基于快速自适应超螺旋算法的制导律
|
摘要
针对地空导弹攻击机动目标的制导律设计问题,提出了一种有限时间稳定的新型二阶滑模制导律。在弹目相对运动模型的基础上,将制导问题转化为一阶系统的控制问题。在超螺旋(ST)算法中引入线性项和一种新的参数自适应律,提出了一种快速自适应超螺旋(FAST)算法,该算法不需要已知系统不确定性的边界且收敛速度较快。利用类二次型Lyapunov函数证明了系统有限时间稳定性,给出了收敛时间估计公式。通过与自适应滑模制导律、ST制导律和光滑二阶滑模制导律的仿真对比,验证了所设计的制导律在保证制导精度的同时,能够在有限时间内提高滑模变量的收敛速度,并且避免了参数选择困难的问题。
A new second-order sliding-mode guidance law with finite time stability is proposed for the design of the guidance law of surface-to-air missile attacking maneuvering target. Based on the relative motion model of the missile and the target,guidance problem is transformed into control problem of first-order system.A fast adaptive super-twisting( FAST) algorithm is proposed by introducing linear terms and a new parameter adaptive law in super-twisting( ST),which improves convergence speed without the prior knowledge of upper bound parameters of uncertainties. A quadratic Lyapunov function is adopted to verify the stability of the system in finite time and compute the convergence time. A comparison with adaptive sliding mode guidance,ST guidance and smooth second-order sliding-mode guidance shows that the proposed method can improve the convergence speed of sliding variable and avoid the difficulty of choosing parameters,and can guarantee the guidance accuracy at the same time.
A new second-order sliding-mode guidance law with finite time stability is proposed for the design of the guidance law of surface-to-air missile attacking maneuvering target. Based on the relative motion model of the missile and the target,guidance problem is transformed into control problem of first-order system.A fast adaptive super-twisting( FAST) algorithm is proposed by introducing linear terms and a new parameter adaptive law in super-twisting( ST),which improves convergence speed without the prior knowledge of upper bound parameters of uncertainties. A quadratic Lyapunov function is adopted to verify the stability of the system in finite time and compute the convergence time. A comparison with adaptive sliding mode guidance,ST guidance and smooth second-order sliding-mode guidance shows that the proposed method can improve the convergence speed of sliding variable and avoid the difficulty of choosing parameters,and can guarantee the guidance accuracy at the same time.
引文
[1]谭健.飞翼布局无人机鲁棒滑模非线性飞行控制研究[D].西安:西北工业大学,2015:72-77.TAN J. Research on robust sliding mode nonlinear flight control for fly wing UAV[D]. Xi’an:Northwestern Polytechnical University,2015:72-77(in Chinese).
[2]杨洁.高阶滑模控制理论及其在欠驱动系统中的应用研究[D].北京:北京理工大学,2015:68-72.YANG J. Higher-order sliding mode control theory and its application on under actuated systems[D]. Beijing:Beijing Institute of Technology,2015:68-72(in Chinese).
[3]陈炳龙.基于二阶滑模算法的航天器相对位姿耦合控制研究[D].哈尔滨:哈尔滨工业大学,2015:77-83.CHEN B L. Research on spacecraft relative position and attitude coupled control on the basis of second-order sliding mode algorithm[D]. Harbin:Harbin Institute of Technology,2015:77-83(in Chinese).
[4]李鹏.传统和高阶滑模控制研究及其应用[D].长沙:国防科技大学,2011:73-78.LI P. Research on application of traditional and high-order sliding mode control[D]. Changsha:National University of Defense Technology,2011:73-78(in Chinese).
[5]韩耀振.不确定非线性系统高阶滑模控制及其在电力系统中的应用[D].北京:华北电力大学,2017:20-21.HAN Y Z. Uncertain nonlinear system higher-order sliding mode control and its application in power system[D]. Beijing:North China Electric Power University,2017:20-21(in Chinese).
[6]李炯,张涛,雷虎民,等.非奇异快速终端二阶滑模有限时间制导律[J].系统工程与电子技术,2018,40(4):860-867.LI J,ZHANG T,LEI H M,et al. Nonsingular fast terminal second order sliding mode guidance law with finite time convergence[J]. System Engineering and Electronics,2018,40(4):860-867(in Chinese).
[7]叶继坤,雷虎民,赵岩,等.基于二阶滑模控制的微分几何制导律[J].系统工程与电子技术,2017,39(4):837-845.YE J K,LEI H M,ZHAO Y,et al. Differential geometric guidance law based on second-order sliding control[J]. System Engineering and Electronics,2017,39(4):837-845(in Chinese).
[8]郭建国,韩拓,周军,等.基于终端角度约束的二阶滑模制导律设计[J].航空学报,2017,38(2):320208.GUO J G,HAN T,ZHOU J,et al. Second order sliding mode guidance law with impact angle constraint[J]. Acta Aeronautica et Astronautica Sinica,2017,38(2):320208(in Chinese).
[9] HE S M,LIN D F,WANG J. Continuous second-order sliding mode based impact angle guidance law[J]. Aerospace Science and Technology,2015,41:199-208.
[10] TENOCH G,JAIME A,LEONID F. Variable gain super-twisting sliding mode control[J]. IEEE Transactions on Automatic Control,2012,57(8):2100-2105.
[11] MORENO J A,OSORIO M. Strict Lyapunov functions for the super-twisting algorithm[J]. IEEE Transactions on Automatic Control,2012,57(4):1035-1040.
[12] SHTESSEL Y,TALEB M,PLESTAN F. A novel adptive-gain supertwisting sliding mode controller:Methodology and application[J]. Automatica,2012,48:759-769.
[13] POLYAKOV A,POZNYAK A. Reaching time estimation for“Super-Twisting”second order sliding mode controller via Lyapunov function designing[J]. IEEE Transactions on Automatic Control,2009,54(8):1951-1955.
[14] SHTESSEL Y B,SHKOLNIKOV I A,LEVANT A. Guidance and control of missile interceptor using second-order sliding modes[J]. IEEE Transactions on Aerospace and Electronic Systems,2009,45(1):110-124.
[15] WANG Z. Adaptive smooth second-order sliding mode control method with application to missile guidance[J]. Transactions of the Institute of Measurement and Control,2017,39(6):848-860.
[16] LEVANT A. Sliding order and sliding accuracy in sliding mode control[J]. International Journal of Control,1993,58(6):1247-1263.
[17]杨鹏飞,方洋旺,伍友利,等.随机快速光滑二阶滑模末制导律设计[J].国防科技大学学报,2017,39(4):131-138.YANG P F,FANG Y W,WU Y L,et al. Terminal guidance law design of stochastic fast smooth second-ordersliding modes[J].Journal of National University of Defense Technology,2017,39(4):131-138(in Chinese).
[18] SHTESSEL Y,TOURNES C,SHKOLNIKOV I. Guidance and autopilot for missile steered by aerodynamic lift and divert thrusters using second order sliding modes:AIAA-2006-6784[R]. Reston:AIAA,2006.
[19] SHTESSEL Y,KOCHALUMMOOTTIL J,EDWARDS C. Continuous adaptive finite reaching time control and second-order sliding modes[J]. IMA Journal of Mathematical Control and Information,2013,30(1):97-113.
[2]杨洁.高阶滑模控制理论及其在欠驱动系统中的应用研究[D].北京:北京理工大学,2015:68-72.YANG J. Higher-order sliding mode control theory and its application on under actuated systems[D]. Beijing:Beijing Institute of Technology,2015:68-72(in Chinese).
[3]陈炳龙.基于二阶滑模算法的航天器相对位姿耦合控制研究[D].哈尔滨:哈尔滨工业大学,2015:77-83.CHEN B L. Research on spacecraft relative position and attitude coupled control on the basis of second-order sliding mode algorithm[D]. Harbin:Harbin Institute of Technology,2015:77-83(in Chinese).
[4]李鹏.传统和高阶滑模控制研究及其应用[D].长沙:国防科技大学,2011:73-78.LI P. Research on application of traditional and high-order sliding mode control[D]. Changsha:National University of Defense Technology,2011:73-78(in Chinese).
[5]韩耀振.不确定非线性系统高阶滑模控制及其在电力系统中的应用[D].北京:华北电力大学,2017:20-21.HAN Y Z. Uncertain nonlinear system higher-order sliding mode control and its application in power system[D]. Beijing:North China Electric Power University,2017:20-21(in Chinese).
[6]李炯,张涛,雷虎民,等.非奇异快速终端二阶滑模有限时间制导律[J].系统工程与电子技术,2018,40(4):860-867.LI J,ZHANG T,LEI H M,et al. Nonsingular fast terminal second order sliding mode guidance law with finite time convergence[J]. System Engineering and Electronics,2018,40(4):860-867(in Chinese).
[7]叶继坤,雷虎民,赵岩,等.基于二阶滑模控制的微分几何制导律[J].系统工程与电子技术,2017,39(4):837-845.YE J K,LEI H M,ZHAO Y,et al. Differential geometric guidance law based on second-order sliding control[J]. System Engineering and Electronics,2017,39(4):837-845(in Chinese).
[8]郭建国,韩拓,周军,等.基于终端角度约束的二阶滑模制导律设计[J].航空学报,2017,38(2):320208.GUO J G,HAN T,ZHOU J,et al. Second order sliding mode guidance law with impact angle constraint[J]. Acta Aeronautica et Astronautica Sinica,2017,38(2):320208(in Chinese).
[9] HE S M,LIN D F,WANG J. Continuous second-order sliding mode based impact angle guidance law[J]. Aerospace Science and Technology,2015,41:199-208.
[10] TENOCH G,JAIME A,LEONID F. Variable gain super-twisting sliding mode control[J]. IEEE Transactions on Automatic Control,2012,57(8):2100-2105.
[11] MORENO J A,OSORIO M. Strict Lyapunov functions for the super-twisting algorithm[J]. IEEE Transactions on Automatic Control,2012,57(4):1035-1040.
[12] SHTESSEL Y,TALEB M,PLESTAN F. A novel adptive-gain supertwisting sliding mode controller:Methodology and application[J]. Automatica,2012,48:759-769.
[13] POLYAKOV A,POZNYAK A. Reaching time estimation for“Super-Twisting”second order sliding mode controller via Lyapunov function designing[J]. IEEE Transactions on Automatic Control,2009,54(8):1951-1955.
[14] SHTESSEL Y B,SHKOLNIKOV I A,LEVANT A. Guidance and control of missile interceptor using second-order sliding modes[J]. IEEE Transactions on Aerospace and Electronic Systems,2009,45(1):110-124.
[15] WANG Z. Adaptive smooth second-order sliding mode control method with application to missile guidance[J]. Transactions of the Institute of Measurement and Control,2017,39(6):848-860.
[16] LEVANT A. Sliding order and sliding accuracy in sliding mode control[J]. International Journal of Control,1993,58(6):1247-1263.
[17]杨鹏飞,方洋旺,伍友利,等.随机快速光滑二阶滑模末制导律设计[J].国防科技大学学报,2017,39(4):131-138.YANG P F,FANG Y W,WU Y L,et al. Terminal guidance law design of stochastic fast smooth second-ordersliding modes[J].Journal of National University of Defense Technology,2017,39(4):131-138(in Chinese).
[18] SHTESSEL Y,TOURNES C,SHKOLNIKOV I. Guidance and autopilot for missile steered by aerodynamic lift and divert thrusters using second order sliding modes:AIAA-2006-6784[R]. Reston:AIAA,2006.
[19] SHTESSEL Y,KOCHALUMMOOTTIL J,EDWARDS C. Continuous adaptive finite reaching time control and second-order sliding modes[J]. IMA Journal of Mathematical Control and Information,2013,30(1):97-113.