A state-space method of parameter identification
State-space method of parameter tracking for adaptive control, using Riccati equation and Kalman filtering
Currie, M. G.↗
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State-space methods for designing digital simulations of continuous fixed linear systems
State-space methods for designing digital computer simulation of time invariant linear systems
Wait, J. V.↗
State-space formulations for flutter analysis
Two state-space methods for true-damping flutter analysis are presented here. The aerodynamic matrix is assumed to be function of the complex reduced frequency p (off-the-imaginary axis aerodynamics) as the ones provided for instance by the computer code SOUSSA (Steady, Oscillatory and Unsteady, Subsonic and Supersonic Aerodynamics). This matrix is approximated by a third order polynomial or by a Pade's matrix approximant. Then the equations are cast into a suitable state space format including the Laplace transform of the space vector, a frequency-independent matrix, and the flight speed. The solution is then obtained by standard root-locus methods. Results are in good agreement with existing ones in a suitable range of the flutter reduced frequency. A discussion on spurious roots is also included.
Weiss, S. J.↗
Modelling, analyses and design of switching converters
A state-space averaging method for modelling switching dc-to-dc converters for both continuous and discontinuous conduction mode is developed. In each case the starting point is the unified state-space representation, and the end result is a complete linear circuit model, for each conduction mode, which correctly represents all essential features, namely, the input, output, and transfer properties (static dc as well as dynamic ac small-signal). While the method is generally applicable to any switching converter, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model. The insights that emerge from the general state-space modelling approach lead to the design of new converter topologies through the study of generic properties of the cascade connection of basic buck and boost converters.
Cuk, S. M.↗
State-space formulations for flutter analysis
Various methods are presented and assessed for approximating the aerodynamic forces so that the State Space formulation and off-the-imaginary axis analysis are retained. The advantages of retaining these features are considerable, not only in simplifying the flutter analysis, but especially for more advanced applications such as optimal design of active control in which the flutter is merely a constraint to the optimization problem.
Weiss, S. J.↗
A methodology for designing robust multivariable nonlinear feedback control systems
This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.
Grunberg, D. B.↗
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.↗
Stability of constant gain systems with vector feedback
The state space, the controllability, and the observability concepts are discussed in connection with the proposed stability analysis which permits drastic dimensional reductions for a vector feedback problem. Any constant gain system's stability can thus be analyzed in the frequency domain with a single Nyquist plot. The analysis considers the total system with all loops closed, a disturbance vector as input, and the feedback vector as output. All constant gain systems are shown to be decomposable into stable subsystems where the degree of the decomposition determines the dimensions. The maximum decomposition results in the state-space approach which is the limit case. The method is demonstrated with the stability analysis of the pogo phenomenon, an oscillatory interaction between the propulsion and the structure of a space vehicle. This problem, with eigenvalues over a hundred, was drastically but rigorously reduced to a stability analysis of a 4x4 matrix.
Vonpragenau, G. L.↗
A general unified approach to modelling switching dc-to-dc converters in discontinuous conduction mode
A method for modelling switching converters in the discontinuous conduction mode is developed, whose starting point is the unified state-space representation, and whose end result is a complete linear circuit model which correctly represents all essential features, namely, the input, output, and transfer properties (static dc as well as dynamic ac small signal). While the method is generally applicable to any switching converter operating in the discontinuous conduction mode, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model.
Cuk, S.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
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↗
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.↗