Research On The Guidance Laws With Terminal Constraints Based On Finite Time Convergence

For homing guidance torpedoes,in order to improve the strike accuracy or to achieve some special tactical strike,the miss-distance is not the only technical indica-tor.In particular,the existence of problems such as unknown disturbance of target acceleration,singularity of guidance instruction,and terminal impact constraints(im-pact angle or impact time constraints),undoubtedly greatly increases the difficulty of torpedo accurate guidance.Due to the influence of the underwater environment,the detection range of the torpedo in the terminal guidance section is very small,so it is necessary to control the trajectory to be straight in finite time by a reasonable guidance instruction,so as to provide the reliability of the terminal guidance.For the above mentioned problems,it is of great strategic significance and far-reaching application prospect to study finite time convergence non-singular precision guidance law with terminal impact angle/impact time constraints.In view of this,the main work and research results of this dissertation are as follows:(1)Finite-time convergence guidance laws design based on nonlinear convergence factorFor the problem of traditional sliding mode-based guidance law,which is a slow convergence rate and no constraint on the convergence time,this dissertation discusses finite time convergence characteristics of sliding mode control,and proposes an im-proved terminal sliding mode control method by introducing nonlinear factors.Then,combined with the exponential reaching law,the finite-time convergence guidance law is designed to satisfy the fast convergence requirements of the system.The theoretical analysis shows that the guidance law proposed satisfies the system stability require-ments,and the simulation verifies the effectiveness of its fast convergence.Compared with the traditional sliding mode guidance law,the convergence rate of the guidance law proposed is faster and the robustness is stronger.(2)Guidance laws with impact angle constraints design based on target distur-bance estimationThe unknown disturbance caused by the target acceleration seriously affects the guidance accuracy of the torpedo,to solve this problem,combining with extended state observer to estimate disturbance,the guidance laws with impact angle constraints are proposed based on backstepping sliding mode control and integral sliding mode control by using sliding mode method,respectively,both guidance laws can ensure the stability of the system.Under the guidance laws proposed,the line of sight(LOS)angle rate can converge to zero,and the impact angle can converge to the desired values.The theoretical analysis proved guidance system stability,and the simulation verified the effectiveness of the guidance laws proposed in this dissertation.(3)Guidance laws with impact angle constraints design based on non-singular sliding mode controlIn view of the singularity problem that may occur in sliding mode control,the non-singular sliding mode control method based on the saturation function is designed by using the limiting amplitude characteristics of the saturation function.Then,con-sidering the impact angle constraints,the guidance law with impact angle constraints are designed based on non-singular sliding mode control method and the finite-time convergence theory.Under the guidance law,the stability of the guidance system is analysed.The singular and non-singular characteristics of the guidance law and the finite-time convergence characteristics of the guidance system variables are discussed in detail respectively.Finally,the autopilot dynamic is considered in the guidance system model,and simulation analysis is performed to verify the effectiveness and non-singularity of the guidance law.(4)Finite-time convergence guidance laws with impact angle constraints design based on feedback-linearization controlFor the problem that feedback linearization control can only achieve asymptotic convergence,we adopt the feedback linearization control and the finite-time conver-gence control to design two kinds of non-singular fast convergence guidance law with impact angle constraints.First,the guidance system model is transformed into a feedback linearization model.Furthermore,the control law is designed by using the finite-time control theory,and the unknown target disturbance existing in the control law is estimated to achieve the system variables fast convergence to the desired values.The numerical simulation shows that the guidance law with impact angle constraints can satisfy the constraints requirement of different initial heading angles and different impact angles,respectively;and the fast convergence and robustness of the guidance law are verified.(5)Sliding mode guidance laws with impact time constraints design based on time-to-go estimationFor the problem of slow convergence rate of the existing guidance law with impact time,the guidance law with impact time constraints is designed by using sliding mode control and Lyapunov stability theory and by analysing the time-to-go estimation method.In order to obtain the faster convergence rate,the guidance law is divided into equivalent controller and sliding mode controller,using the piecewise function to avoid the possible singular value problems.Simulation experimental results verify the effectiveness of the guidance law proposed in this dissertation.