结冰飞机非线性稳定域确定及安全操纵方法
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摘要
结冰会恶化飞机的动力学特性,造成飞行包线收缩,威胁飞行安全,研究结冰后飞机的非线性稳定域变化对于驾驶员操纵应对策略设计以及飞行安全的提高具有重要意义。以NASA的GTM为案例飞机,首先对飞机气动参数进行多项式拟合,同时结合结冰因子模型,建立了飞机在结冰条件下的纵向通道动力学模型;然后通过分岔分析方法对飞机在不同程度结冰条件和操纵指令下的飞行状态变化进行了研究,并将其用于指导驾驶员操纵,同时考虑到分岔分析方法的局限性,利用微分流形理论确定了飞行系统的非线性稳定域,并将其作为飞行安全边界;最后针对结冰情形,提出将分岔分析方法与微分流形理论相结合共同用于操纵指导,并进行了操纵时域验证。研究结果表明,结冰会使安全边界收缩,在小扰动的作用下都可能使飞行状态超出安全边界。随着结冰程度增加,飞机的稳定性质甚至会发生变化,此时飞行状态将很难维持在原有的安全边界以内,提出了通过指导驾驶员操纵指令变化使飞行状态到达新的安全边界。研究结果对于飞行安全操纵及边界保护都具有一定的指导意义。
Icing will destroy the dynamic performance of the aircraft and cause the safety envelope shrink,which seriously affects the flight safety. It is of great significance to study the changes of nonlinear stability region of the icing aircraft for reducing flight accidents. In this paper,the NASA's GTM is taken as the object aircraft. First,the dynamic model of longitudinal channel under icing condition is established based on polynomial fitting of the aerodynamic parameters and the icing factor model. Then,the change of flight state under different icing conditions and control commands is studied by bifurcation analysis method which used to guide flight manipulation. Considering the limitation of bifurcation analysis method,the nonlinear stability region of flight system is determined by differential manifold theory. And the nonlinear stability region is regarded as flight safety boundary. Finally,considering the icing condition,the bifurcation analysis method and differential manifold theory are combined to guide manipulation. Furthermore,the time domain validation of the manipulation is carried out. The results show that icing will shrink the safety boundary,and a slight disturbance may contribute to flight state outside the safety boundary. Moreover,with the increasing degree of icing,the stability of the aircraft will even change and the flight state will be difficult to maintain within the original safety boundary. At this moment,the flight state can be brought to the new safety boundary by changing the pilot's manipulation instruction. The research results are helpful for flight safety manipulation and boundary protection.
Icing will destroy the dynamic performance of the aircraft and cause the safety envelope shrink,which seriously affects the flight safety. It is of great significance to study the changes of nonlinear stability region of the icing aircraft for reducing flight accidents. In this paper,the NASA's GTM is taken as the object aircraft. First,the dynamic model of longitudinal channel under icing condition is established based on polynomial fitting of the aerodynamic parameters and the icing factor model. Then,the change of flight state under different icing conditions and control commands is studied by bifurcation analysis method which used to guide flight manipulation. Considering the limitation of bifurcation analysis method,the nonlinear stability region of flight system is determined by differential manifold theory. And the nonlinear stability region is regarded as flight safety boundary. Finally,considering the icing condition,the bifurcation analysis method and differential manifold theory are combined to guide manipulation. Furthermore,the time domain validation of the manipulation is carried out. The results show that icing will shrink the safety boundary,and a slight disturbance may contribute to flight state outside the safety boundary. Moreover,with the increasing degree of icing,the stability of the aircraft will even change and the flight state will be difficult to maintain within the original safety boundary. At this moment,the flight state can be brought to the new safety boundary by changing the pilot's manipulation instruction. The research results are helpful for flight safety manipulation and boundary protection.
引文
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[14]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.
[15]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).
[16]MILLER R,RIBBENS W. The effects of icing on the longitudinal dynamics of an icing research aircraft:AIAA-1999-0636[R]. Reston:AIAA,1999.
[17]BRAGG M B,HUTCHISON T,MERRET J,et al. Effect of ice accretion on aircraft flight dynamic:AIAA-2000-0360[R]. Reston:AIAA,2000.
[18]POKHARIYAL D,BRAGG M B,HUTCHISON T,et al. Aircraft flight dynamics with simulated ice accretion:AIAA-2001-541[R]. Reston:AIAA,2001.
[19]曹启蒙,李颖晖,徐浩军.考虑作动器速率饱和的人机闭环系统稳定域[J].北京航空航天大学学报,2013,39(2):1237-1253.CAO Q M,LI Y H,XU H J. Stability region for closed-loop pilot-vehicle system with actuator rate saturation[J]. Journal of Beijing University of Aeronautics and Astronautics,2013,39(2):1237-1253(in Chinese).
[20]HINKE M O. Two-dimensional invariant manifolds in four-dimensional dynamical systems[J]. Computers&Graphics,2005,29(2):289-297.
[21]HALLER G,BERONVERA F. Geodesic theory of transport barriers in two-dimensional flows[J]. Physica D Nonlinear Phenomena,2012,241(20):1680-1702.
[2]VIKRANT S,PETROS G. Aircraft autopilot analysis and envelope protection for operation under icing conditions[J]. Journal of Guidance,Control,and Dynamics,2004,27(3):454-465.
[3]ROBERT B. Aircraft icing[EB/OL].(2013-05-01)[2015-05-08]. www. aopa. org/asf/publications/sa11. pdf.
[4]MERRET J M,HOSSAIN K N,BRAGG M B. Envelope protection and atmospheric disturbances in icing encounters:AIAA-2002-0814[R]. Reston:AIAA,2002.
[5]JAN S,BERND K. Control based bifurcation analysis for experiments[J]. Nonlinear Dynamics,2008,51(3):365-377.
[6]XIN Q,SHI Z K. Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack[J]. Chinese Journal of Aeronautics,2015,28(1):250-259.
[7]KHATRI A K,SINHA N K. Aircraft maneuver design using bifurcation analysis and nonlinear control techniques:AIAA-2011-924[R]. Reston:AIAA,2011.
[8]ENGELBRECHT J,PAUCK S,PEDDLE I. Bifurcation analysis and simulation of stall and spin recovery for large transport aircraft:AIAA-2012-4801[R]. Reston:AIAA,2012.
[9]HARRY G K,JEAN T D. Nonlinear analysis of aircraft loss of control[J]. Journal of Guidance,Control,and Dynamics,2013,36(1):149-162.
[10]LARISSA K,BEHZAD S. Estimation of region of attraction for polynomial nonlinear systems:A numerical method[J]. ISA Transactions,2014,53(1):25-32.
[11]TAN W,PACKARD A. Stability region analysis using polynomial and composite polynomial Lyapunov functions and sum-ofsquares programming[J]. IEEE Transactions on Automatic Control,2008,53(2):565-570.
[12]WEEKLY K,TINKA A. Autonomous river navigation using the Hamilton-Jacobi framework for underactuated vehicles[J].IEEE Transactions on Robotics,2011,30(5):1250-1255.
[13]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):100-110.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):100-110(in Chinese).
[14]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.
[15]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).
[16]MILLER R,RIBBENS W. The effects of icing on the longitudinal dynamics of an icing research aircraft:AIAA-1999-0636[R]. Reston:AIAA,1999.
[17]BRAGG M B,HUTCHISON T,MERRET J,et al. Effect of ice accretion on aircraft flight dynamic:AIAA-2000-0360[R]. Reston:AIAA,2000.
[18]POKHARIYAL D,BRAGG M B,HUTCHISON T,et al. Aircraft flight dynamics with simulated ice accretion:AIAA-2001-541[R]. Reston:AIAA,2001.
[19]曹启蒙,李颖晖,徐浩军.考虑作动器速率饱和的人机闭环系统稳定域[J].北京航空航天大学学报,2013,39(2):1237-1253.CAO Q M,LI Y H,XU H J. Stability region for closed-loop pilot-vehicle system with actuator rate saturation[J]. Journal of Beijing University of Aeronautics and Astronautics,2013,39(2):1237-1253(in Chinese).
[20]HINKE M O. Two-dimensional invariant manifolds in four-dimensional dynamical systems[J]. Computers&Graphics,2005,29(2):289-297.
[21]HALLER G,BERONVERA F. Geodesic theory of transport barriers in two-dimensional flows[J]. Physica D Nonlinear Phenomena,2012,241(20):1680-1702.
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