New guidance law for a missile with varying velocity

Abstract

A new guidance law for a missile with varying velocity i s presented. First, the basic guidance equations to compute thc missile acceleration command and time-to-go are derivcd. These equations are available whenever we can predict the intercept point in some way. Taking into account a missile thrust. we obtain the guidance law during boost phase. On the other hand. the guidance law af te r thrust cutoff i s derived by considering an a i r drag. Three forms of guidance laws arc proposed for each phase. One of them, which is called the analytical guidance law, gives the theoretical gujdancc acceleration commands to guide a missile on the collision course. Though this guidance law i s mcaningful from the mathematical viewpoint, the guidance equations are too complicated to perform the computation in real time. Thus, we present the approximate guidance law in order to reduce the computation time. This guidance law i s useful when i t i s implemented on a powerful guidance compulcr on thc ground or on the parent a i r craft. Ncxt, the approximate guidance law i s transformed into the convcnicnt form to realize i t on an existing homing missile. Since the obtained form i s similar to a conventional augmenled proportional navigation. we ca l l i t the modified augmcnted proportional navigation. The guidance laws presenled as well as a conventional proportional navigation and an augmented proportional navigation are applied to a simple model of a short range airto-air miss i lc . Some simulations are performed and then the inner launch envelopes are generated. The simulation results show that the guidance laws presented can intercept the target using fa r smaller acceleration requirement than prepared for the conventional navigations. When the miss i l e velocity varies significantly, the performance of the conventional navigations arc seriously influenced. The inner launch envelopes show that the guidance laws presented provide an overall performance improvement over the conventional navigations. Especially, the modified augmented proportional navigation i s useful and at t ract ive from the real i s t i c viewpoint. * Asso. Professor. NDA. Yokosuka. Japan 239, Member AIAA ** Postgraduate Rcsearcher. NDA. Yokosuka. Japan 239 *** Lecturc. NDA, Yokosuka, Japan 239, Member A I A A = missile axial acceleration vector, a m = 1 a m ] = target la teral acceleration vector, a ,= 1 a, 1 = target la teral acceleration perpendicular to LOS = target axial acceleration vector, a , = 1 a , 1 = zero-l i f t drag coefficient = desired acceleration command vector = acceleration due to gravity = specific impulse = mass of missile = navigation constant = effective navigation constant = position vector of the impact point with respect to the present target position. P = I PI = position vector of the impact point with respect to the present missile position. Q = I Q I = relative distance vector, R = IR I = missile reference area = differential operator = thrust = total f l igh t time = time-to-go or intercept time = I , ,W/T = closing velocity = missile velocity vector, V, = 1 V , 1 = correct missile velocity vector. V,= I V,, I = target velocity vector. V , = 1 V , 1 = missile weight = i n i t i a l missile weight = ba l l i s t i c coefficient = vm v,, = missile flight-path angle = 4 , E = missile flight-path rate vector = P S C ~ d 2 r n = $ , d m = target flight-path angle to LOS = a i r density = LOS angle = LOS rate vector = missile flight-path angle to LOS = the angle between P and LOS Copyrighl c 1994 by the American I n s t i t u t e of Aeronautics and Astronautics. Inc. All r i g h t reserved.