The Control of Nonlinear Stochastic Control Systems Under Discounted Performance Criteria
Finite Markov chain control and numerical algorithm for optimal control
Harris, C. A.↗
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Application of parameter optimization techniques to space shuttle thermal protection design
Space shuttle thermal protection system optimal weight by numerical parameterization, discussing temperature constraints and material rearrangement effects
Curry, D. M.↗
Optimal analytic rendezvous using Clohessy-Wiltshire equations
The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
Stability analysis for laminar flow control, part 2
Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.
Orszag, S. A.↗
An analytic approach to optimal rendezvous using Clohessy-Wiltshire equations
An analytic approach is used to obtain the optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous for the Clohessy-Wiltshire equations. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
Computation of the modes and polar moment of inertial of the blades of an HAWT
The coupled differential equations of motion of the blades of a horizontal axis wind turbine are solved numerically, permitting the optimization of the design at relatively low cost. The equation of motion is transformed into a set of first order equations and solved with fourth order Runge-Kutta integrators. This technique is applied to a twisted, tapered blade of variable cross section and stiffness including discontinuities. The first six natural frequencies and mode shapes are obtained. The polar moment of inertia of the blades is obtained as a function of frequency and rotational speed.
Beaulieu, G.↗
Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer
The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.
Miele, A.↗
Optimal impulsive manoeuvres and aerodynamic braking
A method developed for obtaining solutions to the aerodynamic braking problem, using impulses in the exoatmospheric phases is discussed. The solution combines primer vector theory and the results of a suboptimal atmospheric guidance program. For a specified initial and final orbit, the solution determines: (1) the minimum impulsive cost using a maximum of four impulses, (2) the optimal atmospheric entry and exit-state vectors subject to equality and inequality constraints, and (3) the optimal coast times. Numerical solutions which illustrate the characteristics of the solution are presented.
Jezewski, D. J.↗
Guidance and control strategies for aerospace vehicles
A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed.
Hibey, Joseph L.↗
Physical insight into the simultaneous optimization of structure and control
Recent trends in spacecraft design which yield larger structures with more stringent performance requirements place many flexible modes of the structure within the bandwidth of active controllers. The resulting complications to the spacecraft design make it highly desirable to understand the impact of structural changes on an optimally controlled structure. This work uses low structural models with optimal H(sub 2) and H(sub infinity) controllers to develop some basic insight into this problem. This insight concentrates on several basic approaches to improving controlled performance and how these approaches interact in determining the optimal designs. A numerical example is presented to demonstrate how this insight can be generalized to more complex problems.
Jacques, Robert N.↗
Weight minimization of a support structure
This paper addresses the weight minimization of a circular plate-like structure which resulted in a 26 percent weight reduction. The optimization was performed numerically with the COPES/ADS program using the modified method of feasible directions. Design parameters were the inner thickness and outer thickness of the plate with constraints on maximum yield stress and maximum transverse displacement. Also, constraints were specified for the upper and lower bounds of the fundamental frequency and plate thicknesses. The MSC/NASTRAN finite element program was used for the evaluation of response variables. Original and final designs of the plate were tested using an Instron tension-compression machine to compare finite element results to measured strain data. The difference between finite element strain components and measured strain data was within engineering accuracy.
Kluberdanz, Donald J.↗
Gain weighted eigenspace assignment
This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.
Davidson, John B.↗
Enhancement of thickness uniformity of thin films grown by pulsed laser deposition
A peculiarity of the pulsed laser deposition technique of thin-film growth which limits its applicability is the very rapid drop of resulting film thickness as a function of distance from the deposition axis. This is due to the narrow forward peaking of the emission plume characteristic of the laser ablation process. The plume is usually modeled by a cos(sup n) theta function with n greater, and in some cases, much higher, than 1. Based on this behavior, a method is presented to substantially enhance coverage uniformity in substrate zones of the order of the target-substrate distance h, and to within a specified thickness tolerance. Essentially, target irradiation is caused to form an annular emission source instead of the usual spot. By calculating the resulting thickness profiles, an optimum radius s is found for the annular source, corresponding to a given power in the emission characteristic and a given value of h. The radius of this annulus scales with h. Calculated numerical results for optimal s/h ratios corresponding to a wide range of values for n are provided for the case of +/- 1% tolerance in deviation from the thickness at deposition axis. Manners of producing annular illumination of the target by means of conic optics are presented for the case of a laser beam with radially symmetric profile. The region of uniform coverage at the substrate can be further augmented by extension of the method to multiple concentric annular sources. By using a conic optic of novel design, it is shown also how a single-laser beam can be focused onto a target in the required manner. Applicability of the method would be limited in practice by the available laser power. On the other hand, the effective emitting area can be large, which favors extremely high growth rates, and since growth can occur uniformly over the whole substrate for each laser pulse, single-shot depositions with substantial thicknesses are possible. In addition, the simultaneity of growth over the complete substrate is desirable when monitoring the growth in situ.
Fernandez, Felix E.↗
An Initial Multi-Domain Modeling of an Actively Cooled Structure
A methodology for the simulation of turbine cooling flows is being developed. The methodology seeks to combine numerical techniques that optimize both accuracy and computational efficiency. Key components of the methodology include the use of multiblock grid systems for modeling complex geometries, and multigrid convergence acceleration for enhancing computational efficiency in highly resolved fluid flow simulations. The use of the methodology has been demonstrated in several turbo machinery flow and heat transfer studies. Ongoing and future work involves implementing additional turbulence models, improving computational efficiency, adding AMR.
Steinthorsson, Erlendur↗
Conversion from Engineering Units to Telemetry Counts on Dryden Flight Simulators
Dryden real-time flight simulators encompass the simulation of pulse code modulation (PCM) telemetry signals. This paper presents a new method whereby the calibration polynomial (from first to sixth order), representing the conversion from counts to engineering units (EU), is numerically inverted in real time. The result is less than one-count error for valid EU inputs. The Newton-Raphson method is used to numerically invert the polynomial. A reverse linear interpolation between the EU limits is used to obtain an initial value for the desired telemetry count. The method presented here is not new. What is new is how classical numerical techniques are optimized to take advantage of modem computer power to perform the desired calculations in real time. This technique makes the method simple to understand and implement. There are no interpolation tables to store in memory as in traditional methods. The NASA F-15 simulation converts and transmits over 1000 parameters at 80 times/sec. This paper presents algorithm development, FORTRAN code, and performance results.
Fantini, Jay A.↗
Current Grid Generation Strategies and Future Requirements in Hypersonic Vehicle Design, Analysis and Testing
Recent advances in computational power enable computational fluid dynamic modeling of increasingly complex configurations. A review of grid generation methodologies implemented in support of the computational work performed for the X-38 and X-33 are presented. In strategizing topological constructs and blocking structures factors considered are the geometric configuration, optimal grid size, numerical algorithms, accuracy requirements, physics of the problem at hand, computational expense, and the available computer hardware. Also addressed are grid refinement strategies, the effects of wall spacing, and convergence. The significance of grid is demonstrated through a comparison of computational and experimental results of the aeroheating environment experienced by the X-38 vehicle. Special topics on grid generation strategies are also addressed to model control surface deflections, and material mapping.
Papadopoulos, Periklis↗
Bi-Level Integrated System Synthesis (BLISS)
BLISS is a method for optimization of engineering systems by decomposition. It separates the system level optimization, having a relatively small number of design variables, from the potentially numerous sub-system optimizations that may each have a large number of local design variables. The subsystem optimizations are autonomous and may be conducted concurrently. Subsystem and system optimizations alternate, linked by sensitivity data, producing a design improvement in each iteration. Starting from a best guess initial design, the method improves that design in iterative cycles, each cycle comprised of two steps. In step one, the system level variables are frozen and the improvement is achieved by separate, concurrent, and autonomous optimizations in the local variable subdomains. In step two, further improvement is sought in the space of the system level variables. Optimum sensitivity data link the second step to the first. The method prototype was implemented using MATLAB and iSIGHT programming software and tested on a simplified, conceptual level supersonic business jet design, and a detailed design of an electronic device.
Sobieszczanski-Sobieski, Jaroslaw↗
Mechanics of Re-Torquing in Bolted Flange Connections
It has been widely accepted that the phenomenon of time-dependent loosening of flange connections is a strong consequence of the viscous nature of the compression seal material. Characterizing the coupled interaction between gasket creep and elastic bolt stiffness has been useful in predicting conditions that facilitate leakage. Prior advances on this sub-class of bolted joints has lead to the development of (1) constitutive models for elastomerics, (2) initial tightening strategies, (3) etc. The effect of re-torque, which is a major consideration for typical bolted flange seals used on the Space Shuttle fleet, has not been fully characterized, however. The current study presents a systematic approach to characterizing bolted joint behavior as the consequence of sequentially applied torques. Based on exprimenta1 and numerical results, the optimal re-torquing parameters have been identified that allow for the negligible load loss after pre-load application
Gordon, Ali P.↗