Engineering topics
Publications and source records attributed to Athans, M..
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.
The design of a multivariable feedback control system for the Pratt and Whitney F-100 turbofan jet engine is a challenging task for control engineers. This paper employs a linearized model of the F-100 engine to demonstrate the use of the newly developed Linear Quadratic Gaussian/Loop Transfer Recovery (LQG/LTR) design methodology, which adopts an integrated frequency-domain and time-domain approach to multivariable feedback control synthesis so as to meet stability-robustness, command-following, and disturbance-rejection specifications.
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.
The state of stochastic system and control theory as it impacts restructurable control issues is addressed. The multivariable characteristics of the control problem are addressed. The failure detection/identification problem is discussed as a multi-hypothesis testing problem. Control strategy reconfiguration, static multivariable controls, static failure hypothesis testing, dynamic multivariable controls, fault-tolerant control theory, dynamic hypothesis testing, generalized likelihood ratio (GLR) methods, and adaptive control are discussed.
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.
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering techniques, for application in VTOL aircraft landing. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.
Recently Zames (1981) has introduced the so-called model reference transformation which can be used to conveniently parameterize the class of linear time-invariant multivariable compensators that lead to stable feedback control systems. A very popular design methodology for designing stable and robust multivariable control systems is that based on the Linear-Quadratic-Gaussian (LQG) methodology with Loop Transfer Recovery (LTR). Thus, it is natural to inquire upon the relationship between the Zames representation and the LQG/LTR compensators. This paper summarizes this relationship.
It has been shown that several similar Model Reference Adaptive Controllers (MRAC's) are globally stable under certain restrictive assumptions, including the assumption that the order and relative degree of the plant are exactly known, and that no disturbances are present. Under certain 'sufficiently rich' excitation conditions, the origin is globally asymptotically stable for the adaptive controller parameter error. The time-evolution of the parameter error vector represents the key factor to the stability of the adaptive controller. This time-evolution is described by a complicated set of time-varying nonlinear differential equations. The present investigation is concerned with an approximate analysis technique for studying the long term trends of the parameter error vector trajectory for an adaptive controller under periodic excitation.
A landing scheme for landing V/STOL aircraft on rolling ships was sought using computerized simulations. The equations of motion as derived from hydrodynamics, their form and the physical mechanisms involved and the general form of the approximation are discussed. The modeling of the sea is discussed. The derivation of the state-space equations for the DD-963 destroyer is described. Kalman filter studies are presented and the influence of the various parameters is assessed. The effect of various modeling parameters on the rms error is assessed and simplifying conclusions are drawn. An upper bound for prediction time of about five seconds is established, with the exception of roll, which can be predicted up to ten seconds ahead.
The purpose of this informal paper is to discuss certain robustness issues associated with existing adaptive control algorithms. A modeling framework for incorporating high-frequency unknown dynamics in the adaptive control framework is suggested. Possible fundamental limitations of existing adaptive control framework is suggested. Possible fundamental limitations of existing adaptive control algorithms are also discussed, with emphasis upon their closed-loop stability properties in the presence of unmodeled high-frequency dynamics.
The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory.
A method of analysis for digitally implemented (hybrid) control systems based on conic sector concepts from functional analysis was established. Data sampling is addressed.
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
In the present study the estimation of the heave and pitch motion of a ship is considered, using Kalman filtering techniques. A significant part of the study is devoted to constructing appropriate models for the sea and the ship. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A numerical application is considered for a DD-963 destroyer.
In order to provide a theoretical tool well suited for use in characterizing the stability margins (e.g., gain and phase margins) of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with 'centers' and 'radii' determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency-dependent convex set of modeling errors (including nonlinearities, gain variations, and phase variations) which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed-loop stability in the presence of such frequency-dependent modeling errors, even when the modeling errors occur simultaneously in all loops.
The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Available and new results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, robustness results associated with multivariable control systems designed on the basis of linear-quadratic (LQ) and the linear-quadratic Gaussian (LQG) design methodologies are presented.
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.