Aerospace Science and Technology
Morteza Sharafi; Mahdi Jafari; mojtaba alavipour
Abstract
In this paper, optimal guidance law design considering fixed final state and time for the final phase a spacecraft or launch vehicle is investigated and studied. This guidance law, not only satisfied a specific optimality criterion, but it also has the least sensitivity to the initial state’s deviations; ...
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In this paper, optimal guidance law design considering fixed final state and time for the final phase a spacecraft or launch vehicle is investigated and studied. This guidance law, not only satisfied a specific optimality criterion, but it also has the least sensitivity to the initial state’s deviations; which is due to the inclusion of the nonlinear terms in the mathematical modeling using the high order expansions method. The main goal of this research, is to investigate the development and to augment the capability of the high order expansions method for guidance law design. Different implementations of this approach including the differential algebra high order, the generating function based high order and vectorized high order expansions methods have been investigated. After reviewing the implementation concepts of the high order expansions method, the effectiveness of this method has been studied. Then a 3-dimensional injection of a satellite problem has been chosen as the case study and after extracting the mathematical model and nominal optimal solution, the sensitivity variables have been extracted up to the 3rd order. Afterwards, to investigate the performance of the designed guidance law, the Monte Carlo simulations have been performed and it has been shown that the designed guidance law on the basis of the Taylor series and high order expansions method has a good accuracy and is a valuable alterative to the nominal trajectory tracking guidance approach.
Aerospace Science and Technology
Morteza Sharafi; Nasser Rahbar; Ali Moharrampour; Abdorreza Kashaninia
Abstract
This study proposes a new non-linear guidance law for a Falcon 9 missile booster landing's terminal phase using a non-linear vectorized high expansion method. For this purpose, At first, the dynamic modeling of the landing problem is presented, assuming mass, gravity, and density are variables. Then, ...
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This study proposes a new non-linear guidance law for a Falcon 9 missile booster landing's terminal phase using a non-linear vectorized high expansion method. For this purpose, At first, the dynamic modeling of the landing problem is presented, assuming mass, gravity, and density are variables. Then, sensitivity variables are extracted using the vectorized high order expansion method and assuming the parameters constant. Then, the guidance law is extracted to update the path and optimal commands using sensitivity variables. The path and commands of the near-optimal guidance are extracted online using the proposed guidance law. Considering initial deviations, the guidance law performance in simulations are studied using a combination of various initial deviations. The results shown as charts and numerical values of errors indicate that the landing point errors are insignificant, and the vectorized high order expansion method has a desirable performance for the reusable booster's vertical landing.
Aerospace Science and Technology
Ali Arabian Arani; S.H. Jalali Naini; Mohammad Hossein Hamidi Nejad
Abstract
This study presents the miss distance analysis of the first-order explicit guidance law due to seeker noise using the adjoint method. For this purpose, linearized equations are utillized and the adjoint model is developed. Then the first-order equations are obtained and converted into nondimensional ...
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This study presents the miss distance analysis of the first-order explicit guidance law due to seeker noise using the adjoint method. For this purpose, linearized equations are utillized and the adjoint model is developed. Then the first-order equations are obtained and converted into nondimensional ones. The analysis is carried out for different values of the power of the alpha function, defined as the time decrease rate of the zero-effort miss distance to unit control input. The unity power gives the first-order optimal guidance strategy, minimizing the integral of the square of the commanded acceleration during the total flight time.The seeker and control system is assumed as a fifth-order binomial transfer function. Due to computational error and stability consideration, the effective navigation ratio is kept constant for very small time-to-go until intercept, which its effect on the miss distance is also investigated. Finally, approximate formulas are obtained using curve fitting method for rms miss distance due to seeker noise.