# Integrated Autopilot Guidance Based on Zero-Effort-Miss Formulation for Tail-Controlled Missiles
## 1 Introduction  
General fixed-wing aircraft perform maneuvers in a specific direction by generating aerodynamic forces based on attitude control. Specifically, in the case of aerodynamic-driven missiles, tail or canard wings are used to produce the angle-of-attack for generating the required acceleration. Since canard wings are mounted near the missile warhead, the lift by the control input of a canard-controlled missile is in the same direction as the main maneuver by the angle-of-attack. Based on this property, canard control is generally considered a method to easily secure flight stability. However, due to the short distance from the center of gravity, the maximum magnitude of the moment that can be generated from the canard is limited in comparison with the tail-controlled configuration. On the contrary, a tail-controlled missile can yield a greater moment than a canard-controlled missile with the same magnitude of the control input since tail wings are commonly located far away from the missile's center of mass. However, tail control leads to a non-minimum phase problem as the direction of the aerodynamic force produced by the tail fin is opposite to the direction of the main maneuver produced by the angle-of-attack of the fuselage. For these reasons, the existing studies that aim at developing autopilot for tail-controlled missiles have focused on dealing with the non-minimum phase problem [1; 2; 3; 4; 5; 6]. The study presented in [1] applied plant inversion techniques to develop a controller for the angle-of-attack. To avoid difficulties in dealing with non-minimum phase dynamics, the outer loop that converts the acceleration command into the angle-of-attack signal is combined. The work in [2] developed nonlinear autopilot based on feedback linearization methods with the use of time-scale separation techniques and redefinitions of the system outputs. The autopilot designed by [3] used augmented lateral acceleration to overcome stabilization difficulties in non-minimum phase dynamics, and the optimal control theory has been applied with the conventional three-loop autopilot topology in [4]. A classical proportional-integral controller has been used to configure the cascaded control structureable to overcome the non-minimum phase problem in [5], and various three-loop topologies have been investigated among comparisons of linear and nonlinear approaches in [6]. As in the studies described above, it is common for the autopilot loop to be designed separately from the guidance loop. In this configuration, the autopilot loop is structured to track the desired acceleration command generated from the guidance loop, such as in [7; 8]. This separate loop configuration has advantages, making both the design and analysis for each loop easier. However, rapid changes in each loop can incur instability to the other loop because the stability of whole system is not considered concurrently. For such reasons, there have been several approaches to develop an integrated guidance and control loop to enhance the terminal performance. In the studies of [9; 10; 11], the dynamics of canard-controlled missiles are considered for the design of integrated guidance autopilot. Since there is no need to deal with non-minimum phase dynamics, unlike in tail-controlled missiles, these studies have applied various control techniques in a straightforward manner. The integrated guidance autopilot methods presented in [12; 13; 14] have been designed without close consideration of the non-minimum phase problem because models of dual-controlled missiles have been adopted for such studies. For these reasons, the existing approaches for canard [9; 10; 11] or dual [12; 13; 14] controlled missile dynamics cannot be properly adopted for tail-controlled missiles because they do not consider zero-dynamics stability. In this study, we propose a control configuration that integrates guidance and control loops for tail-controlled missile dynamics.