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Application of dynamic programming to optimizing the orbital control process of a 24-hour communications satellite
Application of dynamic programming to optimizing the orbital control process of a 24-hour communications satellite
Information pertinent to users of the program to optimize simulated trajectories (POST) is presented. The input required and output available is described for each of the trajectory and targeting/optimization options. A sample input listing and resulting output are given.
A general purpose FORTRAN program for simulating and optimizing point mass trajectories (POST) of aerospace vehicles is described. The equations and the numerical techniques used in the program are documented. Topics discussed include: coordinate systems, planet model, trajectory simulation, auxiliary calculations, and targeting and optimization.
Computer program for launch vehicle trajectory optimization
Program aids research in analysis and optimization. Programing Structural Synthesis System (PROSSS2) developed to provide structural-synthesis capability by combining access to SPAR with CONMIN program and set of interface procedures. SPAR is large general-purpose finite-element structural-analysis program, and CONMIN is large general-purpose optimization program. PROSSS2 written in FORTRAN IV for batch execution.
A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.
A capability to simulate trajectories Of Multiple interacting rigid bodies has been developed. This capability uses the Program to Optimize Simulated Trajectories II (POST II). Previously, POST II had the ability to simulate multiple bodies without interacting forces. The current implementation is used for the Simulation of parachute trajectories, in which the parachute and suspended bodies can be treated as rigid bodies. An arbitrary set of connecting lines can be included in the model and are treated as massless spring-dampers. This paper discusses details of the connection line modeling and results of several test cases used to validate the capability.
A capability to simulate trajectories of multiple interacting rigid bodies has been developed, tested and validated. This capability uses the Program to Optimize Simulated Trajectories II (POST 2). The standard version of POST 2 allows trajectory simulation of multiple bodies without force interaction. In the current implementation, the force interaction between the parachute and the suspended bodies has been modeled using flexible lines, allowing accurate trajectory simulation of the individual bodies in flight. The POST 2 multibody capability is intended to be general purpose and applicable to any parachute entry trajectory simulation. This research paper explains the motivation for multibody parachute simulation, discusses implementation methods, and presents validation of this capability.
The basic equations and models used in a computer program (6D POST) to optimize simulated trajectories with six degrees of freedom were documented. The 6D POST program was conceived as a direct extension of the program POST, which dealt with point masses, and considers the general motion of a rigid body with six degrees of freedom. It may be used to solve a wide variety of atmospheric flight mechanics and orbital transfer problems for powered or unpowered vehicles operating near a rotating oblate planet. Its principal features are: an easy to use NAMELIST type input procedure, an integrated set of Flight Control System (FCS) modules, and a general-purpose discrete parameter targeting and optimization capability. It was written in FORTRAN 4 for the CDC 6000 series computers.
POST/6D POST is set of two computer programs providing ability to target and optimize trajectories of powered or unpowered spacecraft or aircraft operating at or near rotating planet. POST treats point-mass, three-degree-of-freedom case. 6D POST treats more-general rigid-body, six-degree-of-freedom (with point masses) case. Used to solve variety of performance, guidance, and flight-control problems for atmospheric and orbital vehicles. Applications include computation of performance or capability of vehicle in ascent, or orbit, and during entry into atmosphere, simulation and analysis of guidance and flight-control systems, dispersion-type analyses and analyses of loads, general-purpose six-degree-of-freedom simulation of controlled and uncontrolled vehicles, and validation of performance in six degrees of freedom. Written in FORTRAN 77 and C language. Two machine versions available: one for SUN-series computers running SunOS(TM) (LAR-14871) and one for Silicon Graphics IRIS computers running IRIX(TM) operating system (LAR-14869).
NOP is versatile digital-computer program devoloped for parametric analysis of beryllium-reflected, graphite-moderated nuclear rocket engines. Facilitates analysis of performance of engine with respect to such considerations as specific impulse, engine power, type of engine cycle, and engine-design constraints arising from complications of fuel loading and internal gradients of temperature. Predicts minimum weight for specified performance.
A description and applications of a computer capability for determining the ultimate optimal behavior of a dynamically loaded structural-mechanical system are presented. This capability provides characteristics of the theoretically best, or limiting, design concept according to response criteria dictated by design requirements. Equations of motion of the system in first or second order form include incompletely specified elements whose characteristics are determined in the optimization of one or more performance indices subject to the response criteria in the form of constraints. The system is subject to deterministic transient inputs, and the computer capability is designed to operate with a large linear programming on-the-shelf software package which performs the desired optimization. The report contains user-oriented program documentation in engineering, problem-oriented form. Applications cover a wide variety of dynamics problems including those associated with such diverse configurations as a missile-silo system, impacting freight cars, and an aircraft ride control system.
An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.
The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.
Astronauts experience disturbances in functional mobility following their return to Earth due to adaptive responses that occur during exposure to the microgravity conditions of space flight. Despite significant time spent performing in-flight exercise routines, these training programs have not been able to mitigate postflight alterations in postural and locomotor function. Therefore, the goal of our two inter-related projects (NSBRI-ground based and ISS flight study, "Mobility") is to develop and test gait training programs that will serve to optimize functional mobility during the adaptation period immediately following space flight, thereby improving the safety and efficiency of planetary ambulation. The gait training program entails manipulating the sensory conditions of treadmill exercise to systematically challenge the balance and gait control system. This enhances the overall adaptability of locomotor function enabling rapid reorganization of gait control to respond to ambulation in different gravitational environments. To develop the training program, we are conducting a series of ground-based studies evaluating the training efficacy associated with variation in visual flow, body loading, and support surface stability during treadmill walking. We will also determine the optimal method to present training stimuli within and across training sessions to maximize both the efficacy and efficiency of the training procedure. Results indicate that variations in both visual flow and body unloading during treadmill walking leads to modification in locomotor control and can be used as effective training modalities. Additionally, the composition and timing of sensory challenges experienced during each training session has significant impact on the ability to rapidly reorganize locomotor function when exposed to a novel sensory environment. We have developed the capability of producing support surface variation during gait training by mounting a treadmill on a six-degree-of-freedom motion device. This hardware development will allow us to evaluate the efficacy of this type of training in conjunction with variation in visual flow and body unloading.
The flexibility necessary for such diverse utilizations is achieved by combining, in a modular manner, a state-of-the-art optimization program, a production level structural analysis program, and user supplied and problem dependent interface programs. Standard utility capabilities in modern computer operating systems are used to integrate these programs. This approach results in flexibility of the optimization procedure organization and versatility in the formulation of constraints and design variables. Features shown in numerical examples include: variability of structural layout and overall shape geometry, static strength and stiffness constraints, local buckling failure, and vibration constraints.
The results of a study are presented in which a computerized optimal control techique was applied to the synthesis of a load relief control system for an advanced Saturn 5 derivative launch vehicle. This technique included selection of a load relief control law and computerized optimization of the controller gain schedules for a set of preselected adverse synthetic wind speed profiles. The gain optimization was effected using a hybrid optimizer program to minimize (optimize) a direct performance functional which specified the design goal (load relief) in engineering terms (explicit representation of maximum bending moments).