Research On The Dynamics And Nonlinear Control Of The Submarine-launched Missile In Multimedia Environment

Submarine-launched missile takes an important role in the modern warbecause of its advantages in secret launch and high precision. Therefore, most ofcountries in the world are developing or planning to develop submarine-launchedmissile. The modern war requires that submarine-launched missile can be launchedfrom large water depth or variable depth. So, submarine-launched missile needs tohave good underwater and water-exit ballistics, the stable sailing postures and thestarting conditions required by the air flight segment after water exiting. Theresearch on dynamic and control for submarine-launched missile is particularlycomplex and necessary, because of the medium (sea water) which thesubmarine-launched missile sails in and different medium that thesubmarine-launched missile sails across. The dynamic equation ofsubmarine-launched missile is strong nonlinear, which needs to be solved by thecontrol algorithm. This paper researches on the underwater and water-exit processof submarine-launched missile, particular on the factors which have effect on theunderwater and water-exit ballistic, such as the speed, current, wave and wind. Onthis basis, the nonlinear control problem of trajectory tracking control and attitudetracking control are studied.The submarine-launched missile is influenced by the velocity of submarine.As a result, the attack angle is generated and the attitude of missile which islaunched vertically is changed by the pitching torque. The effect on the attitude ofmissile launched from different depth by the velocity of submarine is discussed.During increasing the launch depth, the influence degree on the attitude by thevelocity becomes more and more great. The sailing process is influenced by thecurrent. The effect on the water dynamic is analyzed by the different currentgradient, velocity and convection using the CFD(Computational Fluid Dynamics)technique.The water-exit process of submarine-launched missile is influenced by oceanwaves and sea breeze. The2-d and3-d sea wave are simulated by the second orderSTOKES wave based on the CFD technique. The3-d simulated sea wave isutilized to investigate the wave forces during the process of water-exit for themissile. The analytical expression of wave forces is obtained by the data fitting.The effect by the sea wave is analyzed based on the kinematic model of missile.The relation between the limit deviation of ballistic parameters and the classes anddirection of sea wave can be calculated by the Monte Carlo method. During theresearch on the effect of sea wind on the missile, the sea wind will be considered as the wind load. The analytical expression of load force and moment is derivedduring the water-exit process. The relation between attitude and velocity anddirection of wind will be found by simulation.The submarine-missile is generally launched without control for the shallowdepth circumstance. The missile is ejected, and powered out of water by gas-steam.However, when the missile is launched from large water depth or variable depth,the time of under-water sailing will increase. The attitude of missile divergesseriously, because of the effect by the velocity of marine and the sea current. In themean time, the derivation of ballistic becomes large. Therefore, the success oflaunch without control can not be guaranteed. The underwater ballistic trackingcontrol problem is investigated in this paper, and the adaptive longitudinaltrajectory tracking control method based on Backstepping is presented. The theoryof optimal approximation is used to approximate nonlinear term in longitudinaltrajectory control model by constructing a suitable basis function, and themodified approximation model can be obtained. Then two stable functions areintroduced to designed adaptive controller using the Backstepping technique, andthe stability of control system is proved with Lyapunov method. For thethree-dimensional trajectory tracking problem, the theory of differential geometryis used to carry out the full state feedback linearization to the nonlinear motionmodel of submarine-launched missiles and get the control model of the chain-formstructure. This method leads to the accurate linearization in nonlinear system.Based on chain structure model, the stable control law of dynamic feedbackcontrol index is designed to track the three-dimensional ballistic accurately.The attitude of missile has to satisfy the requirement by the air flight segmentafter the water-exiting process. However, the attitude diverges seriously as thedisturbance by environment during the under water and water-exit process,especially when the missile is launched from deep water. In order to solve theattitude tracking control problem of submarine-launched missiles, the implicitincremental dynamic inversion control attitude tracking control algorithm isderived, which reduces the rate of dependency the controller to the accuracy of themissile model. Making use of introducing the state variable rate feedback, therobustness of the structure error (such as parameter perturbation) of model isimproved. The algorithm can be applied directly in the condition of4class seawave and below. As the water-exit process is a cross medium movement, the LPVgain scheduling multiple medium regional integration control method is proposedin this paper which changes the motion model into LPV model, and takes thescheduling parameter space divided into limited height space as the whole sailingarea. In each subspace, LPV controller is designed based on submarine-launchedmissile LPV model, using fusion function to fuse each subspace controller into the whole space LPV controller. The stability of the closed-loop system is proved bythe parameter dependent Lyapunov function.