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NASA NTRS1976

A general unified approach to modelling switching-converter power stages

A method for modeling switching-converter power stages is developed, whose starting point is the unified state-space representation of the switched networks and whose end result is either a complete state-space description or its equivalent small-signal low-frequency linear circuit model. A new canonical circuit model is proposed, whose fixed topology contains all the essential input-output and control properties of any dc-to-dc switching converter, regardless of its detailed configuration, and by which different converters can be characterized in the form of a table conveniently stored in a computer data bank to provide a useful tool for computer aided design and optimization. The new canonical circuit model predicts that, in general, switching action introduces both zeros and poles into the duty ratio to output transfer function in addition to those from the effective filter network.

Middlebrook, R. D.↗

NASA NTRS1985

Dynamic loads analyses of flexible airplanes - New and existing techniques

This paper reviews existing techniques for calculating dynamic loads for flexible airplanes and presents a new technique. The new technique involves the summation-of-forces method of writing dynamic loads equations. Until now this form of the dynamic loads equations has been formulated in the frequency domain. The new technique uses s-plane approximation methods (previously applied only to the equations of motion) to transform the dynamic loads equations from a second-order frequency-domain formulation with frequency-dependent coefficients into a linear-time-invariant state-space formulation. Several numerical examples demonstrate the usefulfness of the new technique and the high quality of the results. In addition, a convergence investigation establishes that the summation-of-forces method converges more quickly (that is, with fewer modes) than does the mode displacement method.

Pototzky, A. S.↗

NASA NTRS1974

Time response simulation of the 1975 Viking Orbiter digital tape recorder

The objective of the present study was to verify and understand in depth the performance of the speed control (frequency loop) servo of the 1975 Viking Orbiter (VO75) digital tape recorder (DTR). The time response method employed is written in the continuous system simulation language (CSSL) for the Univac 1108 computer system. In order to demonstrate the power and flexibility of the graphic interactive simulation program, four aspects of system dynamics are interactively adjusted to arrive at a number of stable system configurations that have significantly different tape transport and/or summing amplifier gain, larger static/dynamic Coulomb friction, and different system lag than envisioned in the nominal design by linear methods. Work is currently underway to derive a new higher-order DST transfer function and to simulate the servo using state-space variable techniques.

Mukhopadhyay, A. K.↗

NASA NTRS1980

Identification of flexible aircraft from flight data

This paper describes a frequency-domain method for the estimation of the aeroelastic equations of motion of an aircraft using discrete sinusoidal inputs to the control surface actuators. The theory of estimation of the signal inputs and outputs is described as well as the method of obtaining accurate transfer functions from the resulting Bode plots. Methods of quantifying the accuracy of the results from more than one control input are discussed along with ways to obtain state-space and reduced-order models from the transfer function estimates. Presented is a summary of the results obtained in using the technique to develop a model of the USAF Total In-Flight Simulator (TIFS) aircraft which includes five symmetrical elastic modes of motion of the aircraft.

Eulrich, B. J.↗

NASA NTRS1973

State space approach to mixed boundary value problems.

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Chen, C. F.↗

NASA NTRS1990

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.↗

NASA NTRS1987

State-space formulation of multi-shaker modal analysis

As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results have increased. This paper describes a new multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Craig, Roy R., Jr.↗

NASA NTRS1989

OPTICON: Pro-Matlab software for large order controlled structure design

A software package for large order controlled structure design is described and demonstrated. The primary program, called OPTICAN, uses both Pro-Matlab M-file routines and selected compiled FORTRAN routines linked into the Pro-Matlab structure. The program accepts structural model information in the form of state-space matrices and performs three basic design functions on the model: (1) open loop analyses; (2) closed loop reduced order controller synthesis; and (3) closed loop stability and performance assessment. The current controller synthesis methods which were implemented in this software are based on the Generalized Linear Quadratic Gaussian theory of Bernstein. In particular, a reduced order Optimal Projection synthesis algorithm based on a homotopy solution method was successfully applied to an experimental truss structure using a 58-state dynamic model. These results are presented and discussed. Current plans to expand the practical size of the design model to several hundred states and the intention to interface Pro-Matlab to a supercomputing environment are discussed.

Peterson, Lee D.↗

NASA NTRS1983

Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

Frequency domain methods are developed to obtain explicit equations for the angles of arrival and departure for multivariable root loci. The techniques involve an evaluation of polynomials formulated within the transfer function matrix. The equations defined require simpler computations than the state-space results of Shaked (1976). A class of higher order poles and zeros is formulated in terms of simpler equations than Shaked's, and the equations are shown to be generalizations of the single-input-single-output root locus equations.

Yagle, A. E.↗

NASA NTRS1981

The use of frequency methods in rotorcraft system identification

A new approach to model structure determination is examined. Flight data from the Rotor Systems Research Aircraft (RSRA) are transformed into the frequency domain and truncated to provide band limiting. The stepwise regression technique is then used to identify a quasistatic state-space model from the transformed data. The data processing requirements for both time domain and frequency domain identification are discussed and the results of the two techniques are compared.

Duval, R. W.↗

NASA NTRS1986

Flight control synthesis for flexible aircraft using Eigenspace assignment

The use of eigenspace assignment techniques to synthesize flight control systems for flexible aircraft is explored. Eigenspace assignment techniques are used to achieve a specified desired eigenspace, chosen to yield desirable system impulse residue magnitudes for selected system responses. Two of these are investigated. The first directly determines constant measurement feedback gains that will yield a close-loop system eigenspace close to a desired eigenspace. The second technique selects quadratic weighting matrices in a linear quadratic control synthesis that will asymptotically yield the close-loop achievable eigenspace. Finally, the possibility of using either of these techniques with state estimation is explored. Application of the methods to synthesize integrated flight-control and structural-mode-control laws for a large flexible aircraft is demonstrated and results discussed. Eigenspace selection criteria based on design goals are discussed, and for the study case it would appear that a desirable eigenspace can be obtained. In addition, the importance of state-space selection is noted along with problems with reduced-order measurement feedback. Since the full-state control laws may be implemented with dynamic compensation (state estimation), the use of reduced-order measurement feedback is less desirable. This is especially true since no change in the transient response from the pilot's input results if state estimation is used appropriately. The potential is also noted for high actuator bandwidth requirements if the linear quadratic synthesis approach is utilized. Even with the actuator pole location selected, a problem with unmodeled modes is noted due to high bandwidth. Some suggestions for future research include investigating how to choose an eigenspace that will achieve certain desired dynamics and stability robustness, determining how the choice of measurements effects synthesis results, and exploring how the phase relationships between desired eigenvector elements effects the synthesis results.

Davidson, J. B.↗

NASA NTRS1989

Identification of nonlinear systems

Given a Volterra series representations of an input-output system, the authors present a result concerning conditions under which there exists a feedback linearizable realization of the nonlinear system. In addition, they have developed a method to compute the unknown parameters in a canonical form realization from the known Volterra kernels. A finite number of parameters can be calculated from an associated finite number of the kernels. The authors restrict themselves to single-input, single-output continuous-time systems. It is assumed that the systems have real analytic state-space representations. The realization results are local, taking place a neighborhood of the origin in state space.

Hunt, L. R.↗

NASA NTRS1988

Transonic stability and control of aircraft using CFD methods

Implementation of a capability to calculate longitudinal short-period response in the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) finite-difference code is described. The code, developed recently at the NASA Langley Research Center, is capable of solving steady and unsteady flows about complete aircraft configurations and is used primarily for aeroelastic calculations in the critical transonic speed range. The longitudinal short-period equations of motion in state-space form have been coupled to the time-accurate lift and moment calculated by the program. Transient responses to an elevator pulse for free-flying aircraft demonstrate the new capability. A trim routine is also added to the code to obtain trim automatically during steady-state flow field convergence. Stability and control derivatives are estimated from the calculated transient response by a maximum likelihood estimation program. Results for a fighter configuration and a general aviation configuration are presented to assess the capability.

Vinh, Lam-Son↗

NASA NTRS2008

An Investigation of State-Space Model Fidelity for SSME Data

In previous studies, a variety of unsupervised anomaly detection techniques for anomaly detection were applied to SSME (Space Shuttle Main Engine) data. The observed results indicated that the identification of certain anomalies were specific to the algorithmic method under consideration. This is the reason why one of the follow-on goals of these previous investigations was to build an architecture to support the best capabilities of all algorithms. We appeal to that goal here by investigating a cascade, serial architecture for the best performing and most suitable candidates from previous studies. As a precursor to a formal ROC (Receiver Operating Characteristic) curve analysis for validation of resulting anomaly detection algorithms, our primary focus here is to investigate the model fidelity as measured by variants of the AIC (Akaike Information Criterion) for state-space based models. We show that placing constraints on a state-space model during or after the training of the model introduces a modest level of suboptimality. Furthermore, we compare the fidelity of all candidate models including those embodying the cascade, serial architecture. We make recommendations on the most suitable candidates for application to subsequent anomaly detection studies as measured by AIC-based criteria.

Martin, Rodney Alexander↗

NASA NTRS1990

Parallelized reliability estimation of reconfigurable computer networks

A parallelized system, ASSURE, for computing the reliability of embedded avionics flight control systems which are able to reconfigure themselves in the event of failure is described. ASSURE accepts a grammar that describes a reliability semi-Markov state-space. From this it creates a parallel program that simultaneously generates and analyzes the state-space, placing upper and lower bounds on the probability of system failure. ASSURE is implemented on a 32-node Intel iPSC/860, and has achieved high processor efficiencies on real problems. Through a combination of improved algorithms, exploitation of parallelism, and use of an advanced microprocessor architecture, ASSURE has reduced the execution time on substantial problems by a factor of one thousand over previous workstation implementations. Furthermore, ASSURE's parallel execution rate on the iPSC/860 is an order of magnitude faster than its serial execution rate on a Cray-2 supercomputer. While dynamic load balancing is necessary for ASSURE's good performance, it is needed only infrequently; the particular method of load balancing used does not substantially affect performance.

Nicol, David M.↗

NASA NTRS1974

Computer programs for calculation of matrix stability and frequency response from a state-space system description

FORTRAN computer subroutines stemming from requirements to process state variable system equations for systems of high order are presented. They find the characteristic equation of a matrix using the method of Danilevsky, the number of roots with positive real parts using the Routh-Horwitz alternate formulation, convert a state variable system description to a Laplace transfer function using the method of Bollinger, and evaluate that transfer function and obtain its frequency response. A sample problem is presented to demonstrate use of the subroutines.

Seidel, R. C.↗

NASA NTRS1987

State-space self-tuning controllers for general multivariable stochastic systems

This paper presents a state-space approach for self-tuning control of a more general class of multivariable stochastic systems having a number of inputs equal or different from the number of outputs. The dynamic system is represented in the state-space innovation form with Luenberger's canonical structures. The model parameters and the Kalman gain are identified via either the extended least-squares algorithm or the least-squares ladder algorithm. The Kalman gain matrix and states can be estimated from the identified parameters without utilizing the standard state estimation algorithm. A long division method is introduced for finding the similarity transformation matrix.

Shieh, L. S.↗

NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

Tiffany, Sherwood H.↗