Research On Guidance Law Of Air-to-Surface Missile With Terminal Angle Constraint Based On Optimal Control Theory

As air-to-surface missiles are affected by overload constraints,seeker sight angle measurement range,autopilot delay,interference and other factors,they cannot cause fatal damage to the attacking target.Based on the optimal control theory,in this paper,the optimal control theory is used to study guidance accuracy with terminal landing angle constraints.The optimization problem is to propose a terminal guidance law that meets both the miss distance requirement and the expected terminal landing angle.The main research contents are as follows:Firstly,the equation of relative motion between missile and target is derived according to the relationship between missile and target in terminal guidance stage.In order to better understand and study the derivation process of the guidance law,linearization and small-angle assumptions are made on the movement model of the projectile and eye.Simulations verified that the linearization of the model brings convenience to the research of terminal guidance without changing the guidance effect and is feasible.On the basis of linearization,the optimal control theory is introduced,the terminal guidance law of the missile is studied,the optimal performance index is first designed,and then the guidance law with terminal landing angle constraint is derived,which consumes less energy.In order to better understand the form of guidance law,this paper presents the optimal guidance law with terminal landing angle constraint under the condition of zero lag.The simulation results show that the guidance law satisfies the guidance requirement and has a small miss distance,and the missile itself can meet the required normal overload.Secondly,the robustness of the guidance law based on the optimal control theory is relatively poor,so sliding mode variable structure control is used to improve it,and the approaching law method is used to design a suitable sliding mode surface,combined with the guidance law in chapter 3.The optimal sliding mode guidance law with terminal landing angle constraint and good robustness is derived.Aiming at the ensuing chattering problem,a low-pass filter is used to improve it.Through simulation under the conditions of noise interference and target maneuvering,the correctness of the optimal sliding mode guidance law is verified.Finally,in order to realize that the seeker can track the target in real time when the expected terminal landing angle of the missile is large,the missile’s field of view can observe the target in real time.Two guidance laws are proposed.One is based on the traditional proportional guidance method,combined with the sliding mode variable structure theory,plus a bias term,and proved the stability and accessibility.Proportional guidance law is based on the traditional proportional guidance law with a bias term.The optimal guidance law first analyzes the convergence conditions of the seeker’s field of view,and discusses it in sections according to the change of the field of view.The simulation parameters of the guidance law in MATLAB show that the above two guidance methods can achieve the terminal landing angle constraint,and the missile can still observe the target when the terminal landing angle is large.but the optimal guidance law consumes less energy.Then,aiming at the constraints of the field of view and landing angle of the seeker in practical engineering,A terminal guidance law based on ballistic shaping is proposed,which can satisfy the constraints of large landing angle and field of view at the same time,and is suitable for engineering practice.