• 한국정밀공학회지
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• 제15권6호
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• pp.97-106
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• 1998

In this Paper, a fuel minimizing closed loop explicit inertial guidance algorithm for orbit injection of a rocket is developed. In the formulation, the fuel burning rate and magnitude of thrust are assumed constant. The motion of rocket is assumed to be subject to the average inverse-square gravity, but negligible effects from atmosphere. The optimum thrust angle to obtain a given velocity vector in the shortest time with minimizing fuel consumption is first determined, and then the additive thrust angle for targeting the final position vector is determined by using Pontryagin's maximum principle. To establish real time processing, many algorithms of onboard guidance software are simplified. The explicit guidance algorithm is simulated on the 2nd-stage flight of the N-1 rocket developed in Japan. The results show that the explicit guidance algorithm works well in the presence of the maximum $\pm$10% initial velocity and altitude errors, and exhibits better performance than the open-loop program guidance. The effects of the guidance cycle time are also examined.

• 한국항공우주학회지
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• 제36권9호
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• pp.874-883
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• 2008

본 논문에서는 위성발사체의 폐루프 유도방식중 하나인 Powered Explicit Guidance에 대해서 연구하였다. 반복계산 과정이 없도록 변형시킨 알고리듬을 사용했으며, 추력변화가 큰 엔진 모델에 적용가능 하도록 단일 목표궤도에 대한 알고리듬에 대해서 기술하였다. 정상 및 비정상 비행조건에 대해서 6-자유도 컴퓨터 모의시험을 통해 얻어진 유도 알고리듬의 궤도 투입 정밀도 분석을 하였다.

• 제어로봇시스템학회논문지
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• 제7권2호
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• pp.173-182
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• 2001

Ascent trajectory optimization and optimal explicit guidance problems for a satellite launch vehicle in a 2-dimensional pitch plane are studied. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the pitch attitude control variable, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn are imposed. An optimal explicit guidance algorithm in the exoatmospheric phase is also presented, the guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. To verify the optimality and accuracy of the algorithm simulations are performed.

• 한국항공우주학회지
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• 제40권10호
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• pp.853-861
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• 2012

본 논문에서는 주어진 3단형 발사체의 상단부 폐루프 유도 방식 선정을 위해 널리 알려져 있는 Space Shuttle의 PEG 알고리듬보다 유도명령의 형태가 최적화 해에 가까운 Jaggers가 제안한 직접식 유도 방식에 대해서 다루었다. 이 알고리듬을 주어진 발사체의 상단부인 2단 및 3단 비행 구간에 적용할 경우에 대해서 유도 성능을 분석했다. 또한 보다 정밀한 유도를 위해 알고리듬 유도를 위해 사용된 근사식들을 가능한 사용하지 않도록 했으며 원래의 알고리듬에 비해 성능이 개선됨을 확인하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.419-424
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• 1991

In this paper, a fuel minimizing closed loop explicit inertial guidance algorithm for the orbit injection of a rocket is developed. In this formulation, the fuel burning rate and magnitude of thrust are assumed constant, and the motion of a rocket is assumed to be subject to the average inverse-square gravity, but with negligible atmospheric effects. The optimum thrust angle for obtaining the given velocity vector in the shortest time with minimizing fuel consumption is first determined, and then the additive thrust angle for targeting the final position vectors is determined by using Pontryagin's Maximum Principle. To establish the real time processing, many algorithms of the onboard guidance software are simplified. Simulations for the explicit guidance algorithm, for the 2nd-stage flight of the N-1 rocket, are carried out. The results show that the guidance algorithm works well in the presence of the maximum .+-.10 % initial velocity and altitude error. The effects of the guidance cycle time is also examined.

• Advances in aircraft and spacecraft science
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• 제9권5호
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• pp.433-447
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• 2022

This work deals with an explicit guidance and control architecture for autonomous lunar ascent and orbit injection, i.e., the locally-flat near-optimal guidance, accompanied by nonlinear reduced-attitude control. This is a new explicit guidance scheme, based on the local projection of the position and velocity variables, in conjunction with the real-time solution of the associated minimum-time problem. A recently-introduced quaternion-based reduced-attitude control algorithm, which enjoys quasi-global stability properties, is employed to drive the longitudinal axis of the ascent vehicle toward the desired direction. Actuation, based on thrust vectoring, is modeled as well. Extensive Monte Carlo simulations prove the effectiveness of the guidance, control, and actuation architecture proposed in this study for precise lunar orbit insertion, in the presence of nonnominal flight conditions.

• 제어로봇시스템학회논문지
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• 제8권7호
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• pp.613-623
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• 2002

Ascent trajectory optimization and explicit guidance problems for a satellite launch vehicle with yaw maneuver in a 3-dimension are considered. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the inertial pitch and yaw attitude control variables, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn and range safety conditions are imposed. An explicit inertial guidance algorithm in the exoatmospheric phase is also presented. The guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. The liquid propelled Delta 2910 launch vehicle is used as a numerical model.

• 항공우주기술
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• 제11권1호
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• pp.169-177
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• 2012

본 논문에서는 주어진 발사체의 상단부 유도 방식 선정을 위해서 외연적 유도 알고리듬에 대해서 다루었다. 지구를 평평하게 가정함으로써 얻어지는 매우 단순화된 형태의 알고리듬으로 온보드 응용에 있어서 유리한 유도 방식에 대해서 다루었다. 그러나 주어진 발사체에 적용한 결과 단순한 time-to-go 예측 방정식은 유도 성능을 저하시키는 특성을 보여, Saturn이나 H-II 발사체 사용되었던 정밀한 예측 방법을 도입하였다. 최종적으로 모의시험을 통해 단순한 형태의 유도 방식은 폭넓은 응용을 위해서는 time-to-go 예측 및 중력에 의한 속도 이득을 개선해야 함을 알 수 있었다.

• 항공우주기술
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• 제10권1호
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• pp.89-97
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• 2011

본 논문에서는 발사체 상단의 유도 방식 선정을 위해서 Saturn 발사체의 주차 궤도 및 달 전이 궤도 투입에 성공적으로 사용된 IGM을 개선한 외연적 유도 알고리듬에 대해서 다루었다. 이 알고리듬을 주어진 발사체의 상단부인 2단 및 3단 구간에 적용할 경우에 대해서 유도 성능을 분석하였다. 3-자유도 모의시험을 통해 궤도 투입시점에서의 위치 및 속도 정밀도를 계산했으며, 개략적으로 투입지점을 계산함으로 해서 생기는 유도 알고리듬의 성능 저하를 보완하기 위한 방법을 제안하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권3호
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• pp.327-364
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• 2015

In this paper, a generalized guidance law with an arbitrary pair of guidance coefficients for impact angle control is proposed. Under the assumptions of a stationary target and a lag-free missile with constant speed, necessary conditions for the guidance coefficients to satisfy the required terminal constraints are obtained by deriving an explicit closed-form solution. Moreover, optimality of the generalized impact-angle control guidance law is discussed. By solving an inverse optimal control problem for the guidance law, it is found that the generalized guidance law can minimize a certain quadratic performance index. Finally, analytic solutions of the generalized guidance law for a first-order lag system are investigated. By solving a third-order linear time-varying ordinary differential equation, the blowing-up phenomenon of the guidance loop as the missile approaches the target is mathematically proved. Moreover, it is found that terminal misses due to the system lag are expressed in terms of the guidance coefficients, homing geometry, and the ratio of time-to-go to system time constant.