• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.12
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• pp.1184-1194
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• 2010

The descent and ascent phases for a lunar lander are composed of several phases. Accordingly, the constraints and control values adequate for each phase are required in order to generate optimal lander's trajectory. The optimal trajectories for descent and ascent phases are generated by the cost function to minimize fuel consumption & attitude variation rates. In this paper, the optimal control problem to make trajectory uses Gauss pseudo-spectral method which is one of the direct approach method. This problem generates lander's reference trajectory, states and controls.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.5
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• pp.408-415
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• 2011

The moon landing is composed of the de-orbit descent phase, powered descent phase, and the powered descent phase is divide into 3-sub phase of the braking, approach, final landing phase. In this paper, the lunar lander perform landing control using 3-sub phase of optimal trajectory. First, generate the reference trajectory using gauss pseudo-spectral method. Thereafter generate PID controller using altitude and velocity error in each direction. Finally the lunar lander landing system constitute using the Simulink of Matlab, and perform simulation.

• International Journal of Aeronautical and Space Sciences
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• v.10 no.1
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• pp.112-121
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• 2009

This paper deals with supersonic air-breathing missile system. A supersonic air-breathing missile system has very complicated and incoherent thrust characteristics with respect to outer and inner environment during operation. For this reason, the missile system has many maneuver constraints and is allowed to operate within narrow flight envelope. In this paper, trajectory optimization of the missile is accomplished. The trajectory optimization problem is formulated as a discrete parameter optimization problem. For this formulation, Legendre Pseudo-Spectral method is introduced. This method is based on calculating the state and control variables on Legendre-Gauss-Lobatto (LGL) points. This approach helps to find approximated derivative and integration quantities simply. It is shown that, for this trajectory optimization, trend analysis is performed from thrust characteristics on various conditions so that the trajectory optimization is accomplished with fine initial guess with these results.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.264-277
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• 2015

This article investigates various transcription techniques for the Legendre pseudospectral (PS) method to compare the pros and cons of each approach. Eight combinations from four different types of collocation points and two discretization methods for dynamic constraints, which differentiate Legendre PS transcription techniques, are implemented to solve a carefully selected test set of nonlinear optimal control problems (NOCPs). The convergence property and prediction accuracy are compared to provide a useful guideline for selecting the best combination. The tested NOCPs consist of the minimum time, minimum energy, and problems with state and control constraints. Therefore, the results drawn from this comparative study apply to the solution of similar types of NOCPs and can mitigate much debate about the best combinations. Additionally, important findings from this study can be used to improve the numerical efficiency of the Legendre PS methods. Three PS applications to the aerospace engineering problems are demonstrated to prove this point.