Moving Mass Control And Terminal Guidance For Spinning Missiles

Moving mass control (MMC) is a new control method in control field. It is a potentialway to solve the problem of aerodynamic rudder control insufficiency caused by the lowdensity of upper atmosphere, to reduce the high speed missile aerodynamic thermal loadand to solve the problem of rudder surface ablation. It can be applied to the reentry vehicle,kinetic kill interceptor, underwater vehicles, and other fields as well. MMC missiles havemore potential and promising application in the futrue. However, the study on MMCmissles are not enough in-depth, there are still many problems need to be solved forimplementation. Firstly, it is necessary to analyze the characteristic of MMC missiles,which is the foundation of the follow-up study. Second, the spinning of the airframe and themovement of internal moving mass induced the serious dynamic cross-coupling betweenpitch and yaw channel, which may lead to a bad performance of the missile. Therefore it isneeded to solve the design problem of the control system under the cross-coupling and withnonlinerity. Finally, a guidance law with multi-objective constraints is needed for theprecision guidance.In this paper, the mathematical models of MMC spinning missiles with two radialmoving mass is derived by means of the multi rigid body dynamics method. The effects ofdifferent kinds of forces and moments resulted from the moving mass are analyzed on thebasis of their sorting. The ballistic performance of MMC missile is analyzed by numericalsimulation.And it is shown that the angle of attack (AOA) is directly proportional to thelateral and longitudinal offset, and the control capability is influenced by the initial ballisticheight and initial angle of flight path.The dynamic stability condition of MMC missiles without control is studied, and theinfluence of moving mass installation position and the spinning rate on dynamic stability isdiscussed. Then, the differential equation of the spinning missile with rate loop isestablished. The stability condition for both slow spinning rate and fast spinning rate arederived separately considering the different mechanism of AOA caused by MMC, andfurther verified by numerical simulation. For slow spinning rate MMC missiles, the morethe spinning rate, the larger the cross coupling, which makes stable regions of designparameters shrink. While for fast spinning rate MMC missiles, the more the spinning rate,the larger the moment of inertia, which makes stable regions of design parameters expand. The system model is simplified to the affine dynamics model, in which the modeluncertainty and external disturbances are considered. And then, the system is divided intoattitude tracking loop and angular velocity tracking loop. Based on the backsteppingapproach, a regular sliding mode controller is designed for the attitude loop and asecond-order sliding mode controller is designed for the angular velocity loop, and anadaptive control law is designed to adapt the wide variation of system parameters, whichcan increase the system’s robustness in handling of nonlinearity, uncertainty and externaldisturbance. The simulation results show that the controller has a good performance both instability and in robustness.Finally, the guidance law with impact angle, terminal acceleration as well as inputconstraint is researched. Based on the motion equations of missle considering actuator lagand gravity, the multi-constraint online guidance law is designed by MPSP method and itsvalidity and superiority is verified by simulation. It is also noted that the greater thedifference value between guess history output and the expect system output, the longer thetime needed for computing. And modified guess history method was utilized to acceleratethe online computation.