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摘要:
本文首先指出了控制领域中普遍使用的增广一阶系统方法的弊端, 介绍了高阶全驱系统的概念及其在控制器设计方面的优势, 并通过一些基础物理定律、串联系统、严反馈系统和可反馈线性化系统等例子说明了高阶全驱系统的普遍性, 进而指出高阶全驱系统是动态系统的一种描述形式, 是面向控制的模型.然后介绍了一类高阶全驱系统的一种参数化设计方法.通过适当选取一类非线性状态反馈控制律, 可获得一个具有希望特征结构的线性定常闭环系统, 并给出了闭环系统特征向量和反馈控制律的完全参数化表示, 讨论了解的存在性条件以及设计参数集合的稠密性等相关问题.最后对高阶全驱系统方法的后续问题做了说明和展望.
Abstract:In this paper, the drawback of the first-order system approaches which are widely used in the field of control systems is firstly pointed out, meanwhile the concept of high-order fully-actuated systems and, in particular, its advantage in controller design are introduced. The type of systems is demonstrated to be of wide existence by examining a number of basic physical laws and a few examples, including the common cascaded systems, the well-known strict-feedback systems, and those which can be linearized through feedback, and thus can be taken as a description of dynamical systems, more precisely, as a model for control. Then, a parametric design approach for the type of high-order fully-actuated systems is presented. With a proper nonlinear state feedback controller, a linear constant closed-loop system with desired eigenstructure can be derived, and complete parametric presentations for the closed-loop eigenvectors and the feedback law are given. Conditions of existence of solutions as well as the density of the set of design parameters are discussed. Finally, some further comments are made about future problems existing in the field of high-order fully-actuated systems.
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Key words:
- High-order systems /
- fully-actuated systems /
- parametric approaches /
- eigenstructure /
- design degrees of freedom
1) 本文责任编委 贺威 -
[1] 郭玉翠.常微分方程:理论、建模与发展.北京:清华大学出版社, 2010.Guo Yu-Cui. Ordinary Differential Equations: Theory, Modeling and Development. Beijing: Tsinghua University Press, 2010. [2] 莫里斯·克莱因[著], 张理京, 张锦炎, 江泽涵[译].古今数学思想.上海: 上海科学技术出版社, 2002.Klein M[Author], Zhang Li-Jing, Zhang Jin-Yan, Jiang Ze-Han[Translator]. Mathematical Thought from Ancient to Modern Times. Shanghai: Shanghai Science and Technology Press, 2002. [3] Lyapunov A M. The general problem of the stability of motion. International Journal of Control, 1992, 55(3): 531-773 http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_e262aa6f3ea38e2ecacc948c719a35e4 [4] LaSalle J P. Some extensions of Liapunov's second method. IRE Transactions on Circuit Theory, 1960, 7(4): 520-527 http://cn.bing.com/academic/profile?id=4f963ecfd70bf4f7e93c7ac881603030&encoded=0&v=paper_preview&mkt=zh-cn [5] LaSalle J P. The Stability of Dynamical Systems. Philadelphia: SIAM Press, 1976. [6] Khalil H K. Nonlinear Systems (Third Edition). Upper Saddle River, NJ: Prentice Hall, 2002. [7] Bellman R. On the theory of dynamic programming. Proceedings of the National Academy of Sciences of the United States of America, 1952, 38(8): 716-719 http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_6973b2c823cb2b78d5a38d1809cd3227 [8] Bellman R. The theory of dynamic programming. Bulletin of the American Mathematical Society, 1954, 60(6): 503-515 http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_0801.0281 [9] Bellman R. Dynamic Programming. Princeton, NJ: Princeton University Press, 1957. [10] Boltyanski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $ V G, Gamkrelidze R V, Pontryagin L S. On the theory of optimal processes (in Russian). Doklady Akademii Nauk SSSR, 1956, 110: 7-10 [11] Pontryagin L S. Optimal control processes (in Russian). Uspekhi Matematicheskikh Nauk, 1959, 14: 3-20 [12] Pontryagin L S. Optimal processes of regulation. In: Proceedings of the 1960 International Congress Mathematical. New York, USA: Cambridge University Press, 1960. 182-202 [13] Boltyanski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $ V G, Gamkrelidze R V, Pontryagin L S. The theory of optimal processes I. The maximum principle (in Russian). Izvestija Akademii Nauk SSSR Series Mathematics, 1960, 24: 3-42 [14] Pontryagin L S, Boltyanski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $ V G, Gamkrelidze R V, Mishchenko E F. The Mathematical Theory of Optimal Processes. New York: John Wiley & Sons, 1962. [15] Rozonoer L I. The maximum principle of LS Pontryagin in optimal system theory. Automation and Remote Control, 1959, 20(10): 11 [16] Ball J A, Helton J W. Nonlinear ${H}_{\infty}$ control theory: A literature survey. Robust Control of Linear Systems and Nonlinear Control. Birkhauser Boston: Springer, 1990. 1-12 [17] Doyle J, Glover K, Khargonekar P, Francis B. State-space solutions to standard $H_2$ and $H_{\infty}$ control problems. In: Proceedings of the 1988 American Control Conference. Atlanta, USA: IEEE, 1988. 1691-1696 [18] Findeisen R, Imsland L, Allgower F, Foss B A. State and output feedback nonlinear model predictive control: An overview. European Journal of Control, 2003, 9(2-3): 190-206 http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ021756404/ [19] García C E, Prett D M, Morari M. Model predictive control: Theory and practice—A survey. Automatica, 1989, 25(3): 335-348 [20] Kalman R E. On the general theory of control systems. IRE Transactions on Automatic Control, 1959, 4(3): 110 http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1104.4056 [21] Kalman R E. A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 1960, 82(1): 35-45 doi: 10.1115-1.3662552/ [22] Kalman R E, Bucy R S. New results in linear filtering and prediction theory. Journal of Basic Engineering, Series D, 1961, 83(1): 95-108 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=cd3f232942c571827055a5ac9e31044c [23] Sunahara Y. An approximate method of state estimation for nonlinear dynamical systems. In: Proceedings of the 1969 Joint Automatic Control Conference. Colorado, USA: IEEE, 1969. 161-172 [24] Julier S J, Uhlmann J K. New extension of the Kalman filter to nonlinear systems. In: Proceedings of the 1997 Signal Processing, Sensor Fusion, and Target Recognition VI. Orlando, USA: SPIE, 1997. 182-193 [25] Kalman R E, Falb P L, Arbib M A. Topics in Mathematical System Theory. New York: McGraw-Hill, 1969. [26] Kalman R E. A Road Map of Real Mathematics for Circuits. Kailath Lecture, California: Stanford University, 2008. [27] 段广仁.线性系统理论.北京:科学出版社(上下册), 1998.Duan Guang-Ren. Linear System Theory. Beijing: Science Press, 1998. [28] 段广仁.高阶系统方法— Ⅱ.能控性与全驱性.自动化学报, DOI: 10.16383/j.aas.c200369Duan Guang-Ren. High-order system approaches — Ⅱ. Controllability and full-actuation. Acta Automatica Sinica, DOI: 10.16383/j.aas.c200369 [29] Blondel V, Gevers M, Lindquist A. Survey on the state of systems and control. European Journal of Control, 1995, 1(1): 5-23 [30] 段广仁.飞行器控制的伪线性系统方法—第一部分:综述与问题.宇航学报, 2020, 41(6): 633-646Duan Guang-Ren. Quasi-linear system approaches for flight vehicle control—Part 1: An overview and problems. Journal of Astronautics, 2020, 41(6): 633-646 [31] 段广仁.飞行器控制的伪线性系统方法—第二部分:方法与展望.宇航学报, 2020, 41(7)Duan Guang-Ren. Quasi-linear system approaches for flight vehicle control—Part 2: Methods and prospects. Journal of Astronautics, 2020, 41(7) [32] Duan G R. Direct parametric control of fully-actuated second-order nonlinear systems—The normal case. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014. 2406-2413 [33] Duan G R. Direct parametric approach for cascaded systems with application in robot control. In: Proceedings of the 14th International Conference on Control, Automation and Systems. Seoul, South Korea: IEEE, 2014. 29-35 [34] Krstić M, Kanellakopoulos I, Kokotović P. Nonlinear and Adaptive Control Design. New York: John Wiley & Sons, 1995. [35] Khalil H K. Nonlinear Control. Upper Saddle River, NJ: Prentice Hall, 2015. [36] Duan G R. Analysis and Design of Descriptor Linear Systems. New York: Springer, 2010. [37] Duan G R, Yu H H. LMIs in Control Systems—Analysis, Design and Applications. London: CRC Press, 2013. [38] Duan G R. Parametric approaches for eigenstructure assignment in high-order linear systems. International Journal of Control, Automation, and Systems, 2005, 3(3): 419-429 http://cn.bing.com/academic/profile?id=ba5fd841d61dff09ce4bc48f360b06cd&encoded=0&v=paper_preview&mkt=zh-cn [39] Duan G R, Yu H H. Complete eigenstructure assignment in high-order descriptor linear systems via proportional plus derivative state feedback. In: Proceedings of the 6th World Congress on Intelligent Control and Automation. Dalian, China: IEEE, 2006. 500-505 [40] Duan G R. Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control. International Journal of Control, 1998, 69(5): 663-694 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4b0709cf44c601a8147af4fbac04862c [41] Duan G R. Direct parametric control of fully-actuated second-order nonlinear systems — Descriptor case. In: Proceedings of the 11th World Congress on Intelligent Control and Automation. Shenyang, China: IEEE, 2014. 2108-2114 [42] Duan G R. Direct parametric control of fully-actuated high-order nonlinear systems — Normal case. In: Proceedings of the 11th World Congress on Intelligent Control and Automation. Shenyang, China: IEEE, 2014. 3053-3060 [43] Duan G R. Direct parametric control of fully-actuated high-order quasi-linear systems via dynamical feedback. In: Proceedings of the 2014 IEEE International Conference on Information and Automation. Hailar, China: IEEE, 2014. 418-424 [44] Duan G R. Non-cooperative rendezvous and interception — A direct parametric control approach. In: Proceedings of the 11th World Congress on Intelligent Control and Automation. Shenyang, China: IEEE, 2014. 3497-3504 [45] Duan G R. Satellite attitude control — A direct parametric approach. In: Proceedings of the 11th World Congress on Intelligent Control and Automation. Shenyang, China: IEEE, 2014. 3989-3996 [46] Duan G R. Missile attitude control — A direct parametric approach. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014. 2414-2421 [47] Duan G R. A direct parametric approach for missile guidance — Case of sea targets. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014. 1044-1050 [48] Duan G R. Cooperative spacecraft rendezvous — A direct parametric control approach. In: Proceedings of the 11th World Congress on Intelligent Control and Automation. Shenyang, China: IEEE, 2014. 4589-4595 [49] Duan G R. Quaternion-based satellite attitude control — A direct parametric approach. In: Proceedings of the 14th International Conference on Control, Automation and Systems. Seoul, South Korea: IEEE, 2014. 935-941 [50] Duan G R. Parametric solutions to fully-actuated generalized Sylvester equations — The nonhomogeneous case. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014. 3869-3874 [51] Duan G R. Parametric solutions to fully-actuated generalized Sylvester equations — The homogeneous case. In: Proceedings of the 33rd Chinese Control Conference. Nanjing, China: IEEE, 2014. 3863-3868 [52] Fantoni I, Lozano R. Non-linear Control for Underactuated Mechanical Systems. London: Springer-Velag, 2002. [53] 段广仁, 王建宇, 赵天一, 张亮.卫星光通信精确跟踪控制系统的参数化综合优化设计.控制理论与应用, 2020, 37(3): 469-480 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy202003003Duan Guang-Ren, Wang Jian-Yu, Zhao Tian-Yi, Zhang Liang. Parametric comprehensive optimization design of high accuracy tracking control system for satellite optical communication. Control Theory & Applications, 2020, 37(3): 469-480 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy202003003 [54] 张龙, 段广仁.挠性航天器的鲁棒多目标姿态控制器设计.宇航学报, 2011, 32(11): 2326-2332 http://d.old.wanfangdata.com.cn/Periodical/yhxb201111004Zhang Long, Duan Guang-Ren. Flexible spacecraft robust multi-objective attitude controller design. Journal of Astronautics, 2011, 32(11): 2326-2332 http://d.old.wanfangdata.com.cn/Periodical/yhxb201111004 -
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