Summary

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​The optimal guidance of launch vehicles plays a crucial role in maximizing the performance and efficiency of the vehicle throughout its trajectory. This presents a comprehensive overview of the vehicle model employed in the control algorithm to propel a launch vehicle from the Earth’s surface to a desired orbit of 6500 km. The control algorithm utilizes the principles of optimal control theory, integrating the state equations of the launch vehicle, mission-specific constraints specified by boundary conditions, and the performance objective of minimum energy to determine the optimal control inputs required for achieving the desired trajectory. The nominal trajectory of the launch vehicle is obtained by solving a two-point boundary value problem, which incorporates the initial and final conditions of the vehicle’s state. This approach enables the determination of an optimal trajectory that satisfies mission requirements and constraints. To compensate for disturbances that affect the vehicle’s states during the ascent phase, a closed-loop guidance system is designed. This system utilizes feedback control techniques to actively counteract the effects of disturbances and maintain the desired trajectory. The lateral acceleration, derived from the feedback gain of the state, is calculated to guide the launch vehicle towards the nominal path, effectively correcting any deviations caused by disturbances. To handle various process and measurement noises that can affect the accuracy of state estimation, a Kalman filter is applied. This filter leverages the available measurements and system dynamics to estimate the true state of the launch vehicle. By incorporating the estimated state into the guidance algorithm, the launch vehicle can maintain accurate trajectory tracking even in the presence of noise and uncertainties. The combination of the nominal trajectory determination, closed-loop guidance, and the integration of a Kalman filter contributes to the optimal guidance of launch vehicles. This approach ensures precise path tracking, minimizes the impact of disturbances, and enhances the overall performance and efficiency of the launch vehicle during its ascent to the desired orbit