An Adaptive, Optimal Proportional-Integral Guidance For Missiles

Abstract

In this study, a new form of missile guidance law is presented to improve the effectiveness of proportional navigation (PN) guidance law against fast maneuvering targets. Well-known proportional-integral-derivative (PID) controller structure is modified for a method of missile guidance. Line of sight (LOS) rate is used as the error signal in the formulation of the PID structure. As a consequence of the derivations, it is recognized that the derivative term can be dropped without significantly affecting overall performance. Linear optimal control theory is used for determining proportional-integral (PI) controller parameters with appropriate performance index (cost function) based on LOS angle, LOS rate and acceleration command. The resultant guidance formulation is almost as simple to implement as PN guidance with known or estimated knowledge of LOS angle and its rate. In the derivation of the new method, relative kinematics of missile-target engagement is analyzed for both azimuth and elevation planes separately to compute horizontal and vertical acceleration commands in inertial reference frame, respectively. The suggested guidance method has an adaptive and/or time varying structure since it employs relative range term and its rate of change in the state-space formulation of the kinematics. Therefore, proportional and integral gains within the algorithm change during the run according to the updates of these terms. The outputs of the so called adaptive, optimal proportional-integral (AOPI) guidance algorithm are then converted to the body frame components to be used in 6-DOF simulations to drive the autopilots. Simulation results show that for convenient slow and fast maneuvering F16 aircraft target scenarios, proposed new guidance formulation has improved performance than that of the PN guidance law.