,No.2: 445～456.
5. Engin Yaz, Xiaoru Niu. Stability robustness of linear discrete time systems in the presence of uncertaInty. Int. J. Control, 1989, Vol.50, No.1: 173～182.
6. Weibing Gao, Yufu Wang, Abdollah Homaifa. Discrete time variable structure control systems. IEEE. Trans. on IE., 1995, Vol.42,No.2:117～122.
7. F. Yu, Z. X. Chang, and Y. W. Shi. Variable structure control of discrete time systems and their quality. Proc. ICIT'96,1996: 816～820.
8．翟长连，吴智铭．不确定时间系统离散变结构控制设计．自动化学报，2000．Vol．26，No．2：184-191
9. A. Balestrino,A. Landi, Intelligent variable structure control in electrical drive. IEEE Int. WIM. 1990:333～338
10. K. Furuta, K. Kosuge and H. Kobayasshi. Selftuming sliding mode and adaptive control for direct drive motor. IEEE Int. EC., 1985. Vol.32,No.3:238～244.
11．彭永进著．变结构控制的基础与理论讲义．湖南大学
12．高为炳著．变结构控制基础，科学出版社，1989．
13．高为炳著．变结构控制的理论及设计方法．北京：科学出版社，1996．
14．姚琼荟，黄继起，吴汉松编著．变结构控制系统．重庆：重庆大学出版社，1997．
15．李涛，冯勇，安澄全．变加权系数减小变结构系统抖振的设计方法．控制与决策．2000．Vol．15，No．6：645～648．
16．李涛，冯勇，安澄全．变边界饱和特性减小抖振的设计方法．自动化学报．2000．Vol．26，No．1：90～93．
17．叶涛．变结构控制的抖动抑制及其在伺服系统中的应用．湖南大学硕士学位论文．1999
18. M.Letizia Corradini and Giuseppe Orlando. Variable structure control of discretized continuous time systems. IEEE Trans on AC.,1998. Vol.43, No.9:1329～1333.
19. Addisu Tesfaye, Masayoshi Tomizuka. Robust control of discretized continuous systems using the theory of sliding modes. Int. J. Control, 1995,Vol.62,No.1: 209～226.
20. XinKai Chen, Toshio Fukuda. Computer controlled continuous time variable structure systems with sliding modes. Int. J. Control,1997,Vol.(67), No.4:619～639.
21. K.David Young, Vadim I.Utkin. A control engineer's guide to sliding mode control.IEEE Trans on CS.,1999, Vol.7,No.3:328～341.
22. Choon Yik Tang, Eduardo A. Mosawa. Discrete variable structure control for linear Multivariable Systems. ASME.,2000,Vol. 122,No. 10: 783～791.
23. Jung-ho Kim Seung-Hyun Oh,J.Karl Hedrick. Robust discrete time variable structure control Methods. ASME., 2000, Vol. 122 ,No. 10: 766～775.
24. Sami Z. Sarpturk, Yorgo Istefanopulos,Okyay Kaynak. On the stability of discrete time sliding mode control systems.. IEEE. Trans.on AC., 1987, Vol.32, No.10:930～932.
25. Xinghuo Yu, Renfrey B. Protts. Analysis of discrete variable structure systems with pseudo-sliding modes.Int. J.Systems Sci.,1992, Vol. 23, No.4,503～516.
26. Wen-June Wang, Rong-Chyang Lee, Dah-ching Yang. Sliding mode control design in multi-input perturbed discrete time systems. ASME.,1996, Vol. 118, No.6: 322～327.
27. A.Jafafi Koshkouei,A.S.I.Zinober. Sliding mode control of discrete time systems. Trans of the ASME., 2000, Vol. 122,No. 10:793～801.
28. Hebertt Sira-Ramirez. Non-linear discrete variable structure systems in quasi-sliding mode. Int. J. Control, 1991, Vol.54,No.5:1171～1187.
29．高为炳．离散系统的变结构控制．自动化学报：1995，Vol．21，No．2：154～161．
30．姚琼荟，宋立忠，温洪．离散变结构控制系统的比例-等速-变速控制．控制与决策．2000．Vol．15，No．3：329～332．
31．周靖林，肖雁鸿等．离散变结构系统的衰减变速控制．基础自动化，2001，Vol．8，No．5：16～18．
32. Xiao Yanhong.Zhou Jinglin. The reaching law for variable structure control of discrete Time system based on attenuation control. 控制理论与应用．已录用．
33. Xinghuo Yu, Shuanghe Yu. Discrete sliding mode control design with invariant sliding sectors. Trans. of the ASME., 2000, Vol. 122,No. 10:776～781.
34. Hsu L. Smooth sliding control of uncertain systems based on a prediction error, Int J of
Robust and Nonlinear Control..l997,Vol.7No.4:353-372．
35． Shengyuan Xu ,Chengwu Yang . Yuang Niu . Robust stabilization for uncertain discrete singular systems . Automatica, 2001． Vol.37: 769-774．
36． Pan Y,Furuta K. Discrete time VSS controller design. Int.J. of Robust and Nonlinear Control,1997,Vol.7,No.4:373~386．
37． Yongsoon Eun,Dong-Il Dan Cho . Robustness of multivariable discrete time variable structure control. Int.J. Control,1999, Vol.72． No.12 : 1106-1115．
38． Yongsoon Eun,June-Ho Kim.Kwangsoo Kim, Dong-II Cho, Discrete time variable structure controller with a decoupled disturbance compensator and its application to a CNC servomechanism . IEEE Trans on CS.,1999, Vol.7, No.4:414-423．
39． Mooncheol, Won, J.K.Hedrick . Disturbance adaptive discrete time sliding control with application to engine speed control. ASME.,2001, Vol.123 , No.3:1~9．
40． Feng-Hsiag Hsiao, Shing-Tai Pan, Jiing-Dong Hwang . D-stabilization control for discrete time two-time-scale systems . IEEE. Control Systems Magazine ,2000, No.2 : 56-66．
41． Xinkai Chen . Toshio Fukuda . Variable structure system theory based disturbance identification and its application.Int.J.Control,1997, Vol.68, No.2: 373-384．
42． XinKai Chen , Toslu'o Fukuda . Adaptive quasi-sliding mode control for discrete time multivariable systems . Int. J. Control. 1999 Vol. 72, No.2: 133-140．
43． Xiaoqiu Li , Stephen Yurkovich . Neural network based , discrete adaptive sliding mode control for idle speed regulation in IC engines.ASME.,2000, Vol. 122, No.6 :269~278．
44． C.Y.Chan . Discrete time adaptive sliding mode control of a linear system in state space form. Int. J. Control ,1997,Vol. 67, No.6: 859-868．
45． C.Y.Chan .Discrete adaptive quasi-sliding mode control. Int.J. Control,1999, Vol.72, No.4: 365-373．
46． Feng Zhao,Vadim I Utkin . Adaptive simulation and control of variable structure systems in sliding regimes . Automatica ,1996;VoI.32,No.7:1037-1042．
47． 马勇,计晓鸣，李辉．基于模糊逻辑系统的变结构控制．电气自动化，2000,No．1：4-6
48． Steven Ching-Yei Chung . The frequency domain analysis of discrete variable structure control and chattering-free criteria. IJ. of Sys. Sci., 2000,Vol. 31, No.12: 1619-1626．
49． D.Q.Zhang , S.K-Panda . Chattering-free and fast response sliding mode controller . IEE. Proc.-Control Theory Appl. ,1999, Vol.146 e No. 2 :171~177．
50． 于双和,强文义,傅佩琛．无抖振离散准滑模控制．控制与决策 2001．
Vol.16,No.3:380～382.
51. E.A. Misawa. Discrete time sliding mode control: The linear case.ASME., 1997, Vol. 119,No. 12:819～821.
52. Chung. S.C.,Lin C.I. A transformed Lure′ problem for sliding mode control and chattering reduction.IEEE. Trans. on AC.,1999, Vol.44,No.3:563～568.
53. Chung. S.C.,Lin C.I. A general class of sliding surface for the sliding mode control.IEEE. Trans. on AC. ,1998,Vol.43,No.6:1509～1512..
54. Hebrett Sira-Ramirez. Sliding mode controlled relaxation oscillations. IEEE. Trans. on CS.,1990, Vol.37,No.4: 540～543.
55. Jessen Chen, Pei-Chong Tang. Sliding mode current control scheme for DC motor drives. IEEE. Trans. on PE., 1999,Vol.14,No.3:5541～551.
56. Cem Unsal,Pushkin Kachroo. Sliding mode measurement feedback control for antilock braking systems. IEEE Trans. on CS., 1999 ,Vol.7,No.2:271～280.
57. Masahiro Nishimoto, Juan W. Dixon Ashok etc. An Integrate controller current PWM rectifier chopper link for sliding mode position control. IEEE. Trans. on IA.,1987,Vol.23,No.5:894~899.
58．李辉，谢剑英，高卫华．感应电机调速系统的变结构控制．电气自动化，2000，No．4：10～13．
59．吴捷，钱来，杨金明．感应电机锁相及模糊滑动模控制．控制理论与应用，2000，Vol．17，No．2：198～203．
60．夏超英著．交直流传动系统的自适应控制．北京．机械工业出版社，1998：116～159．
61．胡寿松编．自动控制原理．北京．国防工业出版社，1994：518～541．
62．李辉，谢剑英．基于一种新的变结构控制思想的开关型正弦电压源．电气传动，2000，No．5：61～64．
63．何希才编著．新型开关电源设计与应用．北京．科学出版社，2001：37～51．
64．王聪编著．软开关功率变换器及其应用．北京．科学出版社，2000：172～178．