基于变结构自适应控制方法的小卫星姿态控制研究
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摘要
从20世纪80年代美国军方提出现代小卫星的概念以来,现代小卫星由于具有重量轻、性能好、研制周期短、造价低等优点,成为目前航天器发展的一个重要方向。姿态控制系统是小卫星完成各种任务的基本前提,是小卫星的关键技术和研究重点。本文主要针对小卫星姿态控制系统进行了研究。
首先给出了欧拉角和姿态四元数的相关理论,系统的总结了欧拉角和四元数两种卫星姿态描述方法,建立了小卫星动力学、运动学模型。
针对目前运用于小卫星姿态控制系统研究的滑模变结构控制方法和自适应控制方法进行了改进,并将两种方法结合起来进行了研究。并分别用Matlab实现仿真验证。
针对小卫星运动时存在参数摄动,非线性强的特点,设计滑模变结构控制器:选取适当的滑模向量使滑动模态渐近稳定;设计滑模控制律,保证系统状态在有限时间内运动到滑动模态上。用饱和特性取代开关项以减小振颤。
针对用四元数法建立的小卫星姿态动力学及运动学方程有强的非线性耦合,设计了一种基于反馈线性化的模型参考自适应姿态控制器。首先运用反馈线性化方法,将小卫星姿态通道线性化解耦成三个单输入单输出系统,然后运用基于李雅普诺夫稳定性理论的模型参考自适应控制方法对每个系统分别设计自适应控制器,使非线性系统跟踪线性参考模型系统、实现对参数摄动和外部扰动的鲁棒性、跟踪预期的姿态。
进一步设计了一种基于滑模变结构和参数自适应算法的姿态控制器:对前面设计的滑模变结构控制器进行了改进;同时针对由于外界影响造成系统参数难以确定的问题,引入了系统参数自适应算法。改进的控制算法能够使得系统在参数不能确定的情况下仍能保持良好的稳定性。
From the 1980s, the U.S. military introduced the modern concept of small satellites, modern small satellite technology has developed very rapidly due to the advantages of lightweight, good performance, short development cycle, and low cost. Thus modern small satellite becomes an important direction. The attitude control system is the precondition of fulfilling all kinds of tasks, is the key technology and emphasis of study. The focus of this paper is to study the attitude control system of small satellite.
In order to study small satellite attitude control system, the author first gives the theories of Euler Angle and the Quaternion, the attitude representation of Euler Angle and Quaternion are analyzed and generalized. Then the small satellite dynamics, kinematic models are established.
A sliding mode control system is designed according to the feature that small satellite model is highly nonlinear and includes perturbation parameters, which can guarantee global and asymptotical stability of the system, and can ensure the system reaches the sliding surface within a limited time. Saturation characteristics instead of switching term is used to reduce flapping which results from the switching term.
Adaptive attitude control system of small satellite based on feedback linearization is designed according to strong nonlinearity and coupling exist in the small satellite attitude dynamic and kinematic equations based on four quaternion. So the attitude channel of small satellite is decoupled into three SISO linear systems by means of feedback linearization. Then model reference adaptive controller based on the Lyapunov stability theory is designed for each attitude channel, so as to achieve robustness versus perturbation and disturbance, and to track the expected attitude.
Then small satellite attitude control system based on sliding mode control and parameter adaptive algorithm is developed. The sliding mode control system which was designed previously is improved. An adaptive algorithm is proposed for the system parameters which are difficult to determine. The improved algorithm shows good system performances under parameters variance. Simulation results are given to illustrate the efficiency of the proposed method.
首先给出了欧拉角和姿态四元数的相关理论,系统的总结了欧拉角和四元数两种卫星姿态描述方法,建立了小卫星动力学、运动学模型。
针对目前运用于小卫星姿态控制系统研究的滑模变结构控制方法和自适应控制方法进行了改进,并将两种方法结合起来进行了研究。并分别用Matlab实现仿真验证。
针对小卫星运动时存在参数摄动,非线性强的特点,设计滑模变结构控制器:选取适当的滑模向量使滑动模态渐近稳定;设计滑模控制律,保证系统状态在有限时间内运动到滑动模态上。用饱和特性取代开关项以减小振颤。
针对用四元数法建立的小卫星姿态动力学及运动学方程有强的非线性耦合,设计了一种基于反馈线性化的模型参考自适应姿态控制器。首先运用反馈线性化方法,将小卫星姿态通道线性化解耦成三个单输入单输出系统,然后运用基于李雅普诺夫稳定性理论的模型参考自适应控制方法对每个系统分别设计自适应控制器,使非线性系统跟踪线性参考模型系统、实现对参数摄动和外部扰动的鲁棒性、跟踪预期的姿态。
进一步设计了一种基于滑模变结构和参数自适应算法的姿态控制器:对前面设计的滑模变结构控制器进行了改进;同时针对由于外界影响造成系统参数难以确定的问题,引入了系统参数自适应算法。改进的控制算法能够使得系统在参数不能确定的情况下仍能保持良好的稳定性。
From the 1980s, the U.S. military introduced the modern concept of small satellites, modern small satellite technology has developed very rapidly due to the advantages of lightweight, good performance, short development cycle, and low cost. Thus modern small satellite becomes an important direction. The attitude control system is the precondition of fulfilling all kinds of tasks, is the key technology and emphasis of study. The focus of this paper is to study the attitude control system of small satellite.
In order to study small satellite attitude control system, the author first gives the theories of Euler Angle and the Quaternion, the attitude representation of Euler Angle and Quaternion are analyzed and generalized. Then the small satellite dynamics, kinematic models are established.
A sliding mode control system is designed according to the feature that small satellite model is highly nonlinear and includes perturbation parameters, which can guarantee global and asymptotical stability of the system, and can ensure the system reaches the sliding surface within a limited time. Saturation characteristics instead of switching term is used to reduce flapping which results from the switching term.
Adaptive attitude control system of small satellite based on feedback linearization is designed according to strong nonlinearity and coupling exist in the small satellite attitude dynamic and kinematic equations based on four quaternion. So the attitude channel of small satellite is decoupled into three SISO linear systems by means of feedback linearization. Then model reference adaptive controller based on the Lyapunov stability theory is designed for each attitude channel, so as to achieve robustness versus perturbation and disturbance, and to track the expected attitude.
Then small satellite attitude control system based on sliding mode control and parameter adaptive algorithm is developed. The sliding mode control system which was designed previously is improved. An adaptive algorithm is proposed for the system parameters which are difficult to determine. The improved algorithm shows good system performances under parameters variance. Simulation results are given to illustrate the efficiency of the proposed method.
引文
[1]詹亚峰,马正新,曹志刚,现代微小卫星技术以及发展趋势,电子学报,2000,28(7):102~106
[2]张艳娥,常江,秦洁,现代小卫星技术与应用专题讲座,军事通信技术,2006,27(2):71~76
[3]马元申,于小红,尹志忠,现代小卫星技术及其发展对策,国防技术基础,2003,(5):13~15
[4]石卫平,潘坚,微小卫星的发展,国际太空,2001,(9):1~3
[5]林来兴,小卫星技术的发展和应用前景,中国航天,2006,(11):43~47
[6]屠善澄,卫星姿态动力学与控制,北京,宇航出版社,2001:1~15
[7]王蜀泉,基于模糊控制的卫星姿态控制方法研究,[硕士论文],北京,中国科学院空间科学与应用研究中心,2005
[8]王华,刘向东,基于再厉模糊神经网络的三轴稳定卫星姿态智能控制,航天控制,2005,23(2):21~26
[9]马克茂,伞冶,基于鲁棒控制方法的卫星姿态控制,航天控制,2001,19(4):29~34
[10]Sivaprakash N.,Shanmugam J.,Neural Network based three axis satellite attitude control using only magnetic torquers,24th Digital Avionics Systems Conference,2005,2:13.D.4.1~6
[11]Guan P.,Liu X.D.,Chen J.B.,Flexible Satellite Attitude Control via Adaptive Fuzzy Linearization,Journal of Beijing Institute of Technology,2005,14(2):140~144
[12]Ramakrishnan S.,Mary L.R.,Attitude Control of a 3-Axis Stabilized Satellite Using Adaptive Control Algorithm,Proceeding of the 2006 IEEE/SMC International Conference on System of Systems Engineering,Los Angeles,USA,2006:282~287
[13]Terui F.,Position and Attitude Control of a Spacecraft by Sliding Mode Control,Proceedings of the American Control Conference Philadelphia,Pennsylvania,1998:217~221
[14]Kabganian M.,Shahravi M.,Adaptive Sliding Mode Attitude and Vibration Control of an Elastic Spacecraft,International Conference on Control and Automation,Budapest,Hungary,2005:305~310
[15]褚健,俞立,苏宏业,鲁棒控制理论及应用,杭州,浙江大学出版社,2000:1~15
[16]易继锴,侯媛彬,智能控制技术,北京,北京工业大学出版社,2003:1~8
[17]庄开宇,变结构控制理论若干问题研究及其应用,[博士学位论文],杭州,浙江大学,2002
[18]安世奇,简单自适应控制的应用研究,[博士学位论文],北京,北京科技大学,2005
[19]刘金琨,滑模变结构控制MATLAB仿真,北京,清华大学出版社,2005:1~4
[20]Chiang C.Y.,Hussein M,Neural Fuzzy Approach to F/A-18 Aircraft Failure Isolation and Reconfiguration Design,AIAA,1995:48~55
[21]Howard S.H.,Balakrishnan S.N.,A Hierarchincal Fuzzy Logic Controller with a Velocity Modifier for Restructurable Flight Control System,AIAA,1995:505~515
[22]Rovert F.S.,Toward Intelligent Flight Control,IEEE Transactions on Systems Man Cyber,1993,23(6):1699~1717
[23]Vepa R.,Caliskan F.,A Review of Failure Detection,Fault Diagnosis and Reconfiguration Algorithms for Real Time Aircraft Flight Control Systems,IFAC Algorithms and Architectures for Real Time Control,1991:141~146
[24]Emelyanov S.V.,Variable structure automatic control systems,Moscow,1967:32-38
[25]Utkin V.I.,Sliding mode and their application in VSSs,Moscow,1978:45~56
[26]Itkis U.,Control systems of variable structure,John Wiley&Sons,1976:15~22
[27]Utkin V.I.,Variable structure systems with sliding modes,IEEE Transaction Automatic Control,1977,22(2):212~222
[28]Yong K.D.,Utkin V.I.,Ozguner U.,A Control Engineer’s Guide to Sliding Mode Control,IEEE Transactions on Control Systems Technology,1999,7(3):328~342
[29]高为炳,变结构控制的理论及设计方法,北京,科学出版社,1996:34~36
[30]陈新海,李言俊,周军,自适应控制及应用,山西,西北工业大学出版社,1998:1~10
[31]Landau I.D,Adaptive Control-Model Reference Approach,France,Marcel Dekker,1979:1~12
[32]Astrom K.J.,Wittenmark B.,Adaptive Control,Sweden,Addison-Wesly,1989:2~15
[33]Harris C.J.,Billings S. A.,Self-tuning and adaptive control-theory and application,Peter Peregrinus Ltd,1981:8~18
[34]章仁为,卫星轨道姿态动力学与控制,北京,北京航空航天大学出版社,1998:137~154
[35]肖业伦,航空航天器运动学的建模――飞行动力学的理论基础,北京,北京航空航天大学出版社,2003:19~23
[36]黄福铭,郝和年,航天器飞行控制与仿真,北京,国防工业出版社,2004:15~16
[37]刘良栋,卫星控制系统仿真技术,北京,宇航出版社,2003:249~252
[38]柏林,三轴稳定卫星姿态确定和姿态控制系统研究,[硕士学位论文],西安,西北工业大学,2001
[39]Nagarajan N.,Arichandran K.,Attitude Determination and Control of A Micro-satellite in Equatorial LEO(EQLEO),Proceeding of Euro-Asia Space Week on Cooperation in space-“Where East & West Finally Meet”, 1998:23~27
[40]黄忠霖,控制系统MATLAB计算与仿真,北京,国防工业出版社,2004:129~130
[41]周黎妮,唐国金,罗亚中,基于Matlab/Simulink的航天器姿态动力学与控制仿真框架,系统仿真学报,2005,17(10):2517~2520
[42]曹开田,滑模变结构控制理论在飞行器姿态控制系统中的应用研究,[硕士论文],武汉,武汉大学,2004
[43]张菊,导弹姿态系统的模糊变结构控制,[硕士学位论文],哈尔滨,哈尔滨工业大学,2006
[44]孙兆伟,杨旭,杨涤,小卫星磁力矩器与反作用飞轮联合控制算法研究,控制理论与应用,2002,19(2):173~177
[45]王炳全,崔祜涛,杨涤,轻型高精度卫星的变结构姿态控制器,航空学报,2000,21(5):417~420
[46] James H.M.,Yuri B.S.,A De-coupled Sliding Mode Controller and Observer for Satellite Attitude Control,System Theory, Proceedings of the Twenty-Ninth Southeastern Symposium,1997:92 ~ 97
[47] Sahjendra N.S.,Ashok I.,Nonlinear decoupling sliding mode control and attitude control of spacecraft,IEEE Transactions on Aerospace and Electronic System,1989,25(5):621~623
[48]廖晖,周凤岐,周军,三轴轮控小卫星大角度机动变结构控制研究,航天控制,1999,17(4):11~15
[49]Jiang B. , Fahmida C. , Fault estimation and accommodation for linear MIMO discrete-time Systems,IEEE Transactions on Control Systems Technology,2005,13(3):493~499.
[50]吴宏鑫,全系数自适应控制理论于应用,北京,国防工业出版社,1990:2~6
[51]卢强,孙元章,电力系统非线性控制,北京,科学出版社,1993:47~71
[52]Guan P.,Liu X.J.,Liu J.Z.,Flexible Satellite Attitude Control Via Sliding Mode Technique,Proceeding of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005 Seville,Spain,2005:1258~1263
[53]史峻冬,机载雷达伺服系统模型参考自适应控制的设计与实现,现代雷达,1998,20(1):67 ~73
[54]许化龙,赵大炜,陈光军等,战略导弹姿态系统的变结构自适应控制研究,弹箭与制导学报,2003,23(1):17~20
[55]王青,景韶光,张明廉,推力矢量空空导弹的变结构自适应控制,航空学报,2000,21(4):352~354
[2]张艳娥,常江,秦洁,现代小卫星技术与应用专题讲座,军事通信技术,2006,27(2):71~76
[3]马元申,于小红,尹志忠,现代小卫星技术及其发展对策,国防技术基础,2003,(5):13~15
[4]石卫平,潘坚,微小卫星的发展,国际太空,2001,(9):1~3
[5]林来兴,小卫星技术的发展和应用前景,中国航天,2006,(11):43~47
[6]屠善澄,卫星姿态动力学与控制,北京,宇航出版社,2001:1~15
[7]王蜀泉,基于模糊控制的卫星姿态控制方法研究,[硕士论文],北京,中国科学院空间科学与应用研究中心,2005
[8]王华,刘向东,基于再厉模糊神经网络的三轴稳定卫星姿态智能控制,航天控制,2005,23(2):21~26
[9]马克茂,伞冶,基于鲁棒控制方法的卫星姿态控制,航天控制,2001,19(4):29~34
[10]Sivaprakash N.,Shanmugam J.,Neural Network based three axis satellite attitude control using only magnetic torquers,24th Digital Avionics Systems Conference,2005,2:13.D.4.1~6
[11]Guan P.,Liu X.D.,Chen J.B.,Flexible Satellite Attitude Control via Adaptive Fuzzy Linearization,Journal of Beijing Institute of Technology,2005,14(2):140~144
[12]Ramakrishnan S.,Mary L.R.,Attitude Control of a 3-Axis Stabilized Satellite Using Adaptive Control Algorithm,Proceeding of the 2006 IEEE/SMC International Conference on System of Systems Engineering,Los Angeles,USA,2006:282~287
[13]Terui F.,Position and Attitude Control of a Spacecraft by Sliding Mode Control,Proceedings of the American Control Conference Philadelphia,Pennsylvania,1998:217~221
[14]Kabganian M.,Shahravi M.,Adaptive Sliding Mode Attitude and Vibration Control of an Elastic Spacecraft,International Conference on Control and Automation,Budapest,Hungary,2005:305~310
[15]褚健,俞立,苏宏业,鲁棒控制理论及应用,杭州,浙江大学出版社,2000:1~15
[16]易继锴,侯媛彬,智能控制技术,北京,北京工业大学出版社,2003:1~8
[17]庄开宇,变结构控制理论若干问题研究及其应用,[博士学位论文],杭州,浙江大学,2002
[18]安世奇,简单自适应控制的应用研究,[博士学位论文],北京,北京科技大学,2005
[19]刘金琨,滑模变结构控制MATLAB仿真,北京,清华大学出版社,2005:1~4
[20]Chiang C.Y.,Hussein M,Neural Fuzzy Approach to F/A-18 Aircraft Failure Isolation and Reconfiguration Design,AIAA,1995:48~55
[21]Howard S.H.,Balakrishnan S.N.,A Hierarchincal Fuzzy Logic Controller with a Velocity Modifier for Restructurable Flight Control System,AIAA,1995:505~515
[22]Rovert F.S.,Toward Intelligent Flight Control,IEEE Transactions on Systems Man Cyber,1993,23(6):1699~1717
[23]Vepa R.,Caliskan F.,A Review of Failure Detection,Fault Diagnosis and Reconfiguration Algorithms for Real Time Aircraft Flight Control Systems,IFAC Algorithms and Architectures for Real Time Control,1991:141~146
[24]Emelyanov S.V.,Variable structure automatic control systems,Moscow,1967:32-38
[25]Utkin V.I.,Sliding mode and their application in VSSs,Moscow,1978:45~56
[26]Itkis U.,Control systems of variable structure,John Wiley&Sons,1976:15~22
[27]Utkin V.I.,Variable structure systems with sliding modes,IEEE Transaction Automatic Control,1977,22(2):212~222
[28]Yong K.D.,Utkin V.I.,Ozguner U.,A Control Engineer’s Guide to Sliding Mode Control,IEEE Transactions on Control Systems Technology,1999,7(3):328~342
[29]高为炳,变结构控制的理论及设计方法,北京,科学出版社,1996:34~36
[30]陈新海,李言俊,周军,自适应控制及应用,山西,西北工业大学出版社,1998:1~10
[31]Landau I.D,Adaptive Control-Model Reference Approach,France,Marcel Dekker,1979:1~12
[32]Astrom K.J.,Wittenmark B.,Adaptive Control,Sweden,Addison-Wesly,1989:2~15
[33]Harris C.J.,Billings S. A.,Self-tuning and adaptive control-theory and application,Peter Peregrinus Ltd,1981:8~18
[34]章仁为,卫星轨道姿态动力学与控制,北京,北京航空航天大学出版社,1998:137~154
[35]肖业伦,航空航天器运动学的建模――飞行动力学的理论基础,北京,北京航空航天大学出版社,2003:19~23
[36]黄福铭,郝和年,航天器飞行控制与仿真,北京,国防工业出版社,2004:15~16
[37]刘良栋,卫星控制系统仿真技术,北京,宇航出版社,2003:249~252
[38]柏林,三轴稳定卫星姿态确定和姿态控制系统研究,[硕士学位论文],西安,西北工业大学,2001
[39]Nagarajan N.,Arichandran K.,Attitude Determination and Control of A Micro-satellite in Equatorial LEO(EQLEO),Proceeding of Euro-Asia Space Week on Cooperation in space-“Where East & West Finally Meet”, 1998:23~27
[40]黄忠霖,控制系统MATLAB计算与仿真,北京,国防工业出版社,2004:129~130
[41]周黎妮,唐国金,罗亚中,基于Matlab/Simulink的航天器姿态动力学与控制仿真框架,系统仿真学报,2005,17(10):2517~2520
[42]曹开田,滑模变结构控制理论在飞行器姿态控制系统中的应用研究,[硕士论文],武汉,武汉大学,2004
[43]张菊,导弹姿态系统的模糊变结构控制,[硕士学位论文],哈尔滨,哈尔滨工业大学,2006
[44]孙兆伟,杨旭,杨涤,小卫星磁力矩器与反作用飞轮联合控制算法研究,控制理论与应用,2002,19(2):173~177
[45]王炳全,崔祜涛,杨涤,轻型高精度卫星的变结构姿态控制器,航空学报,2000,21(5):417~420
[46] James H.M.,Yuri B.S.,A De-coupled Sliding Mode Controller and Observer for Satellite Attitude Control,System Theory, Proceedings of the Twenty-Ninth Southeastern Symposium,1997:92 ~ 97
[47] Sahjendra N.S.,Ashok I.,Nonlinear decoupling sliding mode control and attitude control of spacecraft,IEEE Transactions on Aerospace and Electronic System,1989,25(5):621~623
[48]廖晖,周凤岐,周军,三轴轮控小卫星大角度机动变结构控制研究,航天控制,1999,17(4):11~15
[49]Jiang B. , Fahmida C. , Fault estimation and accommodation for linear MIMO discrete-time Systems,IEEE Transactions on Control Systems Technology,2005,13(3):493~499.
[50]吴宏鑫,全系数自适应控制理论于应用,北京,国防工业出版社,1990:2~6
[51]卢强,孙元章,电力系统非线性控制,北京,科学出版社,1993:47~71
[52]Guan P.,Liu X.J.,Liu J.Z.,Flexible Satellite Attitude Control Via Sliding Mode Technique,Proceeding of the 44th IEEE Conference on Decision and Control and the European Control Conference 2005 Seville,Spain,2005:1258~1263
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