Six Degrees of Freedom Mathematical Model for Missile Control Using Thrust Vectoring

This paper presents a six degrees of freedom mathematical model for missile control using thrust vectoring. The control method employed in this study does not rely on the dynamic pressure of the atmosphere but is based on the thrust force generated by the missile's engine. The change in the thrust vector is dependent on the control requirements, thereby altering the motion characteristics of the missile. This enables the adjustment of the thrust vector relative to the axis of symmetry of the missile. Many missile engines, whether using solid or liquid propellants, incorporate thrust vector control to achieve the desired attitude during flight. Utilizing thrust vector control, missiles can maintain the desired flight attitude [3,15,16]. The mathematical framework for this evolution is based on object, velocity, and ground coordinates, with the center of gravity of the missile serving as the origin. In the ground coordinate system, the xgzg axis represents the horizontal plane, while the Yg axis represents the vertical rise, supplementing the standard right-hand system. Within the missile body coordinate system, the positive Xb axis corresponds to the centerline of the missile and represents the rolling axis. The positive Zb axis is perpendicular to the Xb axis within the horizontal plane, representing the pitch axis. The positive Yb axis points upwards, signifying the yaw axis. The body axis system remains fixed for the missile and follows its flight. In the velocity coordinates, XV corresponds to the direction of the missile's velocity (Vm) and is related to the direction of the missile's flight. The ZV axis complements the standard right-hand system [1,2,17-19]. The pitch plane corresponds to the X-Y plane, the yaw plane corresponds to the X-Z plane, and the roll plane corresponds to the Y-Z plane. The ground coordinates and body coordinates are determined by the attitude angles (w, ф, ϒ). The ground coordinates and velocity coordinates are related through the angles (θ, σ). The velocity coordinate system is related to the fuselage frame through the angle of attack in the pitch plane (α) and the sideslip angle in the yaw plane (β). The relationships between the various coordinate systems are illustrated in Figure 1 [1,2,17,19,20]. Part 3 focuses on the design of the FPID nonlinear missile pitch channel controller for gain planning.