Heinz A. Preisig

A prototype computer-aided modelling tool for life-support system models

Based on the canonical decomposition of physical-chemical-biological systems, a prototype kernel has been developed to efficiently model alternative life-support systems. It supports (1) the work in an interdisciplinary group through an easy-to-use mostly graphical interface, (2) modularized object-oriented model representation, (3) reuse of models, (4) inheritance of structures from model object to model object, and (5) model data base. The kernel is implemented in Modula-II and presently operates on an IBM PC.

On the Design of a Simple Solver for Nonlinear Two-Point Boundary Value Problems

Abstract The underlying principles and structure of an easy-to-use solver for two-point boundary-value problems described by sets of nonlinear ordinary differential equations is presented. The solution approach is based on the finite difference approximations for the derivatives. The Newton—Raphson iterative scheme with analytical Jacobians is used for solving the resulting large-scale nonlinear set of algebraic equations. Part 1 of the paper presents an in-depth analysis of the general problem and the solution method which results in a split of the overall problem into two distinct parts, a pure mathematical analytical part, which does not depend on the chosen numerical solution method, and a numerical part, which implements all the details of the numerical procedure. The prototype implementation, presented in Part 2, is based on this separation. It makes use of different programs which are specialized for solving particular subproblems identified in the analysis. An algebraic manipulator is used to aid in generating the Jacobians analytically and a matrix-oriented environment is used to implement the numerical matrix operations. The resulting package requires only the essential information from the user, namely the model equations and the solution domain variables as well as initial guesses of the solution. The package is a prototype that can be used to solve second-order problems based on three-point polynomial approximations of the derivatives.

The Application of Finite Automata Theory to Sequential Control of Chemical Processes

Abstract The design of a hierarchical logical programmable controller using finite automata theory for a sample chemical plant is discussed. The state explosion problem is approached by suggesting logical arguments to split the Mealy automaton a priori into smaller elements by vertical and horizontal decomposition. The step by step approach to the state aggregation problem results in a hierarchical set of automata which are easy to design and are of practical relevance, a feature that should make the approach attractive for industrial applications.

A study of dynamic system modelling

Abstract Partial differential equations for the dynamics of heat transfer across a wall between two well mixed regions are represented by finite difference. collocation and finite element models of different order. Comparison of analytical and numerical results in the frequency domain reveal characteristic differences at higher frequencies which are discussed in terms of the algebraic structures of the models.

Estimation of mismatch errors of dynamic models for stirred tank-reactor equipment—I. heat exchange with jacket, impact of model reduction

Abstract Different model reduction techniques are examined for their quality of approximation of the distributed heat transfer between the jacket and the contents. Three techniques are compared, namely finite difference, orthogonal collocation and finite element. Each technique was applied with different order, or which is the same, different number of mesh points in the wall. The modelling mismatch errors are dynamic and thus compared in the frequency domain. The models are studied for the purpose of implementing them in control related procedures, such as observers. Simplicity is thus a requirements, however, should not interfere with the accuracy required by the particular application.

Estimation of mismatch errors of dynamic models for stirred tank-reactor equipment—II. heat dissipation in the contents, impact of mixing

Abstract Negligence of the mixing dynamic in modelling stirred tank reactors introduces dynamic modelling mismatch errors which may be significant when working in higher dynamic regimes. The critical frequency, where the mixing models start to deviate from the ideal STR model, is only slightly higher than the critical frequency for similar errors caused by model reduction of models describing the distributed heat transfer between jacket and contents.

The Jacobi Eigenvalue Criterion: A Dynamic Extension and Stability Theorem

Abstract The Jacobi Eigenvalue criterion is a recently developed, steady state, scaling independent tool for the selection of variable pairing for multiloop control systems (Mijares et al., 1986). This criterion is based on the Jacobi Iteration method for solving sets of linear equations or obtaining the inverse of a matrix. A dynamic extension of the Jacobi Eigenvalue criterion which consists in evaluating the spectral radius of the Jacobi Iteration matrix in the frequency range of interest is presented. The Jacobi Eigenvalue criterion is inherently a diagonal dominance measure, and as such, is readily applied to develop an extension of Rosenbrocks Nyquist stability theorem. The extended Jacobi Eigenvalue criterion is then compared to different interaction and weak coupling measures used for design of decentralized control structures which are based on conditions for generalized diagonal dominance and H-matrices. Two examples are used to illustrate the use of the Jacobi Eigenvalue criterion and its relationship with the other weak coupling measures.

THE JACOBI EIGENVALUE CRITERION: A DYNAMIC EXTENSION AND STABILITY THEOREM

The Jacobi Eigenvalue criterion is a recently developed, steady state, scaling independent tool for the selection of variable pairing for multiloop control systems (Mijares et al., 1986). This criterion is based on the Jacobi Iteration method for solving sets of linear equations or obtaining the inverse of a matrix. A dynamic extension of the Jacobi Eigenvalue criterion which consists in evaluating the spectral radius of the Jacobi Iteration matrix in the frequency range of interest is presented. The Jacobi Eigenvalue criterion is inherently a diagonal dominance measure, and as such, is readily applied to develop an extension of Rosenbrocks Nyquist stability theorem. The extended Jacobi Eigenvalue criterion is then compared to different interaction and weak coupling measures used for design of decentralized control structures which are based on conditions for generalized diagonal dominance and H-matrices. Two examples are used to illustrate the use of the Jacobi Eigenvalue criterion and its relationship with the other weak coupling measures.

Stability and Performance Relations between Triangular and Decentralized Control Systems

Preliminary results which help to understand the relationship between the stability and performance characteristics of diagonal and triangular control structures for 2×2 systems are presented. The results may be applied to larger systems when G(s) is a consistently ordered matrix. The presented development is derived from the theory of linear iterative methods and its duality with control theory.