Search NASA⌕ Search

SEARCH · Search NASA

Results for “state space model”

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 145 records · Page 8

Development of Reduced-Order Models for Aeroelastic and Flutter Prediction Using the CFL3Dv6.0 Code

A reduced-order model (ROM) is developed for aeroelastic analysis using the CFL3D version 6.0 computational fluid dynamics (CFD) code, recently developed at the NASA Langley Research Center. This latest version of the flow solver includes a deforming mesh capability, a modal structural definition for nonlinear aeroelastic analyses, and a parallelization capability that provides a significant increase in computational efficiency. Flutter results for the AGARD 445.6 Wing computed using CFL3D v6.0 are presented, including discussion of associated computational costs. Modal impulse responses of the unsteady aerodynamic system are then computed using the CFL3Dv6 code and transformed into state-space form. Important numerical issues associated with the computation of the impulse responses are presented. The unsteady aerodynamic state-space ROM is then combined with a state-space model of the structure to create an aeroelastic simulation using the MATLAB/SIMULINK environment. The MATLAB/SIMULINK ROM is used to rapidly compute aeroelastic transients including flutter. The ROM shows excellent agreement with the aeroelastic analyses computed using the CFL3Dv6.0 code directly.

Silva, Walter A.↗

Multivariable identification using centralized fixed modes

A procedure to determine a state space model of a multivariable system (lambda inputs, m outputs) is presented. The model is suitable for control studies and uses single input, single output (SISO) system data in the identification procedure. The procedure can be defined in three distinct steps. First, the system's lambda x m SISO transfer functions are identified by using any standard or known identification technique for SISO systems. One objective of this step is to identify SISO transfer functions with as few distinct modes as possible between any two functions. Second, the time domain realization of each SISO transfer function is obtained in a straightforward manner and combined into a total multivariable realization. This total realization, in all probability, has more state variables than are required to define system response. In the third step, these excess or redundant states are removed by using minimal realization theory. The remaining states are related to system centralized fixed modes. Eigenvalue-eigenvector techniques were recently reported that yield a computationally feasible solution to the problem posed in step three. The procedure is applied to QCSEE data to demonstrate its feasibility.

Merrill, W. C.↗

Extending A Correction Method for Unsteady Transonic Aerodynamics to Variable Camber Continuous Trailing Edge Flap

In this study, we have extended our correction method for transonic aerodynamics to baseline and variable camber continuous trailing edge (VCCTEF) geometries of super-critical airfoils at cruise conditions. This correction method modifies Theodorsen theory, which is based on incompressible potential flow over a flat plate. The method is partly based on CFD RANS simulations of oscillating NASA generic transport model (GTM) baseline cruise and VCCTEF airfoil geometries in pitch and shows promise for addressing transonic flutter problems of aeroelasticity. In the earlier study1, the Theodorsen functions were modulated with non-linear functions of Mach number, M, and reduced frequency, k, and thus the correction was demonstrated for the symmetrical NACA0012 airfoil. In the present study, the modulation functions are also allowed to account for the effects of camber and thickness of the airfoil. This is demonstrated by applying the correction method to various symmetric NACA00xx airfoil geometries (NACA001, NACA0002, NACA0012, NACA0015 and NACA0018), the NASA GTM super-critical baseline and VCCTEF airfoil geometries, e.g., the circular airfoil, VCCTEF222. First results indicate that the correction method accounts for a large variation of thickness of airfoils and camber. The present correction method will guide the development of a new state space model for the VCCTEF system and eventually a new transfer function that will be incorporated in a new aeroelastic framework leading to an appropriate transonic flutter model for use in the future aircraft systems in development under the NASA Advanced Air Transportation Technologies (AATT) project.

Kaul, Upender K.↗

Systems identification using a modified Newton-Raphson method: A FORTRAN program

A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

Taylor, L. W., Jr.↗

Identification of rotating assembly inertial and bearing parameters.

The problem of estimating the state of a turbopump rotating assembly and identifying unknown products of inertia and unknown bearing parameters is considered. A linearized, extended Kalman filtering approach has been used and found to be successful for both state estimation and parameter identification in an inherently nonlinear problem. The input data were simulated Bently test data obtained from a verified 12-dimensional state-space model and were compared with real Bently test data obtained from NASA. The results prove the feasibility of using this model and this type of test data to obtain the hidden parameters of a typical turbopump rotating assembly.

Alspach, D. L.↗

Reliability and coverage analysis of non-repairable fault-tolerant memory systems

A method was developed for the construction of probabilistic state-space models for nonrepairable systems. Models were developed for several systems which achieved reliability improvement by means of error-coding, modularized sparing, massive replication and other fault-tolerant techniques. From the models developed, sets of reliability and coverage equations for the systems were developed. Comparative analyses of the systems were performed using these equation sets. In addition, the effects of varying subunit reliabilities on system reliability and coverage were described. The results of these analyses indicated that a significant gain in system reliability may be achieved by use of combinations of modularized sparing, error coding, and software error control. For sufficiently reliable system subunits, this gain may far exceed the reliability gain achieved by use of massive replication techniques, yet result in a considerable saving in system cost.

Cox, G. W.↗

An Eigensystem Realization Algorithm for Application to Modal Testing

Important features of the Eigensystem Realization Algorithm (ERA) are summarized as follows: (1) from the computational standpoint, the algorithm is attractive, since only simple numerical operations are needed; (2) the computational procedure is numerically stable; (3) the structural dynamics requirements for modal parameter identification and the control design requirements for a reduced-state space model are satisfied; (4) data from more than one test can be used simultaneously to efficiently identify the closely spaced eigenvalues; and (5) no restrictions on number of measurements are imposed.

Juang, J. N.↗

Nonlinear global stability analysis of compressor stall phenomena

Compressor stall phenomena are analyzed from the point of view of nonlinear control theory, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well-known compressor instability problems as surge and rotating stall and suggests strategies for recovery. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an induced bifurcation of solution of the unstalled model. Hysteresis effects are shown to exist in the stall/recovery process. Surge cycles are observed for some critical parameter values. The oscillatory behavior is seen to be due to development of limit cycles, generated by Hopf bifurcation of solutions. More specifically, it is observed that at certain critical values of parameters, a family of stable limit cycles with growning and then diminishing amplitudes is generated, then giving rise to an unstable family of limit cycles. This unstable family in turn bifurcates into other unstable families. To further illustrate the utility of the methodology, some partial computation of domains is carried out, and parameter sensitivity analysis is performed.

Razavi, H.↗

Bifurcation techniques for nonlinear dynamic analysis of compressor stall phenomena

Compressor stall phenomena is analyzed from nonlinear control theory viewpoint, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well known compressor instability problems as surge and rotating stall; furthermore it suggests strategies for recovery from stall. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an (induced) bifurcation of solution of the unstalled model. Hysteresis effect is shown to exist in the stall/recovery process. Surge cycles are observed to develop for some critical parameter values. It is shown that the oscillatory behavior is due to development of limit cycles, generated by Hopf bifurcation of solutions. Both stable and unstable limit cycles are observed. To further illustrate the usefulness of the methodology some partial computation of domains of attraction of equilibria is carried out, and parameter sensitivity analysis is performed.

Razavi, H. C.↗

Estimability And Regulability Of Linear Systems

Report presents two new properties of systems characterized by linear state space models (e.g., dynamical systems and associated control systems): estimability and regulability. Provides criteria for reductions of errors and cost functions in control systems. Useful in design of optimal controllers and estimators.

Baram, Yoram↗

Computational tools for multi-linked flexible structures

A software module which designs and tests controllers and filters in Kalman Estimator form, based on a polynomial state-space model is discussed. The user-friendly program employs an interactive graphics approach to simplify the design process. A variety of input methods are provided to test the effectiveness of the estimator. Utilities are provided which address important issues in filter design such as graphical analysis, statistical analysis, and calculation time. The program also provides the user with the ability to save filter parameters, inputs, and outputs for future use.

Lee, Gordon K. F.↗

Active rejection of persistent disturbances in flexible space structures

A dynamic compensator for active rejection of persistent disturbances in flexible space structures is designed on the principle of the H(infinity)-optimization of the sensitivity transfer function matrix. A general state space solution is formulated to the multiinput multioutput H(infinity)-optimal control problem, allowing the use of the H(infinity)-optimal synthesis algorithm for the state-space models of space structures that result from model order reduction. Disturbances encountered in flexible space structures, such as shuttle docking, are investigated using the high-mode and the reduced-order models of a cantilevered two-bay truss, demonstrating the applicability of the H(infinity)-optimal approach.

Hwang, Cheng-Neng↗

Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method

The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed.

Karpel, Mordechay↗

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↗

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

This paper presents a formulation for identification of linear multivariable systems from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identification, by extension of the repetition domain concept to include shifting time intervals. This contrasts 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 the proposed method.

Phan, Minh↗

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer, and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples using simulated noise-free data are presented to illustrate the proposed method.

Phan, Minh↗

Estimation of Kalman filter gain from output residuals

This paper presents a procedure for estimating the Kalman filter gain from output residuals. The system state space model is assumed to be known, but the process and noise covariance are unknown. The proposed procedure consists of three basic steps. First, the output residuals are computed from the given model and a given set of input-output data. Second, a linear regression model for this part of the response is computed by a least squares solution. Third, the Kalman filter gain is then estimated from the coefficients of this model. Numerical results using experimental data are presented to illustrate the validity of the developed procedure.

Juang, Jer-Nan↗