| With the development of military science and technology,precision strike has become the core combat idea of all military powers.Traditional unguided munitions has been unable to meet the requirements of precision strike of modern battlefield.So guidance transformation of conventional ammunition has become a development direction.The course correction fuze with fixed canards has great advantages in the guidance transformation of conventional ammunition due to its low cost,small size,versatility and so on.With the support of the National Defense 973 Program(613145),the 13th Five-year Equipment Research Program(0715A),the Equipment Research Fund(9140C300305140C30140)and the National Natural Science Foundation of China(11402117),this paper takes the spin stabilized 2D trajectory correction projectile with fixed canards as the research object,and some theoretical and technical problems regarding the modeling of multi-body dynamics,linear and nonlinear dynamics analysis,guidance method design are analyzed and studied in this paper.The main contents are as follows:(1)According to the aerodynamic layout,motion characteistics of 2D trajectory correction projectile,the seven degrees of feedom flight dynamic model on the plane surface are established based on momentum theorem and moment of momentum theorem.The aerodynamic and aerodynamic moment act on the projectile are analyzed when there is a wind.Taking a spin stabilized 2D trajectory correction projectile as the object,the unguided flight,open loop guided flight and correction correction capability are simulated.And have a preliminary understanding about the trajectory characteristics of the projectile.(2)A trajectory model is built based on Kane's method in which the curve earth surface and the changes of both the size and the direction of the acceleration of gravity are considered.Firstly,a method to establish the dynamic model for multi-rigid body systems with tree structures is given based on Kane's method.The motions of the body and fixed canards are analyzed.Afterwards,the dynamic models of both parts are established.On this basis,the seven degrees of freedom flight dynamic equations are built.And the kinematics equations are set up based on the quaternion transformation.Finally,the errors of the range calculation between two kinds of trajectory models are compared on the plain and plateau.(3)The linear stability problems of 2D trajectory correction projectile are studied.Fistly,the kinematic equation of the complex attack angle of 2D trajectory correction projectile is established.And the forms of the solution are also discussed.According to calculate the solution of forced motion when the canards spin at a constant rate,the resonance condition of uncontrolled flight is discussed.The constraint conditions of transient and steady attack angle under controlled flight are obtain by deriving the analytical solutions of transient and steady state response when the canards generates step excitation.By deriving the analytical solutions of average velocity deflection angle,the relationships between the amplitude and phase angle of the average deflection angle and the parameters of the fixed canards are proposed.The concept of lead angle is put forward,which lays the foundation for the study of trajectory tracking guidance method based on velocity direction correction.(4)The nonlinear stability problems of 2D trajectory correction projectile are studied.Firstly,the nonlinear angular motion equation of 2D trajectory correction projectile is deduced.And the description model of the nonlinear aerodynamic are discussed.Secondly,the Hopf bifurcation analysis method for nonlinear angular motion based on the center manifold theory and normal form theory is deduced.The Hopf bifurcation of the free motion of the projectile under nonlinear pitching moment,nonlinear pitch damping moment,nonlinear magnusus moment are calculated by using this method,and the bifurcation diagrams and the limit cycles of the nonlinear angular motion are obtained.Then,the method of analyzing the forced motion of projectile under fixed canards is studied by using Poincare map.In this method,the Poincare map is used to predict the change of the periodic solution of the angular motion,and then the amplitude and period of the periodic solution are calculated by the generalized shooting method.And the stability of the periodic solution is analyzed by Floquet theory.The effect of the nonlinear magnus moment on the forced motion of the projectile is calculated by this method Finally,based on the numerical continuation algorithm,the influence of the nonlinear magnus moment on the equilibrium solution is analyzed.(5)A new trajectory tracking guidance method based on the velocity direction correction for the 2D trajectory correction project is proposed.This method tracks the scheme trajectory by modifying the direction of average deflection angle.Firstly,the models of the scheme trajectory and guidance command are derived,and the calculation formula of the roll angle of fixed canards is given according to the lead angle calculated by chapter 4.Then the method to generate the scheme trajectory online through the impact point prediction generation is studied when the trajectory deviation is large.Finally,the tracking effects of the scheme trajectory under two fire angles are simulated.The simulation results show that,when the firing angle is small,the velocity direction correction can be used to track the scheme trajectory on the whole trajectory.When the firing angle is large,the scheme trajectory can be generated on downward phase,and then the velocity direction correction can be used to track the new scheme trajectory.(6)A impact point predication guidance method for 2D trajectory correction projectile is proposed.The method corrects one trajectory by two impact point predications.The azimuth angle of the error between the target and the actual impact point is obtained by the first uncontrolled impact point predication.And the lead angle of the phase angle of impact point correction relative to the roll angle of fixed canards is obtained by the second controlled impact point predication.Then the roll angle of fixed canards which is needed to correct the error of impact point are obtained.The simulation results show that,impact point predication guidance has high accuracy that can be used on downward phase for considering the real-time prediction. |
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