1 INDIRECT ADAPTIVE CONTROL OF MISSILES Ufuk Demirci* and Feza Kerestecioglu** *Turkish Navy Guided Missile Test Station, Beykoz, Istanbul, TURKEY **Department of Electrical and Electronics Engineering, Bogazici University, Bebek, Istanbul,80815, TURKEY Abstract: An indirect adaptive controller is designed for aerodynamically driven missiles. The design is developed using a linearized model of a missile. Recursive least squares estimation method with exponential forgetting is used to estimate the time- varying missile parameters. A covariance management algorithm is suggested to prevent the exponential increase in covariance gain due to lack of persistently exciting inputs produced by the guidance unit. Keywords: Missile, self-tuning control, time-varying systems, recursive least squares. 1. INTRODUCTION The purpose of this paper is to present some results obtained for the indirect adaptive control of a linear missile model. The objective of the controller is to follow a preprogrammed trajectory aerodynamically without saturation at the output of the actuator system. The missile dynamics is time-varying with respect to the Mach number profile and changes in the environmental conditions. The missile is assumed having no roll motion and, hence, is controlled in the pitch and yaw directions independently. The same indirect adaptive controller is used for both directions. 2. MISSILE DYNAMICS The equations of motion of a missile consist of six kinematic and six dynamic first order nonlinear differential equations. Kinematic equations are divided into two groups; three translational kinematics and three rotational kinematics. The kinematic equations of motion may be derived from the geometric relations between the earth and missile axes. Dynamics equations are also divided into two groups; namely, three translational and three rotational dynamics. The dynamic equations of motion may be derived from Newton’s law of motion for a rigid body. A detailed derivation of these equations are given by Mahmutyazicioglu and Eskinat (1994). Missile dynamics also consist of modelling of variation of missile mass and moment of inertia, control surfaces, control actuation system and dynamics of measuring instruments. In addition to these, aerodynamic forces act on the missile should be taken into consideration during the derivation of a missile model. 3. LINEARIZATION OF THE MISSILE MODEL The equations of motion of a missile form a complicated set of coupled nonlinear differential equations. These nonlinear equations are too complicated for the purpose of the controller design. Therefore, they need to be simplified and linearized. 1 This work has been supported under the grants of The Scientific and Technical Research Council of Turkey (TUBITAK-SAGE) and B.U. Research Fund (Grant No. 98A201).