Investigation On Impact Time Control Guidance Laws For Missiles

Controlling the impact time of missiles is an important means to achieve saturation attack.To effectively complete the impact time control of the missile,designing the corresponding guidance law becomes the key.This paper takes the missile's guidance law with impact time constraint as the research object,and carries out systematic and in-depth research on many problems related to the design of this kind of guidance law.The main contents include as follows:1.The time to go estimation method for intercepting stationary targets under pure proportional guidance is studied.(a)Two kinds of time to go estimation models are established;(b)The established time to go estimation model is simplified under the small angle approximation assumption,and four time to go approximation calculation methods are derived for rapid estimation of time to go;(c)Using the time scale method and the special function(incomplete Beta function)construction method,three accurate calculation methods of time to go are derived.(d)Simulation verification of different time to go calculation methods,and comparison with existing literature,the results show that the proposed time to go calculation method has good accuracy and application performance.2.Based on the theoretical framework of pure proportional navigation guidance law,the design of missile's impact time control guidance law is studied.(a)By deeply studying the properties of pure-and retro-proportional navigation guidance law,and combining their respective application advantages,a two-stage impact time control guidance law is designed.The impact time control boundary,the control singularity,maximum acceleration and convergence of the designed guidance law are theoretically analyzed.(b)Combining the pure proportional naigation guidance law with the optimal control theory,this paper proposes an extended proportional guidance impact time control guidance law with field of view constraint.Through theoretical analysis and numerical simulation,the sensitivity to the time to go accuracy,the convergence of the field of view constraint and the influence of the estimation accuracy of the time to go on the guidance performance are studied;(c)By designing the bias term in the biased proportional navigation guidance law,an impact time control guidance law without control singularity and satisfying the fileld of view constraint is proposed.(d)The simulation results under different conditions show that the proposed guidance laws can effectively realize impact time control.Compared with the existing literature,it can adapt to more control conditions and has superior guidance performance.3.The application of sliding mode control theory to the design of missile's impact time control guidance law is studied.(a)Using the derived time to go estimation formula to construct the sliding surface,according to the sliding mode control theory and Lyapunov stability theory,a sliding mode impact time control guidance law without control singularity is proposed;(b)A sliding mode impact time control guidance law with filed of view constraint is designed.The control singularity,the stability and the relationship between the designed guidance law and the pure proportional navigaton guidance law are theoretically analyzed and relevant mathematical proofed;(c)Numerical simulation of the designed impact time control guidance law is carried out under different conditions and applications scenarios,which verifies the feasibility and effectiveness of the designed guidance laws.4.The problem of three-dimensional impac time control guidance is studied.(a)Different from the traditional decoupling dimension reduction processing method,the impact time control guidance model is established considering the three-dimensional kinematics relationship of the missile-target and its coordinate transformation;(b)Extending the two-dimensional two-stage impact time control guidance law based on the pure-and retroproportional navigation guidance law to three-dimensional,the three-dimensional two-stage impact time control guidance law is obtained.The convergence of the designed three dimensional guidance law is proved mathematically;(c)Based on the sliding mode control theory,a three-dimensional sliding mode impact time control guidance law is designed.The stability of the sliding mode guidance law is analyzed,and the existing control singularity problem is theoretically analyzed and improved;(d)Through the research of the relationship between the designed three-dimensional sliding mode guidance law and the three-dimensional pure proportional navigation guidance law,a three-dimensional sliding mode impact time control guidance law with field of view constraint is designed,and the corresponding stability analysis is carried out.The application of the designed guidance law in the case of intercepting a moving target with uniform speed is studied baseded on the predictive interception point method.(e)Through a large number of numerical simulations,the feasibility and effectiveness of several proposed three-dimensional impact time control guidance laws are verified.At the same time,compared with the existing literature,it can be applied to more boundary conditions.