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Stein, G.

Publications and source records attributed to Stein, G..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Beyond singular values and loop shapes

The status of singular value loop-shaping as a design paradigm for multivariable feedback systems is reviewed. It shows that this paradigm is an effective design tool whenever the problem specifications are spacially round. The tool can be arbitrarily conservative, however, when they are not. This happens because singular value conditions for robust performance are not tight (necessary and sufficient) and can severely overstate actual requirements. An alternate paradign is discussed which overcomes these limitations. The alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The state of the art currently permits analysis of feedback systems within this new paradigm. Synthesis remains a subject of research.

Stein, G.↗
NASA NTRS1985

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implications of the existence of such infinite-gain operators is that: (1) sinusoidal reference inputs at specific frequencies and/or (2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

Rohrs, C. E.↗
NASA NTRS1985

Some design guidelines for discrete-time adaptive controllers

There have been many algorithms proposed for adaptive control which will provide globally asymptotically stable controllers if some stringent conditions on the plant are met. The conditions on the plant cannot be met in practice as all plants will contain high frequency unmolded dynamics therefore, blind implementation of the published algorithms can lead to disastrous results. This paper uses a linearization analysis of a non-linear adaptive controller to demonstrate analytically design guidelines which aleviate some of the problems associated with adaptive control in the presence of unmodeled dynamics.

Rohrs, C. E.↗
NASA NTRS1984

Robustness and modeling error characterization

The results on robustness theory presented here are extensions of those given in Lehtomaki et al., (1981). The basic innovation in these new results is that they utilize minimal additional information about the structure of the modeling error, as well as its magnitude, to assess the robustness of feedback systems for which robustness tests based on the magnitude of modeling error alone are inconclusive.

Lehtomaki, N. A.↗
NASA NTRS1984

Adaptive control with variable dead-zone nonlinearities

It has been found that fixed error dead-zones as defined in the existing literature result in serious degradation of performance, due to the conservativeness which characterizes the determination of their width. In the present paper, variable width dead-zones are derived for the adaptive control of plants with unmodeled dynamics. The derivation makes use of information available about the unmodeled dynamics both a priori as well as during the adaptation process, so as to stabilize the adaptive loop and at the same time overcome the conservativeness and performance limitations of fixed-dead zone adaptive or fixed gain controllers.

Orlicki, D.↗
NASA NTRS1983

Conic sectors for sampled-data feedback systems

The conic-sector analysis of the closed-loop stability and robustness of a multivariable-analog-system controller based on sampled-data feedback compensation is investigated. Conic sectors and sampled-data feedback systems are defined, and the existence of a conic sector containing a sampled-data operator is established mathematically. An example is presented to prove that the conic sector is computable and gives sufficient conditions of closed-loop stability. A procedure for determining sampled-data-operator gain is also derived.

Thompson, P. M.↗
NASA NTRS1982

Angles of multivariable root loci

A generalized eigenvalue problem is demonstrated to be useful for computing the multivariable root locus, particularly when obtaining the arrival angles to finite transmission zeros. The multivariable root loci are found for a linear, time-invariant output feedback problem. The problem is then employed to compute a closed-loop eigenstructure. The method of computing angles on the root locus is demonstrated, and the method is extended to a multivariable optimal root locus.

Thompson, P. M.↗
NASA NTRS1982

Self-tuning regulator design for adaptive control of aircraft wing/store flutter

The application of the self-tuning regulator concept to adaptively control aircraft wing/store flutter instability is described. A simple design based on a reduced-order aircraft model has been successfully tested on a high-order simulation of an advanced aircraft, and performance was found to be comparable to another design using on-line maximum likelihood identification of plant parameters. The main advantage of the self-tuning regulator is its simplicity, while the main disadvantage is the inadequacy of prior performance guarantees.

Johnson, T. L.↗
NASA NTRS1982

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally asymptotically stable under certain assumptions, the key ones being (1) that the number of poles and zeroes of the unknown plant are known, and (2) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be guide small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. Previously announced in STAR as N83-16061

Rohrs, C. E.↗
NASA NTRS1981

F-8C adaptive control law refinement and software development

An explicit adaptive control algorithm based on maximum likelihood estimation of parameters was designed. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm was implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer, surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software.

Hartmann, G. L.↗
NASA NTRS1981

Multivariable feedback design - Concepts for a classical/modern synthesis

This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue - feedback design in the face of uncertainties - and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results.

Doyle, J. C.↗
NASA NTRS1981

Robustness tests utilizing the structure of modelling error

The present investigation is essentially concerned with the extension of results presented by Lehtomaki et al. (1981) on the robustness of multivariable linear time invariant feedback control systems. The work reported by Lehtomaki et al. is based on a multivariable version of Nyquist's theorem from which several robustness theorems were derived. In connection with the current investigation a slightly more general approach based on Nyquist's theorem is given in a fundamental robustness theorem from which various robustness tests may be obtained. A fundamental characterization of robustness is considered, and important tools from matrix theory are introduced. Attention is given to robustness tests and unstructured model error, and a robustness analysis for linear systems with structured model error.

Lehtomaki, N. A.↗
NASA NTRS1981

Analytical verification of undesirable properties of direct model reference adaptive control algorithms

The present investigation is concerned with a new method, called 'final approach analysis', which has been developed to analyze the dynamic properties of a class of direct adaptive control algorithms. Particular attention is given to the robustness of these algorithms to a number of aspects. These aspects are related to the generation of high frequencies in the plant control signal, to excessive bandwidth of the adaptive control loop resulting in excitation of unmodeled dynamics, and, consequently, leading to dynamic instability of the closed-loop adaptive system, and, thirdly, to noise corrupted measurements. The final approach analysis is useful because it can be used in a constructive way to adjust the adaptive gains so as to limit the closed-loop system bandwidth and to ameliorate some of the undesirable characteristics of existing adaptive algorithms.

Rohrs, C. E.↗
NASA NTRS1980

Asymptotic Eigenstructures

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Thompson, P. M.↗
NASA NTRS1980

Analysis techniques for multivariate root loci

Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.

Thompson, P. M.↗
NASA NTRS1980

Asymptotic eigenstructures

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain feedback decouples into single input single ouput systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Thompson, P. M.↗
NASA NTRS1979

Digital adaptive controllers for VTOL vehicles. Volume 1: Concept evaluation

A digital self-adaptive flight control system was developed for flight test in the VTOL approach and landing technology (VALT) research aircraft (a modified CH-47 helicopter). The control laws accept commands from an automatic on-board guidance system. The primary objective of the control laws is to provide good command-following with a minimum cross-axis response. Three attitudes and vertical velocity are separately commanded. Adaptation of the control laws is based on information from rate and attitude gyros and a vertical velocity measurement. The final design resulted from a comparison of two different adaptive concepts--one based on explicit parameter estimates from a real-time maximum-likelihood estimation algorithm, the other based on an implicit model reference adaptive system. The two designs were compared on the basis of performance and complexity.

Hartmann, G. L.↗