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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Flight control application of new stability robustness bounds for linear uncertain systems

This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.

Yedavalli, Rama K.↗
NASA NTRS1994

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

Guo, Tong-Yi↗
NASA NTRS2013

Adaptive Control for Linear Uncertain Systems with Unmodeled Dynamics Revisited via Optimal Control Modification

This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

Unmodeled Dynamics↗
NASA NTRS1975

Application of the comparison principle to analysis of nonlinear systems

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Gunderson, R. W.↗
NASA NTRS1979

System theory as applied differential geometry

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Hermann, R.↗
NASA NTRS1981

Global mappings of nonlinear systems

A theorem and its corollary are presented in which conditions are stated for a global transformation of a nonlinear system to a linear system. An explicit method for constructing such a transformation is given, and the important noncharacteristic matrix is introduced. Examples illustrating the technique are presented.

Hunt, L. R.↗
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 NTRS1988

Solution of structural analysis problems on a parallel computer

The problems of a blade-stiffened panel with a hole subjected to compression, and a deployable space mast subjected to tip loads, are treated through the application of FEM to model generation followed by the solution of a linear system of equations. Direct and iterative approaches to the solution of the linear systems are solved in turn; for the panel problems using varying numbers of processors, the incomplete Cholesky-conjugate gradient method was the fastest iterative method on all but two instances in which the number of processors was large.

Storaasli, Olaf↗
NASA NTRS2002

Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

Ito, Daigoro↗
NASA NTRS2005

Performance Analysis on Fault Tolerant Control System

In a fault tolerant control (FTC) system, a parameter varying FTC law is reconfigured based on fault parameters estimated by fault detection and isolation (FDI) modules. FDI modules require some time to detect fault occurrences in aero-vehicle dynamics. In this paper, an FTC analysis framework is provided to calculate the upper bound of an induced-L(sub 2) norm of an FTC system with existence of false identification and detection time delay. The upper bound is written as a function of a fault detection time and exponential decay rates and has been used to determine which FTC law produces less performance degradation (tracking error) due to false identification. The analysis framework is applied for an FTC system of a HiMAT (Highly Maneuverable Aircraft Technology) vehicle. Index Terms fault tolerant control system, linear parameter varying system, HiMAT vehicle.

Shin, Jong-Yeob↗
NASA NTRS1980

The pointable multispectral linear array system and the large format camera for early 1980 shuttle payloads

Design options are described for the multispectral linear arrays which will provide data and facilities beyond those obtained by LANDSAT 1, 2, 3, and D (the thematic mapper) are considered. The features, uses, and risks of a 10M fine resolution pointable imager, a 15M/30M dual resolution pointable imager, a 30M selectable spectral resolution pointing imager, a 30M electronically pointable multi-temporal sampler, and a 40M/80M mixed resolution imager are described. A large format camera scheduled for 1981 shuttle launch which can obtain high spatial ground resolution (approximately 10M), a relative position accuracy of plus or minus 14M, and a relative heightening accuracy, by virtue of stereographic coverage, of between 7 and 28M depending on the base-to-height ratio used. A potential problem of the system is that it will orbit in the shuttle.

Slater, P. N.↗
NASA NTRS1991

Identification of linear multivariable systems from a single set of data by identification of observers with assigned real eigenvalues

A formulation is presented for identification of linear multivariable from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identifications, by extension of the repetition domain concept to include shifting time intervals. This method contrasts with existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate.

Phan, Minh↗
NASA NTRS1993

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

Yedavalli, R. K.↗
NASA NTRS1996

Consideration in selecting crops for the human-rated life support system: a Linear Programming model

A Linear Programming model has been constructed which aids in selecting appropriate crops for CELSS (Controlled Environment Life Support System) food production. A team of Controlled Environment Agriculture (CEA) faculty, staff, graduate students and invited experts representing more than a dozen disciplines, provided a wide range of expertise in developing the model and the crop production program. The model incorporates nutritional content and controlled-environment based production yields of carefully chosen crops into a framework where a crop mix can be constructed to suit the astronauts' needs. The crew's nutritional requirements can be adequately satisfied with only a few crops (assuming vitamin mineral supplements are provided) but this will not be satisfactory from a culinary standpoint. This model is flexible enough that taste and variety driven food choices can be built into the model.

NASA Center JSC↗