非线性非最小相位系统的控制研究综述

苏善伟; 朱波; 向锦武; 林岩

doi:10.16383/j.aas.2015.c140322

非线性非最小相位系统的控制研究综述

doi: 10.16383/j.aas.2015.c140322

苏善伟^1, ,,
朱波²,
向锦武³,
林岩⁴

1.
北京航空航天大学无人机研究所北京 100191;
2.
电子科技大学航空航天学院成都 611731;
3.
北京航空航天大学航空科学与工程学院北京 100191;
4.
北京航空航天大学自动化科学与电气工程学院北京 100191

基金项目:

国家自然科学基金(61403013, 61304016, 61273141);中国博士后基金(2013M530509)资助

详细信息

作者简介:
朱波电子科技大学航空航天学院副教授.主要研究方向为非最小相位系统,控制系统瞬态调节技术,运动同步控制技术.E-mail:zhubo_uestc@163.com

通讯作者:
苏善伟北京航空航天大学无人机研究所讲师.2012年获得北京航空航天大学控制理论与控制工程专业博士学位.主要研究方向为非最小相位系统,飞行控制.本文通信作者. E-mail:sushanwei@aliyun.com

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出版历程
- 收稿日期: 2014-05-07
- 修回日期: 2014-09-19
- 刊出日期: 2015-01-20

A Survey on the Control of Nonlinear Non-minimum Phase Systems

SU Shan-Wei^{1
, ,},
ZHU Bo²,
XIANG Jin-Wu³,
LIN Yan⁴

1.
Research Institute of Unmanned Aerial Vehicle, Beihang University, Beijing 100191;
2.
School of Aeronautics and Astronautics, University of Electronic Science and Technology of China (UESTC), Chengdu 611731;
3.
School of Aeronautics Science and Engineering, Beihang University, Beijing 100191;
4.
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191

Funds:

Supported by National Natural Science Foundation of China (61403013, 61304016, 61273141) and China Postdoctoral Science Foundation (2013M530509)

摘要

摘要: 非线性非最小相位系统是指具有不稳定零动态或内部动态的非线性系统, 其本身固有的非最小相位特性限制了许多常规非线性控制方法(如反推控制、反馈线性化、滑模控制等)的直接应用. 因此, 非最小相位系统的控制比最小相位系统要困难得多, 是控制理论与工程应用中具有挑战性的课题之一. 本文综述了目前非线性非最小相位系统的研究成果, 着重介绍了非最小相位系统的成因、特性、理想内模求解等问题, 并对其镇定、轨迹跟踪及路径跟踪等控制方法进行了分析比较. 最后, 讨论了非线性非最小相位系统研究领域中尚存在的问题, 并对其未来发展方向进行了展望.
- 非最小相位 /
- 非线性控制 /
- 零动态 /
- 镇定 /
- 跟踪控制
Abstract: Nonlinear non-minimum phase systems have unstable zero dynamics or internal dynamics, their non-minimum phase property restricts the direct application of many powerful nonlinear control techniques, such as backstepping, feedback linearization, and sliding mode control. So the control of non-minimum phase systems is more difficult than that of minimum phase systems, and is one of the challenging issues in the control theory and engineering applications. This research summarizes the existing results of nonlinear non-minimum phase systems, and focuses on the topics including the origin of non-minimum phase systems, their characteristics and the solution methods of ideal internal dynamics. The control methods of stabilization, trajectory tracking and path following are analyzed and compared as well. Finally, the problems to be solved and the research trends are prospected at the end of the paper.
- Non-minimum phase /
- nonlinear control /
- zero dynamics /
- stabilization /
- tracking control

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参考文献(95)

[1]	Slotine J J E, Li W P. Applied Nonlinear Control. New York: Prentice-Hall, 1991. 224-228
[2]	Isidori A. Nonlinear Control Systems (3rd edition). London: Springer-Verlag, 1995. 69-83
[3]	Zhao H C, Chen D G. Tip trajectory tracking for multilink flexible manipulators using stable inversion. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 314-320
[4]	Benosman M, Le Vey G. Stable inversion of SISO nonminimum phase linear systems through output planning: an experimental application to the one-link flexible manipulator. IEEE Transactions on Control Systems Technology, 2003, 11(4): 588-597
[5]	Zhang R J, Chen Y B, Sun Z Q, Sun F C, Xu H Z. Path control of a surface ship in restricted waters using sliding mode. IEEE Transactions on Control Systems Technology, 2000, 8(4): 722-732
[6]	Consolini L, Tosques M. A minimum phase output in the exact tracking problem for the nonminimum phase underactuated surface ship. IEEE Transactions on Automatic Control, 2012, 57(12): 3174-3180
[7]	Hauser J, Sastry S, Meyer G. Nonlinear control design for slightly non-minimum phase systems: application to V/STOL aircraft. Automatica, 1992, 28(4): 665-679
[8]	Tomlin C J, Sastry S S. Bounded tracking for non-minimum phase nonlinear systems with fast zero dynamics. International Journal of Control, 1997, 68(4): 819-848
[9]	Martin P, Devasia S, Paden B. A different look at output tracking: control of a VTOL aircraft. Automatica, 1996, 32(1): 101-107
[10]	Devaud E, Siguerdidjane H, Font S. Some control strategies for a high-angle-of-attack missile autopilot. Control Engineering Practice, 2000, 8: 885-892
[11]	Fiorentni L, Serrani A. Adaptive restricted trajectory tracking for a non-minimum phase hypersonic vehicle model. Automatica, 2012, 48(7): 1248-1261
[12]	Sun Chang-Yin, Mu Chao-Xu, Yu Yao. Some control problems for near space hypersonic vehicles. Acta Automatica Sinica, 2013, 39(11): 1901-1913 (孙长银, 穆朝絮, 余瑶. 近空间高超声速飞行器控制的几个科学问题研究. 自动化学报, 2013, 39(11): 1901-1913)
[13]	Serrani A. Nested zero-dynamics redesign for a non-minimum phase longitudinal model of a hypersonic vehicle. In: Proceedings of the 52nd Annual Conference on Decision and Control. Florence, Italy: IEEE, 2013. 4833-4838
[14]	Tomlin C, Lygeros J, Benvenuti L. Output tracking for a non-minimum phase dynamic CTOL aircraft model. In: Proceedings of the 34th Conference on Decision and Control. New Orleans, USA: IEEE, 1995. 1867-1872
[15]	Kanellakopoulos I, Kokotovic P V, Morse A S. Adaptive output-feedback control of a class of nonlinear systems. In: Proceedings of the 30th Conference on Decision and Control. Brighton, England: IEEE, 1991. 1082-1087
[16]	Kristic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: John Wiley-Sons, 1995. 1082-1087
[17]	Huang J Y, Gao W B, Huang J C. Variable structure control: a survey. IEEE Transactions on Industrial Electronics, 1993, 40(1): 2-22
[18]	Shkolnikov I A, Shtessel Y B. Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center. Automatica, 2002, 38(5): 837-842
[19]	Shkolnikov I A, Shtessel Y B. Aircraft nonminimum phase control in dynamic sliding manifolds. Journal of Guidance, Control, and Dynamics, 2001, 24(3): 566-572
[20]	Kokotovic P, Arcak M. Constructive nonlinear control: a historical perspective. Automatica, 2001, 37(5): 637-662
[21]	Grizzle J W, Di Benedetto M D. Approximation by regular input-output maps. IEEE Transactions on Automatic Control, 1992, 37(7): 1052-1055
[22]	Hu Shou-Song. Automatic Control Theory. Beijing: Science Press, 2001. 159-160(胡寿松. 自动控制原理. 北京: 科学出版社, 2001. 159-160)
[23]	Zhou K M. Relative/multiplicative model reduction for unstable and non-minimum-phase systems. Automatica, 1995, 31(8): 1087-1098
[24]	Qiu L, Zhou K M. Introduction to Feedback Control. New Jersey: Pearson Education, Inc., 2010. 168-172
[25]	Stewart J, Devison D E. On overshoot and nonminimum phase zeros. IEEE Transactions on Automatic Control, 2006, 51(8): 1378-1382
[26]	Lau K, Middleton R H, Braslavsky J H. Undershoot and settling time tradeoffs for nonminimum phase systems. IEEE Transactions on Automatic Control, 2003, 48(8): 1389- 1393
[27]	Huang C S, Yuan K. Output tracking of a non-linear non-minimum phase PVTOL aircraft based on non-linear state feedback control. International Journal of Control, 2002, 75(6): 466-473
[28]	Gopalswamy S, Hedrick J K. Tracking nonlinear non-minimum phase systems using sliding control. International Journal of Control, 1993, 57(5): 1141-1158
[29]	Al-Hiddabi S A, McClamroch N H. Tracking and maneuver regulation control for nonlinear nonminimum phase systems: application to flight control. IEEE Transactions on Control Systems Technology, 2002, 10(6): 780-792
[30]	Kapila V, Grigoriadis K M. Actuator Saturation Control. New York: Marcel Dekker, 2002. 221-223
[31]	Al-Hiddabi S A. Position Tracking and Path Following for Flight Vehicles Using Nonlinear Control [Ph.D. dissertation], The University of Michigan, Ann Arbor, USA, 2000.
[32]	Su S W, Lin Y. Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft. International Journal of Control, 2011, 84(11): 1858- 1872
[33]	Devasia S, Chen D G, Paden B. Nonlinear inversion-based output tracking. IEEE Transactions on Automatic Control, 1996, 41(7): 930-942
[34]	Chen D G, Paden B. Stable inversion of nonlinear non-minimum phase systems. International Journal of Control, 1996, 64(1): 81-97
[35]	Devasia S, Paden B. Stable inversion for nonlinear non- minimum-phase time-varying systems. IEEE Transaction on Automatic Control, 1998, 43(2): 283-288
[36]	Hunt L R, Meyer G. Stable inversion for nonlinear systems. Automatica, 1997, 33(8): 1549-1554
[37]	Zou Q Z, Devasia S. Precision preview-based stable-inversion for nonlinear nonminimum-phase systems: the VTOL example. Automatica, 2007, 43(1): 117-127
[38]	Shkolnikov I A, Shtessel Y B. Tracking controller design for a class of nonminimum-phase systems via the method of system center. IEEE Transactions on Automatic Control, 2001, 46(10): 1639-1643
[39]	Su S W, Lin Y. Robust output tracking control for a velocity-sensorless vertical take-off and landing aircraft with input disturbances and unmatched uncertainties. International Journal of Robust and Nonlinear Control, 2013, 23(11): 1198-1213
[40]	Baev S, Shtessel Y, Shkolnikov I. Nonminimum-phase output tracking in causal systems using higher-order sliding modes. International Journal of Robust and Nonlinear Control, 2008, 18(4-5): 454-467
[41]	Shtessel Y B, Baev S, Edwards C, Spurgeon S. HOSM observer for a class of non-minimum phase causal nonlinear MIMO systems. IEEE Transactions on Automatic Control, 2010, 55(2): 543-548
[42]	Isidori A, Byrnes C I. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 1990, 35(2): 131-140
[43]	Karagiannis D, Jiang Z P, Ortega R, Astolfi A. Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems. Automatica, 2005, 41(9): 1609-1615
[44]	Xie B, Yao B. Robust output feedback stabilization of a class of nonminimum phase nonlinear systems. In: Proceedings of the 2006 American Control Conference. Minneapolis, USA: IEEE, 2006. 4981-4986
[45]	Yang B J, Calise A J. Adaptive stabilization for a class of non-affine non-minimum phase systems using neural networks. In: Proceedings of the 2006 American Control Conference. Minneapolis, USA: IEEE, 2006. 2291-2296
[46]	Hoseini S M, Farrokhi M, Koshkouei A J. Adaptive neural network output feedback stabilization of nonlinear non-minimum phase systems. International Journal of Adaptive Control and Signal Processing, 2010, 24(1): 65-82
[47]	Hoseini S M, Farrokhi M, Koshkouei A J. Robust adaptive control of nonlinear non-minimum phase systems with uncertainties. Automatica, 2011, 47(2): 348-357
[48]	Isidori A. A tool for semi-global stabilization of uncertain non-minimum-phase nonlinear systems via output feedback. IEEE Transactions on Automatic Control, 2000, 45(10): 1817-1827
[49]	Nazrulla S, Khalil H K. Robust stabilization of non-minimum phase nonlinear systems using extended high-gain observers. IEEE Transactions on Automatic Control, 2011, 56(4): 802-813
[50]	Boker A M A, Khalil H K. Semi-global output feedback stabilization of a class of non-minimum phase nonlinear systems. In: Proceedings of the 2013 American Control Conference. Washington, D.C., USA: IEEE, 2013. 5270-5275
[51]	Lin F, Zhang W, Brandt R D. Robust hovering control of a PVTOL aircraft. IEEE Transactions on Control Systems Technology, 1999, 7(3): 343-351
[52]	Olfati-Saber R. Global configuration stabilization for the VTOL aircraft with strong input coupling. IEEE Transactions on Automatic Control, 2002, 47(11): 1949-1952
[53]	Wood R, Cazzolato B. An alternative nonlinear control law for the global stabilization of the PVTOL vehicle. IEEE Transactions on Automatic Control, 2007, 52(7): 1282- 1287
[54]	Zavala-Río A, Fantoni I, Lozano R. Global stabilization of a PVTOL aircraft model with bounded inputs. International Journal of Control, 2003, 76(18): 1833-1844
[55]	Ye H W, Wang H, Wang H B. Stabilization of a PVTOL aircraft and an inertia wheel pendulum using saturation technique. IEEE Transactions on Control Systems Technology, 2007, 15(6): 1143-1150
[56]	Chemori A, Marchand N. A prediction-based nonlinear controller for stabilization of a non-minimum phase PVTOL aircraft. International Journal of Robust and Nonlinear Control, 2008, 18(8): 876-889
[57]	Benvenuti L, Di Benedetto M D, Grizzle J W. Approximate output tracking for nonlinear non-minimum phase systems with an application to flight control. International Journal of Robust and Nonlinear Control, 1994, 4(3): 397-414
[58]	Lian K Y, Fu L C, Lian T L. Output tracking control of nonlinear systems with weakly non-minimum phase. In: Proceedings of the 1992 American Control Conference. Chicago, USA: IEEE, 1992. 3081-3085
[59]	Ghanadan R, Blankenship G L. Adaptive approximate tracking and regulation of nonlinear systems. In: Proceedings of the 32nd Conference on Decision and Control. San Antonio, USA: IEEE, 1993. 2654-2659
[60]	Hedrick K J, Gopalswamy S. Nonlinear flight control design via sliding methods. Journal of Guidance, Control, and Dynamics, 1990, 13(5): 850-858
[61]	Hu A P, Sadegh N. Nonlinear non-minimum phase output tracking via output redefinition and learning control. In: Proceedings of the 2001 American Control Conference. Arlington, USA: IEEE, 2001. 4264-4269
[62]	Chen C T, Peng S T. A sliding mode control scheme for non-minimum phase non-linear uncertain input-delay chemical processes. Journal of Process Control, 2006, 16(1): 37-51
[63]	Niemica P M, Kravaris C. Nonlinear model-state feedback control for nonminimum-phase processes. Automatica, 2003, 39(7): 1295-1302
[64]	Roshan Y M, Moallem M. Control of nonminimum phase load current in a boost converter using output redefinition. IEEE Transactions on Power Electronics, 2014, 29(9): 5054 -5062
[65]	Shtessel Y B. Nonlinear nonminimum phase output tracking via dynamic sliding manifolds. Journal of the Franklin Institute, 1998, 335(5): 841-850
[66]	Shkolnikov I A, Shtessel Y B. Nonminimum phase tracking in MIMO systems with square input-output dynamics via dynamic sliding manifolds. Journal of the Franklin Institute, 2000, 337(1): 43-56
[67]	Sira-Ramirez H. A dynamical variable structure control strategy in asymptotic output tracking problems. IEEE Transactions on Automatic Control, 1993, 38(4): 615-620
[68]	Shtessel Y B. Nonlinear output tracking in conventional and dynamic sliding manifolds. IEEE Transactions on Automatic Control, 1997, 42(9): 1282-1286
[69]	Shtessel Y B, Tournes C. Nonminimum phase output tracking in dynamic sliding manifolds with application to aircraft control. In: Proceedings of the 35th IEEE Conference on Decision and Control. Kobe, Japan: IEEE, 1996. 2071-2076
[70]	Pisano A, Baev S, Salimbeni D, Usai E. A new approach to causal output tracking for non-minimum phase nonlinear systems via combined first/second order sliding mode control. In: Proceedings of the 2013 European Control Conference. Zurich, Switzerland: IEEE, 2013. 3234-3239
[71]	Francis B A. The linear multivariable regulator problem. SIAM Journal on Control and Optimization, 1977, 15(3): 486-505
[72]	Byrnes C I, Isidori A. Output regulation for nonlinear systems: an overview. International Journal of Robust and Nonlinear Control, 2000, 10(5): 323-337
[73]	Chen T S, Huang J. Global robust output regulation by state feedback for strict feedforward systems. IEEE Transactions on Automatic Control, 2009, 54(9): 2157-2163
[74]	Huang J. Asymptotic tracking of a nonminimum phase nonlinear system with nonhyperbolic zero dynamics. IEEE Transactions on Automatic Control, 2000, 45(3): 542-546
[75]	Zhu B, Wang X H, Cai K Y. Approximate trajectory tracking of input-disturbed PVTOL aircraft with delayed attitude measurements. International Journal of Robust and Nonlinear Control, 2010, 20(14): 1610-1621
[76]	Do K D, Jiang Z P, Pan J. On global tracking control of a VTOL aircraft without velocity measurements. IEEE Transactions on Automatic Control, 2003, 48(12): 2212-2217
[77]	Zhu B, Wang X H, Cai K Y. Tracking control for angular-rate-sensorless vertical take-off and landing aircraft in the presence of angular-position measurement delay. IET Control Theory and Applications, 2010, 4(6): 957-969
[78]	Wang X H, Chen Z Q, Yang G. Finite-time-convergent differentiator based on singular perturbation technique. IEEE Transactions on Automatic Control, 2007, 52(9): 1731- 1737
[79]	Consolini L, Maggiore M, Nielsen C, Tosques M. Path following for the PVTOL aircraft. Automatica, 2010, 46(8): 1284-1296
[80]	Yue H, Chai T Y, Shao C. Adaptive control of nonlinear non-minimum phase systems using neural networks. In: Proceedings of the 36th Conference on Decision and Control. San Diego, USA: IEEE, 1997. 2211-2212
[81]	Jiya J, Shao C, Chai T Y. Neural network based adaptive predictive control algorithm of nonlinear non-minimum phase systems. In: Proceedings of the 1999 American Control Conference. San Diego, California, USA: IEEE, 1999. 1082-1085
[82]	Ghosh J, Paden B. Iterative learning control for nonlinear nonminimum phase plants with input disturbances. In: Proceedings of the 1999 American Control Conference. San Diego, USA: IEEE, 1999. 2584-2589
[83]	Ghosh J, Paden B. Pseudo-inverse based iterative learning control for nonlinear plants with disturbances. In: Proceedings of the 38th IEEE Conference on Decision and Control. Phoenix, USA: IEEE, 1999. 5206-5212
[84]	Liu Shan, Wu Tie-Jun. Stable-inversion based iterative learning control for non-minimum phase plants. Control Theory and Applications, 2003, 20(6): 831-837 (刘山, 吴铁军. 基于稳定逆的非最小相位系统的迭代学习控制. 控制理论与应用, 2003, 20(6): 831-837)
[85]	He Ye-Ping, Xu Ke-Hu, Shen Chun-Lin. Output tracking of non-minimum phase systems using predictive control. Journal of Nanjing University of Aeronautics and Astronautics, 2000, 32(3): 263-269 (贺也平, 徐克虎, 沈春林. 非最小相位系统输出跟踪的最优预测控制方法. 南京航空航天大学学报, 2000, 32(3): 263-269)
[86]	Chen P C, Jeng Y F, Chang Y H, Wang Y M, Chen G. Robust gain-scheduled control of a vertical takeoff aircraft with actuator saturation via the LMI method. Asian Journal of Control, 2004, 6(1): 112-122
[87]	Wu S L, Chen P C, Hsu C H, Chang K Y. Gain-scheduled control of PVTOL aircraft dynamics with parameter-dependent disturbance. Journal of the Franklin Institute, 2008, 345(8): 906-925
[88]	Zhou P, Chai T Y, Zhao J H. DOB design for nonminimum-phase delay systems and its application in multivariable MPC control. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2012, 59(8): 525-529
[89]	Liu G, Zinober A, Shtessel Y B. Second-order SM approach to SISO time-delay system output tracking. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3638-3645
[90]	Su S W, Lin Y. Output tracking control for a velocity-sensorless VTOL aircraft with measurement delays. International Journal of Systems Science, 2015, 46(5): 885-895
[91]	Wang X H, Liu J K, Cai K Y. Tracking control for a velocity-sensorless VTOL aircraft with delayed outputs. Automatica, 2009, 45(12): 2876-2882
[92]	Aguiar A P, Hespanha J P, Kokotovic P V. Path-following for nonminimum phase systems removes performance limitations. IEEE Transactions on Automatic Control, 2005, 50(2): 234-239
[93]	Aguiar A P, Hespanha J P, Kokotovic P V. Performance limitations in reference tracking and path following for nonlinear systems. Automatica, 2008, 44(3): 598-610
[94]	Dačić D B, Nešić D, Kokotovic P V. Path-following for nonlinear systems with unstable zero dynamics. IEEE Transactions on Automatic Control, 2007, 52(3): 481-487
[95]	Dačić D B, Nešić D, Teel A R, Wang W. Path following for nonlinear systems with unstable zero dynamics: an averaging solution. IEEE Transactions on Automatic Control, 2011, 56(4): 880-886

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非线性非最小相位系统的控制研究综述

doi: 10.16383/j.aas.2015.c140322

作者简介:
朱波电子科技大学航空航天学院副教授.主要研究方向为非最小相位系统,控制系统瞬态调节技术,运动同步控制技术.E-mail:zhubo_uestc@163.com

通讯作者:
苏善伟北京航空航天大学无人机研究所讲师.2012年获得北京航空航天大学控制理论与控制工程专业博士学位.主要研究方向为非最小相位系统,飞行控制.本文通信作者. E-mail:sushanwei@aliyun.com

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A Survey on the Control of Nonlinear Non-minimum Phase Systems

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目录

留言板

非线性非最小相位系统的控制研究综述

doi: 10.16383/j.aas.2015.c140322

作者简介: 朱波 电子科技大学航空航天学院副教授.主要研究方向为非最小相位系统,控制系统瞬态调节技术,运动同步控制技术.E-mail:zhubo_uestc@163.com

通讯作者: 苏善伟 北京航空航天大学无人机研究所讲师.2012年获得北京航空航天大学控制理论与控制工程专业博士学位.主要研究方向为非最小相位系统,飞行控制.本文通信作者. E-mail:sushanwei@aliyun.com

计量

出版历程

A Survey on the Control of Nonlinear Non-minimum Phase Systems

计量

出版历程

目录

作者简介:
朱波电子科技大学航空航天学院副教授.主要研究方向为非最小相位系统,控制系统瞬态调节技术,运动同步控制技术.E-mail:zhubo_uestc@163.com

通讯作者:
苏善伟北京航空航天大学无人机研究所讲师.2012年获得北京航空航天大学控制理论与控制工程专业博士学位.主要研究方向为非最小相位系统,飞行控制.本文通信作者. E-mail:sushanwei@aliyun.com