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At least 253 records · Page 14

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NASA NTRS1972

The optimal control of merging aircraft - Implementation of the hybrid air traffic controller.

The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.

Schatz, J. G.↗

NASA NTRS1973

Application of modern control theory to the design of optimum aircraft controllers

The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.

Power, L. J.↗

NASA NTRS1973

Evaluation of glide paths for landing a VTOL airplane using linear regulator theory.

A method of evaluating certain characteristics of approach paths for VTOL airplanes is presented which is based on the solution of the matrix Riccati equation to obtain an optimal state variable feedback controller. The longitudinal equations of motion of the airplane are linearized about a preselected path and the resulting system of equations is treated as a linear, time-varying regulator. The controller which minimizes a quadratic cost function is applied to the linearized system to determine the airplane's ability to return to the prescribed path given a specified initial error in altitude. The procedure is applied to the XC-142A, tilt-wing, V/STOL airplane, under decelerating approach conditions with a glide path consisting of two segments, the first having a smaller angle of descent than the second.

Reid, G. F.↗

NASA NTRS1974

Propagation of plane waves in a variable area duct carrying a compressible subsonic flow

A complete numerical solution is obtained for plane wave propagation in a variable-area duct which carries a mean compressible flow. The equation solved is a matrix formulation of the equations first derived by Tsien in 1952. Sample calculations are presented for four particular flow configurations: (1) a duct-nozzle-duct combination with the acoustic wave traveling with the flow, (2) a duct-nozzle-duct combination with the acoustic wave traveling against the flow, (3) an inlet-nozzle-duct configuration with the acoustic wave traveling against the flow, and (4) a duct-nozzle-exit configuration with the acoustic wave traveling with the flow. For each of these cases, the variation of energy flux with frequency is shown for particular geometry and flow condition.

Davis, S. S.↗

NASA NTRS1976

Ocean color spectra measured off the Oregon coast - Characteristic vectors

The ocean color spectrum is defined as the ratio of the spectrum of light upwelled from the sea to the spectrum of light incident on the sea surface. Ocean color spectra, observed from an airplane flown over waters off Oregon, are analyzed. The original spectra are resolved into fifty-five wavelength bands, each 5 nm wide. The shapes of these spectra are parameterized by, and shown to be accurately recoverable from, their first four principal components. These components are the scalar projections of each spectrum on the first four characteristic vectors of the sample covariance matrix. Regression equations are found with which phytoplankton pigment concentration and water transparency may be estimated as linear functions of the principal components. Pigment concentration estimates thus obtained are imprecise. The poor fit is at least partly due to the inappropriateness of the linear regression model and the neglect of other optically important substances typically present in sea water.

Mueller, J. L.↗

NASA NTRS1978

On reliable control system designs

A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

Birdwell, J. D.↗

NASA NTRS1980

Reduced-order Kalman filtering with incomplete observability

Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.

Yonezawa, K.↗

NASA NTRS1981

Some experiments on explicit boundary algorithms

Experiments done with the aim of improving the accuracy and efficiency of explicit boundary algorithms for quasilinear hyperbolic systems of partial differential equations in matrix form are described. Existing methods are criticized and a new approach to the problem is presented.

Forester, K.↗

NASA NTRS1981

Effects of displacement and rate saturation on the control of statically unstable aircraft

Methodologies are presented for the analysis and design of stability augmentation control laws for aircraft in which 'hard' displacement and rate limiting are significant. Candidate control laws are derived using the linear-quadratic (LQ) regulator. Analytical and computational estimates of the stability limits imposed by control saturation are presented using state trajectories with control limiting, as well as describing functions and eigenvalue computation. Analysis also includes an investigation of the interaction of the state-space saturation and stability boundaries for various choices of LQ weighting matrices. For minimum-energy control, the saturation and stability boundaries are shown to be parallel. In this case, there is a direct relation between the solution to the matrix Riccati equation and the aircraft's open-loop dynamics.

Hanson, G. D.↗

NASA NTRS1982

Development, implementation, and test results on integrated optics switching matrix

A small integrated optics switching matrix, which was developed, implemented, and tested, indicates high performance. The matrix serves as a model for the design of larger switching matrices. The larger integrated optics switching matrix should form the integral part of a switching center with high data rate throughput of up to 300 megabits per second. The switching matrix technique can accomplish the design goals of low crosstalk and low distortion. About 50 illustrations help explain and depict the many phases of the integrated optics switching matrix. Many equations used to explain and calculate the experimental data are also included.

Rutz, E.↗

NASA NTRS1982

Mechanics aspects of NDE by sound and ultrasound

Nondestructive evaluation (NDE) is considered as a means to detect the energy release mechanism of defects and the interaction of microstructures within materials with sound waves and/or ultrasonic waves. Ultrasonic inspection involves the frequency range 20 kHz-1 GHz with amplitudes depending on the sensitivity of the test instrumentation. Pulse echo systems are most frequently used in NDE. Information is extracted from the signals through measurements of the signal velocity, attenuation, the acoustic emission when stress is applied, and calculation of the acoustoelastic coefficients. Fracture properties, tensile and shear strengths, the interlaminar shear strength, the cohesive strength, yield and impact strengths, the hardness, and the residual stress can be assayed by ultrasonic methods. Finally, attention is given to analytical treatment of the derived data, with mention given to transition matrix, integral equation, and eigenstrain approaches.

Fu, L. S.↗

NASA NTRS1984

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Juang, J.-N.↗

NASA NTRS1986

Discrete-time Markovian-jump linear quadratic optimal control

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.↗

NASA NTRS1986

Orbital maneuvering vehicle thermal design and analysis techniques

This paper describes the OMV thermal design that is required to maintain components within temperature limits for all mission phases. A key element in the OMV thermal design is the application of a motorized thermal shade assembly that is a replacement for the more conventional variable conductance heat pipes or louvers. The thermal shade assembly covers equipment module radiator areas, and based upon the radiator temperature input to onboard computer, opens and closes the shade, varying the effective radiator area. Thermal design verification thermal analyses results are presented. Selected thermal analyses methods, including several unique subroutines, are discussed. A representation of enclosure Script F equations, in matrix form, is also included. Personal computer application to the development of the OMV thermal design is summarized.

Chapter, J.↗

NASA NTRS1987

Methods for design and evaluation of integrated hardware/software systems for concurrent computation

Two testbed programming environments to support the evaluation of a large range of parallel architectures have been implemented under the program Parallel Implementation of Scientific Computing Environments (PISCES). The PISCES 1 environment was applied to two areas of aerospace interest: a sparse matrix iterative equation solver and a dynamic scene analysis system. Currently, the NICE/SPAR testbed system for structural analysis is being modified for parallel operation under PISCES 2; the PISCES 1 applications are also being adapted for PISCES 2. A new formal model of concurrent computation has been developed, based on the mathematical system known as H graph semantics together with a timed Petri net model of the parallel aspects of a system.

Pratt, Terrence W.↗

NASA NTRS1987

Linear quadratic regulators with eigenvalue placement in a horizontal strip

A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.

Shieh, Leang S.↗

NASA NTRS1989

Algorithm For Optimal Control Of Large Structures

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Salama, Moktar A.↗

NASA NTRS1988

Linear quadratic regulators with eigenvalue placement in a specified region

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Shieh, Leang S.↗