Raymond E. Goodson

Parameter identification in distributed systems: A synthesizing overview

This paper surveys the distributed system parameter identification problem and concludes that it can be treated as a series of largely independent subproblems, each of which must be considered in any attempt to treat the problem in applications. An approach is discussed which treats in a unified manner all the inherent subproblems. An annotated bibliography of the literature in the field analyzes the contributions of the various authors to each step in the solution of problems of parameter identification in distributed systems. The applications of existing techniques are discussed, and the paper closes with conclusions and recommendations for future work in the field.

A definition and some results for distributed system observability

The measurement problem in distributed system feedback is posed as an observability question. Sensor location and the information content of the resulting signals relative to a partial differential equation model are the primary questions. A new definition of observability is introduced which allows the specification of the space-time domain where the system is observable. The definition is also applied to the problem of observing a particular set of solution modes. Observability results are given for particular classes of equations. Examples indicate a rationale for using the results in selecting measurement locations in distributed systems.

On parameter identification for distributed systems using Galerkin's criterion

A method is presented for estimating parameters in distributed parameter systems. The system is assumed to be modeled by a set of partial differential equations whose form is known to within a set of unknown constant parameters. Galerkins Method is used to transform the partial differential equations into a set of ordinary differential equations. The approach to the identification problem is given in a step by step procedure. Three optimization schemes for estimating the unknown parameters are discussed. They are a steepest descent method, a search technique, and nonlinear filtering.

Distributed Parameter Identification Using the Method of Characteristics

Abstract : A method is presented for estimating parameters in distributed systems which can be analyzed by the method of characteristics. Both the very real problems of noisy measurements and limited available measurement transducers are discussed in some depth. Convergent algorithms are developed using a Robbins-Munro stochastic approximation scheme. The extension of these methods to the identification of functions, multidimensional systems and diffusion terms is considered. (Author)

Adaptive computer control of a glass coating process

This paper presents the development and implementation of an on-line adaptive controller in an industrial process. The process, drawing and coating of glass rod used in the manufacture of resistors, is described briefly and the control problem formulated. The proposed control system, based on an on-line digital computer system, is outlined. Synthesis of the adaptive controller, including an identification technique and closed loop optimization strategy, is presented. Software development, testing, and implementation of the controller is described; special emphasis is given to on-line programming techniques. Results of the implementation are presented and the development summarized.

A Survey of Parameter Identification in Distributed Systems

Abstract In this paper a survey is made of the main results in parameter identification for systems described by partial differential or integral equations. The work in the field is categorized by defining a series of subproblems which are important steps when solving an identification problem in applications. An annotated bibliography serves to relate the contributions of the various authors to each of the subproblems. Although applications of the available techniques are discussed, no main thrust is evident due, in part, to the wide diversity of applications areas. Furthermore, the majority of papers are not applications oriented. The paper closes with conclusions and recommendations for future work in the field.

A Dynamic Mathematical Model of a Glass Tank, Refiner and Forehearth

Abstract A dynamic mathematical model of a glass melting and conditioning system has been developed based on the conservation of energy and mass. Emphasis has been placed on the dynamic interactions between the gas, batch, glass, and refractory temperatures and glass flow rates in the tank, refiner and forehearth. Models of the composition, glass levels and flow rates, and forehearth centerline drawdown have also been developed, as have design studies of model approximations, parameters and sensitivity coefficients. A digital computer program simulates the dynamic models and design studies. Operating data from a tank, refiner and forehearth have been taken for comparison with the energy and mass flow model.

Parameter identification for the beam equation using Galerkin's criterion

The identification of parameters in the beam equation is investigated. The equations are assumed known to within a set of unknown constant parameters. The boundary and initial conditions associated with the Partial Differential Equation (PDE) are assumed known explicitly. This paper utilizes Galerkins Criterion of the Method of Weighted Residuals (MWR) to transform the PDE problem into an ordinary differential equation problem. The step by step identification procedure is illustrated by the identification of parameters in the beam equation. A test apparatus was constructed and the parameters of the test beam were identified using the actual measurements as input data for the identification procedure.

Modeling for Automatic Control and Process Design

Abstract The effect of mathematical and physical modeling of processes has had relatively little effect on the glass industry. However, significant modeling results are available as indicated by a wide range of publications. In this paper, the published modeling work is grouped by area with discussion where appropriate. In addition, the major physical phenomena along a glass line are discussed with an assessment of the degree of difficulty in modeling them to an accuracy sufficient for either process control or process design. In this assessment the major assumptions and simplifications currently used in model derivative and specification are noted. It is concluded that many of the phenomenon are of such a complexity that models have not had sufficient accuracy for design purposes. One of these areas is the furnace with the main problems being the convection currents in the melt, the radiative heat transfer, and the melting physics and chemistry. Finally, the results of a questionnaire sent to glass industry technical personnel polling modeling efforts and results are discussed. An extensive bibliography of modeling work is a part of the paper.

Mapping stability regions in planar slices

A method is developed for determining the stability region in the loop-gain space for a linear multivariable control system. Two new interpretations of the return difference determinant are employed, allowing the stability region boundaries to be determined accurately by means of an algorithm.