Robust Graded Sliding Mode Tracking Control for Low Speed Spinning Ballistic Missiles

The nonlinear dynamic model of spinning ballistic missiles is established during the first boosting phase of the missile. Based on the conventional backstepping sliding mode control and the assumption of a two time-scale separation of missile dynamics, a graded sliding mode controller is designed with two sub-sliding surfaces which have invariability to external disturbances and parameter perturbations, and a matrix which comprises three first order low pass filters is introduced to prevent “explosion of terms”. Owing to the upper bounds of the uncertainties are difficult to obtain in advance, adaptive laws are introduced to estimate the values of the uncertainties in real-time. Eventually, the numerical simulation results given to show the proposed controller can ensure the steady flight of missiles.