This dissertation presents three types of closed-form guidance law that maximizes the terminal speed of guided missiles in the final flight section. The first proposed guidance law is the closed-form guidance that only maximizes the terminal speed. And the second one is the closed-form guidance that satisfies the impact angle constraint and maximizes the terminal speed. The final one is the weighted closed-form guidance that satisfies the impact angle constraint and enables the acceleration command to converge to zero before impact. It should be selected to satisfy the more important performance among the convergence of the acceleration command before impact and the impact speed. To obtain a closed-form guidance law, this study will define the specific geometries of nose-diving all the way to the terminal phase, then focus on maneuvering to maximize impact speed with or without the impact angle constraint.
In order to increase the success rate of the mission to neutralize the target, the warhead must have high destructive power or performance. As the importance of underground target missions has recently increased, researches to maximize the warhead power are being conducted in developed countries, such as maximizing the terminal speed. And missions of modern missiles have trajectories that fly from high to low altitudes to increase their survivability, so they experience drastic changes in air density over short flight times. This means that in the case of a missile that fly without a powerful propulsion system in the descending section, changes of air density can act as a drag force that causes a decrease in speed. The difficulties of handling air density in the system equations due to its nonlinear properties made most previous researches for the guidance problems for maximizing the terminal speed use numerical optimization techniques, or find analytic solutions applied multiple assumptions.
In this study, air density change according to altitude was included in the system model and the missile speed dynamics were included in the optimization problem formulation. We solved the difficulties due to non-linearity by presenting the equivalent problem for maximizing terminal speed. Through this thesis, a closed-form guidance law was proposed that considered density of the air according to the altitude, the impact angle control, and maximizing terminal speed. The proposed closed-form solution has the advantage of being relatively easy to apply to a real-time system because it can be calculated in a very short time compared to on-line open-loop optimal solution finding.