lunar_lander_project

lunar_lander_project - Project I, MAE 4720/7720 Modern...

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Project I, MAE 4720/7720 – Modern Control, Fall 2008 Due date: Oct 30 The below diagram is from the 1971 MIT report on the Apollo lunar descent guidance design. The spacecraft (LM) fires a short de-orbit burn to descend from a circular lunar parking orbit, and then fires the main engine for a continuous powered retro-burn to the desired target state. The overall goal is to determine the thrust profile (magnitude and direction) which minimizes the fuel expenditure and meets the target state for proper landing. The simplified figure below shows the powered descent phase of a lunar lander spacecraft (modeled on the Apollo LM).
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The guidance solution can be determined from the following optimal control problem (the Apollo descent guidance was also based on the optimal control solution): Find the optimal horizontal and vertical thrust-acceleration components, u 1 and u 2 , and powered transfer time T that minimize the performance index J ( 29 + = T dt u u J 0 2 2 2 1 2 1 subject to the “flat-moon” equations of motion:
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lunar_lander_project - Project I, MAE 4720/7720 Modern...

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