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The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
The state-of-the-art in the field of alleviating rotary-wing aeroservoelastic problems (by using active controls that modify the pitch of a helicopter rotor blade so as to alleviate dynamic effects) is assessed, and the more promising developments are identified. Special attention is given to the active control of aeromechanical and aeroelastic problems, such as the active control of ground resonance, active control of air resonance, and active control of blade aeroelastic instabilities; individual blade control; active control of vibration reduction using a conventional swashplate; and coupled rotor/fuselage vibration reduction using open-loop active control. Some results are presented for each of these topics, illustrating the efficiency of the techniques which have been developed.
A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.
An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one- and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.
An analytical derivation of frozen orbit eccentricities and their location over the range of possible orbital inclinations in the J2 + J3 problem is presented. A gravitational field with only J2 and J3 terms is considered, because the equation defining frozen orbits in this field is an algebraic equation of the third order and an analytical formula for roots of this equation exists. An equation for the frozen orbit eccentricity is derived in a convenient form using only two independent parameters: the inclination and a parameter which is the product of the ratio of the radius of the central body to the orbital semimajor axis and the ratio of the J2 and J3 coefficients. The equation is solved, and, on the basis of its roots, frozen orbits in the J2 + J3 problem are classified.
Sufficient conditions for a weak relative minimum are derived for a form of the Bolza problem of variational calculus. The derivation ties together first-order and second-order conditions in a unified consistent manner, addresses controllability considerations in some detail, and clarifies some small inconsistencies in earlier work. The resulting second-order conditions of optimality involve the integration of fewer backward-sweep matrix elements than the standard conditions in the literature for problems with an unspecified final time. As a result, the backward-sweep matrices have the same general structure and dimensionality whether the final time is specified or free, with the terminal values of two of three sweep matrices being more complicated in the latter case.
In rule-based AI planning, expert, and learning systems, it is often the case that the left-hand-sides of the rules must be repeatedly compared to the contents of some 'working memory'. The traditional approach to solve such a 'match phase problem' for production systems is to use the Rete Match Algorithm. Here, a new technique using a multilayer perceptron, a particular artificial neural network model, is presented to solve the match phase problem for rule-based AI systems. A syntax for premise formulas (i.e., the left-hand-sides of the rules) is defined, and working memory is specified. From this, it is shown how to construct a multilayer perceptron that finds all of the rules which can be executed for the current situation in working memory. The complexity of the constructed multilayer perceptron is derived in terms of the maximum number of nodes and the required number of layers. A method for reducing the number of layers to at most three is also presented.
The minimum-time attitude maneuvers of a rigid spacecraft are considered. Generally, the associated nonsingular, nonlinear two-point boundary-value problem, derived by using Pontryagin's Maximum Principle, can be solved through shooting methods to find the switching times for the bang-bang control. However, a good initial guess for the missing initial costates is important because the convergence range of the initial costates is very narrow, especially when a multi-bang-bang control strategy is needed. This paper proposes a numerical approach to generate the initial costates so that they are very close to the converged values. The initial costates are first generated by using a recently developed quasi-linearization technique for the near-minimum-time problem and then reduced in magnitude, through some properly designed scales, before the shooting method is used. Numerical examples indicate the closeness of the results from these two techniques (quasi-linearization and shooting).
The authors analyzed the problems associated with the detection of boundary-layer transition to turbulence by using the IR imaging techique in cryogenic wind-tunnel testing. It is shown that testing at low temperatures forces this implementation to run against the physical laws of diminishing returns. The most difficult obstacle resulted from the considerable decrease in the overall level of IR radiation and the parallel shift of the bulk of the radiated energy to longer wavelengths, beyond 30 microns at 100 K. Some measures to alleviate the problem are described. The thermal signature of transition can be enhanced by allowing the flow in the wind tunnel to heat incrementally, thus inducing a transient heat transfer to the model. As a result, the model area under the turbulent regime is revealed by its higher heating rate compared to the laminar regime.
A formulation of the longitudinal glideslope tracking of a transport-class aircraft in severe wind shear and turbulence for application to robust control system design is presented. Mathematical wind shear models are incorporated into the vehicle mathematical model, and wind turbulence is modeled as an input disturbance signal. For this problem formulation, the horizontal and vertical wind shear gradients are treated as real uncertain parameters that vary over an entire wind shear profile. The primary objective is to examine the formulation of this problem into an appropriate design format for use in m-synthesis control system design.
In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.
Network transmission errors such as collisions, CRC errors, misalignment, etc. are statistical in nature. Although errors can vary randomly, a high level of errors does indicate specific network problems, e.g. equipment failure. In this project, we have studied the random nature of collisions theoretically as well as by gathering statistics, and established a numerical threshold above which a network problem is indicated with high probability.
The U.S. military uses a large number of simulators to train and sustain the flying skills of helicopter pilots. Despite the enormous resources required to purchase, maintain, and use those simulators, little effort has been expended in assessing their training effectiveness. One reason for this is the lack of an evaluation methodology that yields comprehensive and valid data at a practical cost. Some of these methodological problems and issues that arise in assessing simulator training effectiveness, as well as problems with the classical transfer-of-learning paradigm were discussed.
The objectives are to introduce basic problem-solving techniques for product safety including problem identification, definition, solution criteria, test process and design, and data analysis. The students are given a recycled milk jug made of high density polyethylene (HDPE) by blow molding. The objectives are to design and perform proper material test(s) so they can evaluate the product safety if the milk jug is used in a certain way which is specified in the description of the procedure for this investigation.
The wall and centerline vapor temperatures and heat output are determined experimentally for a low-temperature copper-water heat pipe under uniform circumferential heating and block heating. The time required to reach a vapor temperature of 60 C from an initial ambient temperature of 21 C is determined for both modes of heating. The experimental capillary limit of the heat pipe is compared to the generalized capillary limits for block-heated pipes over a range of vapor temperatures. A three-dimensional numerical model is then developed for determining the temperature, pressure, and velocity distributions in the entire domain of a circumferentially heated and a block-heated pipe. The problem is formulated as a conjugate problem, without the assumption of a uniform vapor temperature. The predictions of the model are found to be in good agreement with the experimental data.
A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.
The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.
A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.