Three-dimensional guidance law design with impact time constraint

For the missile-target relative motion equations in the three-dimensional space, a three-dimensional impact time control guidance law is proposed for multiple missiles in attacking a stationary or a slowly moving target. The engagement dynamics is decoupled approximately into the pitch channel and the yaw channel. In order to augment guidance robustness against changes of system parameters and external uncertain disturbances, the sliding mode variable structure guidance system is adopted in the pitch channel, the yaw channel is controlled by a maneuver control command using the dynamic inversion control method. We separately design the dynamic inversion controllers for the defined slow subsystem and the fast one, the yaw maneuver command is able to adjust the impact time to a desired value through the lateral maneuvering flight. Time-to-go error will converge to zero ultimately to achieve the impact time control. Numerical simulation results demonstrate that the proposed guidance law can satisfy the requirements of the impact time as well as the guidance precision.