Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Linear dynamics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Closed-form solutions for feedback control with terminal constraints

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fixed and/or free end condition problems. In the maneuvers using control-rate penalties, smooth profiles are generated throughout the maneuvers, in the sense that the initial condition jump discontinuities have been eliminated. Several examples involving large-angle maneuvers of a spacecraft are demonstrated. Results include control maneuvers from one state to another such as rest to rest and spin to rest, which effectively justify the solutions developed in this paper.

Juang, J.-N.↗
NASA NTRS1985

Residue-Measure Model-Reduction Technique

New residue-measure criterion simplifies mathematical models of feedback-control systems. Although originally developed for flight control, approach applied to any flexible structural system involving dominantly linear dynamics.

Gluch, D. P.↗
NASA NTRS1984

On the design of robust LQ regulators

Sufficient conditions are obtained for global asymptotic stability of linear systems controlled by linear quadratic (LQ) regulators when nonlinearities or unmodeled linear dynamics are present in the loop. The conditions are less conservative than the standard LQ robustness results because they generally yield phase margins greater than 60 deg, and tolerance to nonlinearities having gains greater than 1/2. The conditions also provide a measure of robustness of a given LQ design to unmodeled dynamics and nonlinearities. For open-loop stable plants, it is proved that a class of LQ regulators can always be designed to have plus or minus 90 deg phase margin and tolerance to nonlinearities in the (0, infinity) sector.

Joshi, S. M.↗
NASA NTRS1985

On the design of pole modules for inverse systems

When a linear dynamical system admits more than one inverse, it is known that the pole module of any inverse must contain, either as a submodule or as a factor module, a module of fixed poles isomorphic to the zero module of the original system. Design of the pole module for such an inverse system is resolved by introducing a variable pole module for the inverse, by determining necessary and sufficient conditions for a desired module to be a variable pole module, and by studying the manner in which the fixed and variable modules assemble into the pole module of the inverse. If the fixed and variable pole spectra are disjoint, the pole module of the inverse system is a direct sum of the fixed- and variable-pole modules; if not, procedures for addressing the Jordan structure are presented.

Wyman, B. F.↗
NASA NTRS1985

Preliminary design study of a lateral-directional control system using thrust vectoring

A preliminary design of a lateral-directional control system for a fighter airplane capable of controlled operation at extreme angles of attack is developed. The subject airplane is representative of a modern twin-engine high-performance jet fighter, is equipped with ailerons, rudder, and independent horizontal-tail surfaces. Idealized bidirectional thrust-vectoring engine nozzles are appended to the mathematic model of the airplane to provide additional control moments. Optimal schedules for lateral and directional pseudo control variables are calculated. Use of pseudo controls results in coordinated operation of the aerodynamic and thrust-vectoring controls with minimum coupling between the lateral and directional airplane dynamics. Linear quadratic regulator designs are used to specify a preliminary flight control system to improve the stability and response characteristics of the airplane. Simulated responses to step pilot control inputs are stable and well behaved. For lateral stick deflections, peak stability axis roll rates are between 1.25 and 1.60 rad/sec over an angle-of-attack range of 10 deg to 70 deg. For rudder pedal deflections, the roll rates accompanying the sideslip responses can be arrested by small lateral stick motions.

Lallman, F. J.↗
NASA NTRS1986

Analytical comparison of transient and steady state visual evoked cortical potentials

To better describe the linear-dynamic properties of the human visual-cortical response system, transient and steady state Visual Evoked Response Potentials (VERP) were observed. The stimulus presentation device provided both the evoking stimulus (flickering or pulsing lights) and a video task display. The steady state stimulus was modulated by a complex, ten frequency, sum-of-sines, wave. The transient VERP was the time-locked average of the EEG to a series of narrow light pulses (pulse width of 10 msec). The Fourier transform of the averaged pulses had properties that approximate band limited white noise, i.e., a flat spectrum over the frequency region spanned by the 10 summed sines. The Fourier transform of both the steady state and the transient evoked potentials resulted in transfer that are equivalent and therefore comparable. To investigate the effects of task loading on evoked potentials, a grammatical reasoning task was provided. Results support the relevancy of continued application of a systems engineering approach for describing neurosensory functioning.

Junker, A. M.↗
NASA NTRS1987

High speed simulation of flexible multibody dynamics

A multiflexible body dynamics code intended for fast turnaround control design trades is described. Nonlinear rigid body dynamics and linearized flexible dynamics combine to provide efficient solution of the equations of motion. Comparison with results from the DISCOS code provide verification of accuracy.

Jacot, A. D.↗
NASA NTRS1987

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

Hinnant, Howard E.↗
NASA NTRS1986

Transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems

The existence of a compensator which simultaneously renders a given r-tuple of multiinput-multioutput p x m linear dynamical systems internally stable is investigated. In particular, a set of simultaneously stabilizable r-tuples of plants is parametrized, and it is shown that, provided r = max(m,p) or less, the above set is semialgebraic and dense in the space Sigma of r-tuples of plants. An extension of the classical pole placement and stabilization problems is considered, and the simultaneous partial pole placement problem is investigated.

Ghosh, B. K.↗
NASA NTRS1987

Module theoretic zero structures for system matrices

The coordinate-free module-theoretic treatment of transmission zeros for MIMO transfer functions developed by Wyman and Sain (1981) is generalized to include noncontrollable and nonobservable linear dynamical systems. Rational, finitely-generated-modular, and torsion-divisible interpretations of the Rosenbrock system matrix are presented; Gamma-zero and Omega-zero modules are defined and shown to contain the output-decoupling and input-decoupling zero modules, respectively, as submodules; and the cases of left and right invertible transfer functions are considered.

Wyman, Bostwick F.↗
NASA NTRS1987

Application of GRASP to nonlinear analysis of a cantilever beam

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyze the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformation. The correlation is excellent in all cases.

Hinnant, Howard E.↗
NASA NTRS1989

Vibration analysis of rotor systems using reduced subsystem models

A general impedance method using reduced submodels has been developed for the linear dynamic analysis of rotor systems. Formulated in terms of either modal or physical coordinates of the subsystems, the method enables imbalance responses at specific locations of the rotor systems to be efficiently determined from a small number of 'master' degrees of freedom. To demonstrate the capability of this impedance approach, the Space Shuttle Main Engine high-pressure oxygen turbopump has been investigated to determine the bearing loads due to imbalance. Based on the same formulation, an eigenvalue analysis has been performed to study the system stability. A small 5-DOF model has been utilized to illustrate the application of the method to eigenvalue analysis. Because of its inherent characteristics of allowing formulation of reduced submodels, the impedance method can significantly increase the computational speed.

Fan, Uei-Jiun↗
NASA NTRS1989

True covariance simulation of the EUVE update filter

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1989

Effective techniques for the identification and accommodation of disturbances

The successful control of dynamic systems such as space stations, or launch vehicles, requires a controller design methodology that acknowledges and addresses the disruptive effects caused by external and internal disturbances that inevitably act on such systems. These disturbances, technically defined as uncontrollable inputs, typically vary with time in an uncertain manner and usually cannot be directly measured in real time. A relatively new non-statistical technique for modeling, and (on-line) identification, of those complex uncertain disturbances that are not as erratic and capricious as random noise is described. This technique applies to multi-input cases and to many of the practical disturbances associated with the control of space stations, or launch vehicles. Then, a collection of smart controller design techniques that allow controlled dynamic systems, with possible multi-input controls, to accommodate (cope with) such disturbances with extraordinary effectiveness are associated. These new smart controllers are designed by non-statistical techniques and typically turn out to be unconventional forms of dynamic linear controllers (compensators) with constant coefficients. The simplicity and reliability of linear, constant coefficient controllers is well-known in the aerospace field.

Johnson, C. D.↗
NASA NTRS1990

Coupled rotor-body equations of motion hover flight

A set of linearized equations of motion to predict the linearized dynamic response of a single rotor helicopter in a hover trim condition to cyclic pitch control inputs is described. The equations of motion assume four fuselage degrees of freedom: lateral and longitudinal translation, roll angle, pitch angle: four rotor degrees of freedom: flapping (lateral and longitudinal tilt of the tip path plane), lagging (lateral and longitudinal displacement of the rotor plane center of mass); and dynamic inflow (harmonic components). These ten degrees of freedom correspond to a system with eighteen dynamic states. In addition to examination of the full system dynamics, the computer code supplied with this report permits the examination of various reduced order models. The code is presented in a specific form such that the dynamic response of a helicopter in flight can be investigated. With minor modifications to the code the dynamics of a rotor mounted on a flexible support can also be studied.

Curtiss, H. C., Jr.↗
NASA NTRS1989

Optical laboratory solution and error model simulation of a linear time-varying finite element equation

The use of simplified error models to accurately simulate and evaluate the performance of an optical linear-algebra processor is described. The optical architecture used to perform banded matrix-vector products is reviewed, along with a linear dynamic finite-element case study. The laboratory hardware and ac-modulation technique used are presented. The individual processor error-source models and their simulator implementation are detailed. Several significant simplifications are introduced to ease the computational requirements and complexity of the simulations. The error models are verified with a laboratory implementation of the processor, and are used to evaluate its potential performance.

Taylor, B. K.↗
NASA NTRS1990

Reliable algorithm for modal decomposition

This paper describes a reliable, general algorithm for modal decomposition in real arithmetic and its use in analyzing and synthesizing control logic for linear dynamic systems. The numerical difficulties are described associated with computing the Jordan canonical form when the system has repeated, or nearly repeated, eigenvalues. A new algorithm is described that satisfactorily solves these numerical difficulties. The relation and extension to related numerical analysis research are discussed to clarify the reliability of the techniques. Finally, its implementation as a practical modal decomposition method for efficiently computing the matrix exponential, transfer functions, and frequency response is also described.

Walker, Robert A.↗
NASA NTRS1990

Integrated system identification and modal state estimation for control of flexible space structures

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

Chen, Chung-Wen↗