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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.

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NASA NTRS1985

New Directions in Asymptotically Stable Finite-dimensional Adaptive Control of Linear Distributed Parameter Systems

Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.

Balas, M. J.↗
NASA NTRS1976

Nonlinear behavior of acoustic waves in combustion chambers. I, II

The general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber is treated in three parts: (1) the general conservation equations are expanded in two small parameters, and then combined to yield a nonlinear inhomogeneous wave equation, (2) the unsteady pressure and velocity fields are expressed as a synthesis of the normal modes of the chamber, but with unknown time-varying amplitudes, and (3) the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. This approximate analysis is applied to the investigation of the unstable motions in a solid propellant rocket engine and in a T burner.

Culick, F. E. C.↗
NASA NTRS1974

Connective stability of nonlinear matrix systems

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

Siljak, D. D.↗
NASA NTRS1985

Sub-Optimal Control of Nonlinear Flexible Space Structures

A simple yet effective method is presented for the on-line vibration control of nonlinear distributed parameter systems, with constant or time-varying properties, responding to a wide class of dynamic environments. The control procedure uses pulse generators located at selected positions throughout a given system. The degree of system oscillation near each controller determines the controller's activation time and pulse amplitude. The direct method of Liapunov is used to establish that the response of the controlled nonlinear system is Lagrange stable. Analytical and experimental studies of a wing-like plate demonstrate the feasibility, reliability, and robustness of the proposed vibration-suppression method.

Dehghanyar, T. J.↗
NASA NTRS1979

Time-varying linear systems and the theory of non-linear waves

The isospectral deformation of a Sturm-Liouville equation is extended to general linear time-varying systems and a method is described for determining the resulting nonlinear partial differential equations. Consideration is given to (1) isospectral deformation of I/O systems with boundary value conditions and (2) the spectral vector bundles attached to linear time-varying systems.

Hermann, R.↗
NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗
NASA NTRS1972

Stability of large-scale systems under structural perturbations.

A large-scale system is considered as a system constituted of subsystems which may be connected or disconnected from each other during operation. A new concept of connective stability is introduced by which a large-scale system is regarded as stable if it remains stable (in the sense of Lyapunov) under structural perturbations produced by the on-off participation of the subsystems. Algebraic conditions are developed that guarantee exponential connective stability of large-scale systems which may be composed of linear and nonlinear time-varying subsystems coupled by linear or nonlinear connections.

Siljak, D. D.↗
NASA NTRS1975

Connective stability of competitive equilibrium

The purpose of this paper is to derive necessary and sufficient conditions for the connective stability of nonlinear matrix systems described by the equation x-dot = A(t, x) x, where the matrix A(t, x) has time-varying nonlinear elements. The results obtained can be used to study the stability of competitive equilibrium in fields as diverse as economics and engineering, model ecosystems, and the arms race.-

Siljak, D. D.↗
NASA NTRS1975

Nonlinear behavior of acoustic waves in combustion chambers

The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.

Culick, F. E. C.↗
NASA NTRS1973

Marshall system for aerospace system simulation (MARSYAS), user's manual

The capabilities of the Marshall system for aerospace system simulation (MARSYAS) and how to use it are described. MARSYAS is a software system that allows easy setup and control of the simulation of the dynamics of large physical systems on a digital computer. The physical systems are modeled in the form of block diagrams or equations. The blocks can have multiple inputs and multiple outputs, and they can be nested to form hierarchies. The block diagrams can contain transfer functions, nonlinear and logical functions, equations, analog computer elements and FORTRAN programs. The input format of the equations can be combinations of nonlinear, time-varying differential equations and algebraic equations in their original format. MARSYAS could also serve as a storage and retrieval system for models as a basis for a model configuration control system on a central time-shared computer. The outputs of the simulation system can be not only time-responses but also other analysis data such as frequency response, power spectrum and stability parameters. The MARSYAS translator is written in FORTRAN running on the Univac 1108 computer under the EXEC 8 operating system.

Ventre, A.↗
NASA NTRS1973

A sequence solution to the Fokker-Planck equation.

In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer.

Mayfield, W. W.↗
NASA NTRS1976

Aeroelastic characteristics of composite bearingless rotor blades

Owing to the inherent unique structural features of composite bearingless rotors, various assumptions upon which conventional rotor aeroelastic analyses are formulated, are violated. Three such features identified are highly nonlinear and time-varying structural twist, structural redundancy in bending and torsion, and for certain configurations a strongly coupled low frequency bending-torsion mode. An examination of these aeroelastic considerations and appropriate formulations required for accurate analyses of such rotor systems is presented. Also presented are test results from a dynamically scaled model rotor and complementary analytic results obtained with the appropriately reformulated aeroelastic analysis.

Bielawa, R. L.↗
NASA NTRS1973

A new approach to the design of time varying control systems with application to the space shuttle booster

A general approach toward the analysis and design of closed loop control for slowly time-varying linear systems was investigated. The approach is by the method of generalized multiple scales, in which slow and fast dynamics are systematically separated by employing different clocks which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, so that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock functions are shown to satisfy an algebraic characteristic equation and can be determined in general in terms of the coefficients.

Ramnath, R. V.↗
NASA NTRS1973

A new approach to the design of time-varying control systems with application to the Space Shuttle Boost

A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.

Ramanth, R. V.↗
NASA NTRS1978

Prediction, evaluation, and specification of flying qualities by means of step target tracking

A new approach to flying qualities specification and evaluation is presented which coordinates current research in the areas of pilot ratings, pilot-aircraft modeling techniques, and simulation and flight test procedures. A time-domain pilot model is described which can model discontinuous and nonlinear pilot behavior in conjunction with completely general time-varying nonlinear aircraft models to simulate discrete maneuvers. This pilot-aircraft model is applied to an existing set of in-flight simulation data, and calculates tracking error and time-on-target statistics for step target tracking that directly relate to the reported pilot comments and ratings. Predicted step target tracking data for eighteen F-5E flight conditions are presented, and the use of the method for control system design is demonstrated using the YF-17.

Onstott, E. D.↗