Aerospace Engineering

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Optimal turning maneuvers for six-degree-of-freedom high angle-of-attack aircraft models

1995 , Chou, Jen-nai , Bion L. Pierson , Aerospace Engineering

Various Minimum-Time Turning Maneuvers for two high angle-of-attack, six-degree-of-freedom, aircraft models have been investigated. The primary aircraft model is for a nonlinear 6-DOF F-16 fighter aircraft with high angle-of-attack maneuverability. The other model is for a linearized 6-DOF F-18 fighter which also can be flown in the high angle-of-attack range. Standard 6-DOF equations are employed except that the Quaternion attitude representation system is used instead of Euler Angles to avoid the pitch angle singularity of Euler Angles;These Optimal Control problems have been transformed into Nonlinear Programming problems via Parameter Optimization techniques. Different parameterization techniques were tested on the Van der Pol Problem and Soliman's Problem and their variations before applying them on the main turning problems. These techniques include Control Parameterization and State Parameterization (Inverse Dynamics Approach). Also, a novel Control-Integration Method is proposed to find the discontinuous control history of the possible Singular Arc Problems. Different ways to deal with various types of constraints are also discussed. In particular, when dealing with path constraints of the original optimal control problems, an Extreme-Bounds-on-Intervals method was created. However, it has not been actually developed and tested. The resulting sparse Hessian matrix from this method can speed up the calculations if a specially arranged NLP code is used;The Sequential Quadratic Programming method is primarily relied on to search for the optimum. Several different performance indices are utilized, including 3-D minimum-time-to-turn and 3-D minimum-time-to-half-loop. Several new solutions for these maneuvers are obtained. Moreover, since multiple local minima are present, several global optimization schemes have been studied. A Genetic Algorithm, Adaptive Simulated Annealing, and a Hybrid method which combines the merits of both genetic algorithms and sequential quadratic programming have been used to find the global optimum.

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Minimum-fuel lunar transfers with engine switching and transients

1996 , Rivas, Matthew , Bion L. Pierson , Aerospace Engineering

The investigation of minimum-fuel planar Lunar transfers are investigated for a variety of mission profiles. The problem is set within the context of the classic restricted three-body problem. Two different types of propulsive systems are studied including electric propulsion and nuclear thermal rockets (NTR) providing a range of initial thrust-to-weight ratios. The solution of the transfers is achieved by solving a series of simpler subproblems to obtain an estimate of the fully optimal trajectory. The series of subproblems is solved by a new dynamic boundary evaluation method. The full solution is then found using this estimate and a hybrid "direct/indirect" method. This solution determines the total time-of-flight based on a fixed thrust-coast-thrust engine firing sequence. The optimal transfers for a range of initial thrust-to-weight ratios are found and presented. The true optimal solution for a power limited spacecraft for a fixed time-of-flight depends on the engine firing switching function. The solution of the switching problem is extremely difficult and a three-stage methodology is developed. The first stage uses mixed-integer nonlinear programming (MINLP) to approximate the switching function's discrete characteristics. The second stage uses the MINLP solution and problem characteristics to solve a relaxation of the full switching problem and the final stage solves the full two-point boundary value problem from the estimates of the preceding stages. The switching solutions for a range of flight times are presented. The use of NTR propulsion introduces thrust transients which are modeled using the point mass mono-energetic nuclear equations and the rocket itself is modeled by a lumped heat-exchange system. The effects on an optimal transfer of the transients is found and presented.

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Optimal low-thrust, Earth-Moon trajectories

1993 , Kluever, Craig , Bion L. Pierson , Aerospace Engineering

A variety of optimal trajectories from a circular low-Earth parking orbit to a circular low-lunar parking orbit are computed for a range of low-thrust spacecraft. The problem is studied in the context of the classical restricted three-body problem. Minimum-fuel, planar trajectories with a fixed thrust-coast-thrust engine sequence are computed for both a "high-end" low-thrust spacecraft and "moderate" low-thrust nuclear electric propulsion (NEP) spacecraft. Since a low-thrust trajectory is a long duration transfer with slowly developing spirals about the Earth and Moon, the minimum-fuel Earth-Moon trajectory is obtained by formulating and successively solving a hierarchy of sub-problems. The subproblems include optimal Earth-escape and Moon-capture trajectories and sub-optimal translunar trajectories. The complete minimum-fuel trajectory problem is eventually solved using a "hybrid" direct/indirect method which utilizes the benefits of a direct optimization method and an indirect method from optimal control theory. Minimum-fuel transfers are also computed using a switching function structure which results in multiple thrust and coast arcs. In addition, a new combined vehicle and trajectory optimization problem of maximum payload fraction is formulated and solved. Finally, three-dimensional minimum-fuel trajectories are obtained for both the "high-end" and "moderate" low-thrust spacecraft. Numerical results are presented for various optimal Earth-Moon trajectories.

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Development of a finite-difference neighboring optimal control law and application to the optimal landing of a reusable launch vehicle

1996 , Wetzel, Todd , Bion L. Pierson , Aerospace Engineering

A new neighboring optimal control methodology is developed and applied to the fuel-optimal landing of a reusable launch vehicle. Two new methods, both based on perturbation analysis, are explored. A fast open-loop optimal trajectory solver is developed to handle the numerically intensive perturbation analysis phase of control law synthesis. High accuracy closed-loop simulation of both the optimal control law and plant model shows that the optimal control law is robust for a number of different off-nominal conditions.

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Sequential quadratic programming solutions to related aircraft trajectory optimization problems

1992 , Ong, Shaw , Bion L. Pierson , Aerospace Engineering

Aircraft performance optimization continues to play an important role in the aerospace sciences. The studies undertaken in this dissertation explore the performance of high-speed aircraft with regard to missile evasion, minimum-time-to-climb, minimum-time-to-turn, and the unorthodox approach of obtaining a robust optimality-based control law for real-time aircraft control. The dissertation includes four papers presented or accepted for presentation at major conferences and presently in various stages of review for publication in scholarly journals;The similarity in each paper, in addition to the focus on optimal aircraft trajectories, is that an existing nonlinear programming method, sequential quadratic programming (SQP), is used to treat each trajectory optimization problem. This approach is suitable since the emphasis is on applications and problem solving, and the method is accurate and computationally inexpensive. Also, the flexibility of SQP allows for performance index, mathematical model, and constraint changes with relatively little reprogramming. This enables a wide range of trajectory optimization problems to be formulated and studied;In the study of the aircraft missile-evasion problem in horizontal planar flight, unlike earlier investigations, the full original equations of motion are used. Also, no linearization about a nominal pursuit triangle is done. The velocity ratio, that is, the velocity of the aircraft to the velocity of the missile for the duration of the confrontation, becomes a major factor in deciding optimal evasive strategies. Evasion against a surface-to-air missile involves a large nonlinear optimal control problem of dynamic order of at least thirteen. "Inward", "outward", pull-up, dive, and inverted pull-down evasive maneuvers are investigated. The results show that the missile enters the "hit region" of the aircraft for constrained vertical plane flight, but not for constrained horizontal flight. The optimal throttle setting for constrained horizontal plane flight is of "bang-bang" type;For the minimum-time turn problems, having free final velocity provides the biggest impact on turn times, which can be reduced by as much as fifty percent. For a wide range of final energies studied in the three-dimensional turns, it was found that the aircraft tends to initially lose altitude in the optimal turn even though the nominal control from which the optimization process started corresponds to an initial climbing turn. This tendency of favoring kinetic energy over potential energy had not been featured in earlier papers;Finally, the investigation of optimality-based control laws for real-time aircraft control is a significant departure from the usual open-loop solutions to trajectory optimization problems. It was found that the robustness of the optimal control obtained from the "optimality-condition" is not guaranteed, but by introducing a certain "correction" term, it can be enhanced significantly. It appears that this technique of enhancing robustness has not been used until now.