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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

On stability theory

It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.

Safonov, M. G.↗
NASA NTRS1975

Sustained small oscillations in nonlinear control systems

Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.

George, J. H.↗
NASA NTRS1983

FINDS: A fault inferring nonlinear detection system. User's guide

The computer program FINDS is written in FORTRAN-77, and is intended for operation on a VAX 11-780 or 11-750 super minicomputer, using the VMS operating system. The program detects, isolates, and compensates for failures in navigation aid instruments and onboard flight control and navigation sensors of a Terminal Configured Vehicle aircraft in a Microwave Landing System environment. In addition, FINDS provides sensor fault tolerant estimates for the aircraft states which are then used by an automatic guidance and control system to land the aircraft along a prescribed path. FINDS monitors for failures by evaluating all sensor outputs simultaneously using the nonlinear analytic relationships between the various sensor outputs arising from the aircraft point mass equations of motion. Hence, FINDS is an integrated sensor failure detection and isolation system.

Lancraft, R. E.↗
NASA NTRS1984

Nonlinear control of aircraft

Transformations of nonlinear systems were used to design automatic flight controllers for vertical and short takeoff aircraft. Under the assumption that a nonlinear system can be mapped to a controllable linear system, a method using partial differential equations was constructed to approximate transformations in cases where exact ones cannot be found. An application of the design theory to a rotorcraft, the UH-1H helicopter, was presented.

Hunt, L. R.↗
NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗
NASA NTRS1986

Output time response approximation

The approximation of the output response of a nonlinear system by the output response of a linear system to a desired order irrespective of the admissible input applied should prove useful for purposes of control generation and simulation. Given a nonlinear system, an integer k, and an open subset of state space, sufficient conditions are stated that such a linear approximation exists to order k for every point in the set. In addition, a method for finding the approximating linear systems is presented.

Hunt, L. R.↗
NASA NTRS1983

Nonlinear transformat

A technique for designing automatic flight controllers for aircraft which utilizes the transformation theory of nonlinear systems to linear systems is presently being developed at NASA Ames Research Center. A method is considered in which a given nonlinear is transformed to a controllable linear system in Brunovsky canonical form. A linear approximation is introduced to the nonlinear system called the modified tangent model. This model is easily computed. Constructing the transformation for this model enables the designer to find an approximate transformation for the nonlinear system.

Ford, H.↗
NASA NTRS1983

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.↗
NASA NTRS1988

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗
NASA NTRS1990

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗
NASA NTRS1975

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗
NASA NTRS2013

Optimal Propellant Maneuver Flight Demonstrations on ISS

In this paper, first ever flight demonstrations of Optimal Propellant Maneuver (OPM), a method of propulsive rotational state transition for spacecraft controlled using thrusters, is presented for the International Space Station (ISS). On August 1, 2012, two ISS reorientations of about 180deg each were performed using OPMs. These maneuvers were in preparation for the same-day launch and rendezvous of a Progress vehicle, also a first for ISS visiting vehicles. The first maneuver used 9.7 kg of propellant, whereas the second used 10.2 kg. Identical maneuvers performed without using OPMs would have used approximately 151.1kg and 150.9kg respectively. The OPM method is to use a pre-planned attitude command trajectory to accomplish a rotational state transition. The trajectory is designed to take advantage of the complete nonlinear system dynamics. The trajectory choice directly influences the cost of the maneuver, in this case, propellant. For example, while an eigenaxis maneuver is kinematically the shortest path between two orientations, following that path requires overcoming the nonlinear system dynamics, thereby increasing the cost of the maneuver. The eigenaxis path is used for ISS maneuvers using thrusters. By considering a longer angular path, the path dependence of the system dynamics can be exploited to reduce the cost. The benefits of OPM for the ISS include not only reduced lifetime propellant use, but also reduced loads, erosion, and contamination from thrusters due to fewer firings. Another advantage of the OPM is that it does not require ISS flight software modifications since it is a set of commands tailored to the specific attitude control architecture. The OPM takes advantage of the existing ISS control system architecture for propulsive rotation called USTO control mode1. USTO was originally developed to provide ISS Orbiter stack attitude control capability for a contingency tile-repair scenario, where the Orbiter is maneuvered using its robotic manipulator relative to the ISS. Since 2005 USTO has been used for nominal ISS operations.

Bhatt, Sagar↗
NASA NTRS1987

Response of joint dominated space structures

An approximate method is developed for estimating the transient response of nonlinear systems in terms of linearized modes of response. Its advantages are that it is computationally more efficient than the time integration method and that it is possible to view the design problem in the more traditional physical terms of modal response. The major drawback of the approximate method is loss of accuracy. It seems that both approximate methods and time integration have their roles in design. Approximate methods provide efficient tools for performing parametric studies and they supply physical insights into how to optimize system performance that are not easily inferred from strictly numerical methods. Time integration provides a method for assessing the accuracy of the approximate solution for key simulations and for fine tuning the final design. In the procedure presented the nonlinear system is approximated by an equivalent linear system in which the system parameters are constant over the range of transient response.

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