Analytic Solutions of Generalized Impact-Angle-Control Guidance Law for First-Order Lag System

Abstract

To examine the effects of system lag on performance of a generalized impact-angle-control guidance law, analytic solutions of the guidance law for a first-order lag system are investigated. Under the assumptions of a stationary target and a first-order missile system with constant speed and small flight-path angle, the analytic solutions are obtained by solving a third-order linear time-varying ordinary differential equation. The solutions are expressed by combinations of polynomial, logarithmic, and infinite power series functions. The analytic solutions provide an insight into the behavior of the missile near the target: the guidance command, the acceleration of the missile, and the velocity component perpendicular to the collision course tend to diverge as the missile approaches the target. Terminal misses due to the system lag are discussed using the analytic solutions, and effects of guidance coefficients on the terminal misses are examined. Linear and nonlinear simulations are performed to verify the proposed results.