结冰飞机着陆阶段飞行安全包线确定及操纵应对策略
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摘要
结冰会导致飞行安全包线收缩、严重威胁飞行安全,研究结冰后安全包线变化对于操纵应对策略设计及提高飞行安全具有重要意义。以美国国家航空航天局(NASA)的项目飞机GTM(Generic Transport Model)为研究对象,通过对飞机的气动参数进行多项式拟合,建立了结冰飞机纵向通道的动力学模型。为了得到能随结冰程度变化的安全包线,将可达性分析理论引入到对结冰飞机着陆过程的安全性分析。提出将正向可达集与反向可达集的交集作为飞行安全包线,其中可达集的确定是基于水平集方法求解哈密尔顿-雅克比方程的最优解。最后针对不同程度的结冰条件进行了操纵时域验证,并提出了相应的操纵控制策略。研究结果表明,轻度结冰对安全包线影响较小,整个着陆过程的飞行状态始终能在最优控制指导下保持在安全包线以内;但对于重度结冰,飞行安全包线收缩严重,常规操纵已经很难使飞机达到着陆要求,需要进行飞行状态改出处理。研究结果为指导飞行操纵及实时包线保护打下基础。
Icing will lead to shrinkage of flight safety envelope and thus a serious threat to flight safety.The study on the changes of flight safety envelope after icing is of great significance for designing maneuvering coping strategy and improving flight safety.In this paper,a dynamic model for the longitudinal channel of the iced NASA Generic Transport Model(GTM)is established based on polynomial fitting of the aerodynamic parameters of the icing aircraft.To obtain the safety envelope that can vary with the degree of icing,the reachability analysis theory is applied to the safety analysis of the icing aircraft during the landing phase.The intersection of the forward reachable set and backward reachable set is proposed as the flight safety envelope.The reachable set is obtained via computing the optimal solution for the Hamilton-Jacobi partial differential equation via the level set method.Finally,the time domain verification is carried out for different degrees of icing conditions,and the corresponding maneuvering coping strategies are proposed.The results show that mild icing condition has little effect on the safety envelope,and the flight state can be maintained within the safety envelope all the time under the guidance of the optimal control during the landing phase.However,for the severe icing condition,the safety envelope shrinks severely and regular manipulation cannot meet the landing requirements.At this time,the behavior of the aircraft should be changed.The research results lay the foundation for flight control and real-time envelope protection.
Icing will lead to shrinkage of flight safety envelope and thus a serious threat to flight safety.The study on the changes of flight safety envelope after icing is of great significance for designing maneuvering coping strategy and improving flight safety.In this paper,a dynamic model for the longitudinal channel of the iced NASA Generic Transport Model(GTM)is established based on polynomial fitting of the aerodynamic parameters of the icing aircraft.To obtain the safety envelope that can vary with the degree of icing,the reachability analysis theory is applied to the safety analysis of the icing aircraft during the landing phase.The intersection of the forward reachable set and backward reachable set is proposed as the flight safety envelope.The reachable set is obtained via computing the optimal solution for the Hamilton-Jacobi partial differential equation via the level set method.Finally,the time domain verification is carried out for different degrees of icing conditions,and the corresponding maneuvering coping strategies are proposed.The results show that mild icing condition has little effect on the safety envelope,and the flight state can be maintained within the safety envelope all the time under the guidance of the optimal control during the landing phase.However,for the severe icing condition,the safety envelope shrinks severely and regular manipulation cannot meet the landing requirements.At this time,the behavior of the aircraft should be changed.The research results lay the foundation for flight control and real-time envelope protection.
引文
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[8] TAN W,PACKARD A.Stability region analysis using polynomial and composite polynomial Lyapunov functions and sum-of-squares programming[J].IEEE Transactions on Automatic Control,2008,53(2):565-570.
[9] ZHENG W J,LI Y H,QU L,et al.Dynamic envelope determination based on differential manifold theory[J].Journal of Aircraft,2017,54(5):2005-2009.
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[11] BAYENA M,MITCHELL I,OISHI M K.Aircraft autolander safety analysis through optimal control-based reach set computation[J].Journal of Guidance,Control,and Dynamics,2007,30(1):68-77.
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[15]屈亮,李颖晖,袁国强,等.基于相平面法的结冰飞机纵向非线性稳定域分析[J].航空学报,2016,37(3):865-872.QU L,LI Y H,YUAN G Q,et al.Longitudinal nonlinear stabilizing region for icing aircraft based on phasephane method[J].Acta Aeronautica et Astronautica Sinica,2016,37(3):865-872(in Chinese).
[16]郑无计,李颖晖,屈亮,等.基于正规形法的结冰飞机着陆阶段非线性稳定域[J].航空学报,2017,38(2):567-588.ZHENG W J,LI Y H,QU L,et al.Nonlinear stability region of icing aircraft during landing phase based on normal form method[J].Acta Aeronautica et Astronautica Sinica,2017,38(2):567-588(in Chinese).
[17]袁国强,李颖晖,徐浩军,等.积冰对飞机本体纵向非线性动力学稳定域的影响[J].西安交通大学学报,2017,51(9):153-158.YUAN G Q,LI Y H,XU H J,et al.Effect of ice accretion on aircraft’s longitudinal nonlinear dynamic stability region[J].Journal of Xi'an Jiaotong University,2017,51(9):153-158(in Chinese).
[18]刘瑛,李敏强,陈富赞.飞行器机动动作风险定量评估模型[J].系统工程与电子技术,2014,36(3):469-475.LIU Y,LI M Q,CHEN F Z.Risk quantitative evaluation model of the aircraft maneuver[J].Systems Engineering and Electronics,2014,36(3):469-475(in Chinese).
[19] HARRYG K,JEAN T D.Nonlinear analysis of aircraft loss of control[J].Journal of Guidance Control&Dynamics,2013,36(1):149-162.
[20] MILLER R,RIBBENS W.The effects of icing on the longitudinal dynamics of an icing research aircraft:AIAA-1999-0636[R].Reston,VA:AIAA,1999.
[21]刘瑛,杜光勋,全权.基于Hamilton-Jacobi方程的飞行器机动动作可达集分析[J].自动化学报,2016,42(3):347-357.LIU Y,DU G X,QUAN Q.Reachability calculation for aircraft maneuver using Hamilton-Jacobi function[J].Acta Automatica Sinica,2016,42(3):347-357(in Chinese).
[22] OSHER S,FEDKIW R.Level set methods and dynamic implicit surfaces[J].New York:Springer,2003:25-37.
[2] HILTNER D W.A nonlinear aircraft simulation of ice contaminated tailplane stall[D].Columbus:Ohio State University,1998.
[3] Safety Advisor Aircraft icing[EB/OL].(2013-05-01)[2015-05-08].http:∥www.aopa.org_media/Files/AOPA/Home/Pilot%20Resources/ASI/Safety%20Advisors/sall.pdf.
[4]赵安家,孟哲理,高洪权,等.飞行包线对飞行安全影响研究[J].飞机设计,2017,37(1):11-16.ZHAO A J,MENG Z L,GAO H Q,et al.The research on the flight envelope of aircraft effect on safety of flight[J].Aircraft Design,2017,37(1):11-16(in Chinese).
[5] MERRETJ M,HOSSAIN K N,BRAGG M B.Envelope protection and atmospheric disturbances in icing encounters:AIAA-2002-0814[R].Reston,VA:AIAA,2002.
[6] LARISSAK,BEHZAD S.Estimation of region of attraction for polynomial nonlinear systems:A numerical method[J].ISA Transactions,2014,53(1):25-32.
[7] SARA H,REIHANEH K M.Enlarging the guaranteed region of attraction in nonlinear systems with bounded parametric uncertainty[J].Journal of Zhejiang University—Science C,2013,14(3):214-221.
[8] TAN W,PACKARD A.Stability region analysis using polynomial and composite polynomial Lyapunov functions and sum-of-squares programming[J].IEEE Transactions on Automatic Control,2008,53(2):565-570.
[9] ZHENG W J,LI Y H,QU L,et al.Dynamic envelope determination based on differential manifold theory[J].Journal of Aircraft,2017,54(5):2005-2009.
[10]WEEKLY K,TINKA A.Autonomous river navigation using the Hamilton-Jacobi framework for underactuated vehicles[J].IEEE Transactions on Robotics,2014,30(5):1250-1255.
[11] BAYENA M,MITCHELL I,OISHI M K.Aircraft autolander safety analysis through optimal control-based reach set computation[J].Journal of Guidance,Control,and Dynamics,2007,30(1):68-77.
[12] GILLULA J H,HOFFMANN G M,HUANG H M,et al.Applications of hybrid reachability analysis to robotic aerial vehicles[J].The International Journal of Robotics Research,2011,30(3):335-354.
[13] VANOORT E R,CHU Q P,MULDER J A.Maneuver envelope determination through reachability analysis[C]∥Advances in Aerospace Guidance,Navigation and Control.Berlin Heidelberg:Springer,2011:91-102.
[14] MITCHELL I M.A toolbox of level set methods:TR-2004-09[R].Vancouver,2004.
[15]屈亮,李颖晖,袁国强,等.基于相平面法的结冰飞机纵向非线性稳定域分析[J].航空学报,2016,37(3):865-872.QU L,LI Y H,YUAN G Q,et al.Longitudinal nonlinear stabilizing region for icing aircraft based on phasephane method[J].Acta Aeronautica et Astronautica Sinica,2016,37(3):865-872(in Chinese).
[16]郑无计,李颖晖,屈亮,等.基于正规形法的结冰飞机着陆阶段非线性稳定域[J].航空学报,2017,38(2):567-588.ZHENG W J,LI Y H,QU L,et al.Nonlinear stability region of icing aircraft during landing phase based on normal form method[J].Acta Aeronautica et Astronautica Sinica,2017,38(2):567-588(in Chinese).
[17]袁国强,李颖晖,徐浩军,等.积冰对飞机本体纵向非线性动力学稳定域的影响[J].西安交通大学学报,2017,51(9):153-158.YUAN G Q,LI Y H,XU H J,et al.Effect of ice accretion on aircraft’s longitudinal nonlinear dynamic stability region[J].Journal of Xi'an Jiaotong University,2017,51(9):153-158(in Chinese).
[18]刘瑛,李敏强,陈富赞.飞行器机动动作风险定量评估模型[J].系统工程与电子技术,2014,36(3):469-475.LIU Y,LI M Q,CHEN F Z.Risk quantitative evaluation model of the aircraft maneuver[J].Systems Engineering and Electronics,2014,36(3):469-475(in Chinese).
[19] HARRYG K,JEAN T D.Nonlinear analysis of aircraft loss of control[J].Journal of Guidance Control&Dynamics,2013,36(1):149-162.
[20] MILLER R,RIBBENS W.The effects of icing on the longitudinal dynamics of an icing research aircraft:AIAA-1999-0636[R].Reston,VA:AIAA,1999.
[21]刘瑛,杜光勋,全权.基于Hamilton-Jacobi方程的飞行器机动动作可达集分析[J].自动化学报,2016,42(3):347-357.LIU Y,DU G X,QUAN Q.Reachability calculation for aircraft maneuver using Hamilton-Jacobi function[J].Acta Automatica Sinica,2016,42(3):347-357(in Chinese).
[22] OSHER S,FEDKIW R.Level set methods and dynamic implicit surfaces[J].New York:Springer,2003:25-37.