W. Marquardt

Structural analysis of differential-algebraic equation systems—theory and applications

Abstract The choice of a feasible numerical method for the solution of a Differential-Algebraic Equation (DAE) model of general type F(z,z,u) = 0 requires knowledge about its solvability, index, number and type of dynamic degrees of freedom as well as the set of equations to be satisfied by consistent initial conditions. Furthermore, a set of design quantities has to be specified. Important properties of DAEs are concisely defined and related among each other. A new structural algorithm which determines structural properties of DAEs is developed and compared to another conceptually different structural algorithm proposed earlier by Pantelides [(1988) SIAM J. Sci. Stat. Comput. 9 , 213 231]. Both algorithms were implemented as structural analysis tools to provide a fast a prion characterization of general DAEs F(z,z,u)=0 prior to any numerical solution. Some examples illustrate how the information obtained can be used to address various significant issues in process modelling, simulation, and in the evaluation of control configurations for nonlinear systems.

DIVA : an open architecture for dynamic simulation

Abstract During 3 yr of application of the dynamic flowsheet simulator DIVA, existing features have been extended and new capabilities have been added. This expansion leads to an improved open architecture for the dynamic simulation environment. Interfaces are developed for interactive communication with the user during all stages of the simulation. A graphical flowsheet editor is used to define the simulation problem. The execution of a simulation problem is organized in separately operable tasks including the simulator, system theoretical methods, a graphic utility and a post processor. For real-time application a data management system and a real-time process interface are implemented. Communication among all tasks is divided into a command transfer level and a process database.

DIVA: a powerful tool for dynamic process simulation

Abstract A program for dynamic simulation of chemical plants is presented. The dynamic plant equations and the corresponding Jacobian matrix are generated automatically. The full exploitation of sparse matrix techniques in combination with stiff ODE solvers allows an efficient solution of all equations in parallel.

An observer-based solution of inverse heat conduction problems

Abstract An inverse heat conduction problem arises when temperature measurements are taken in the interior of a body, and the temperature and heat flux on the surface are desired. A new approach to the solution of this class of problems is introduced. It relies on the concept of state and disturbance observers which is well-known from systems theory. The complete temperature profile in the heat conducting body as well as the surface heat flux and temperature can be computed from one or several interior temperature measurements by means of a non-linear distributed parameter observer. The technique is introduced and analysed theoretically by means of a simple tutorial example. The approach is finally applied to a difficult inverse problem of technical significance. The time history of local heat flux and temperature oscillations at the inner surface of an evaporator tube are estimated during transition boiling conditions. Experimental results with boiling refrigerant R114 flowing upward in an electrically heated tube are presented.

Computing consistent initial conditions for differential-algebraic equations

Abstract To solve differential-algebraic equation systems (DAEs) successfully initial conditions must be consistent, i.e. they must satisfy the corresponding extended system of the DAEs. For index one DAEs they can be obtained by either taking an implicit Euler step or solving the extended system together with a feasible set of specifications. We present computational algorithms for determining consistent initial conditions based on either approach. In addition, a purely numerical algorithm reported recently for computing initial values for higher index DAEs is modified here to reduce the computational complexity by using structural information on the DAEs.

An object-oriented representation of structured process models

Abstract Efficient process modeling is a key requirement for widespread use of model-based techniques for process design and operation in an industrial environment. It can only be met by advanced knowledge based software tools to cut down the effort for model development and maintenance. A suitably designed model base providing generic modeling knowledge as well as a validated family of models of varying degree of detail for a certain process is one of the main components of such a modeling system. This contribution focuses on the design of the model base which is treated as a database design problem. Proper process model structuring, formalization of the modeling knowledge by means of an object-oriented data model, and some implementational issues are considered.

Order reduction of non-linear differential-algebraic process models

Abstract A method for order reduction of non-linear differential-algebraic models arbitrary index is presented. The approach is a direct generalization of a method suggested by Pallaske in 1987 for the reduction of explicit differential equation models. It relies on an optimal orthogonal projection of the solution trajectories into a subspace of the original state space. A rigorous development of the reduction technique is given. Strong emphasis is on implementational issues such as the choice of tuning parameters for a particular problem. A theoretical and numerical evaluation of the method is provided. The case studies discussed include the reduction of a strongly non-linear catalytic fixed bed reactor model.

CONCENTRATION PROFILE ESTIMATION AND CONTROL IN BINARY DISTILLATION

Abstract A new physically motivated approach to model based control and estimation of binary distillation is suggested. A nonlinear reduced model which relies on nonlinear wave propagation phenomena in separation processes is used as a starting point for multivariable control system synthesis applying state-space methods. Apart from controlling product compositions using only few temperature measurements along the column, profile estimation is accomplished with moderate additional effort. The resulting linear control system is evaluated in nonlinear simulations of a high purity distillation column. Satisfactory control performance is exhibited.

An Observer-based Solution of an Inverse Heat Transfer Problem in Transition Boiling

Abstract An inverse heat conduction problem arises when temperature measurements are taken in the interiour of a body, and the temperature and heat flux on the surface are desired. A new approach to the solution of this class of problems is introduced. It is based on the concept of state and disturbance observers which is well-known from systems theory. The complete temperature profile in the heat conducting body as well as the surface heat flux and temperature can be computed from one or several interior temperature measurements by means of a nonlinear distributed parameter observer. The technique is applied to the estimation of the time history of local heat flux and temperature oscillations at the inner surface of a tube during transition boiling conditions. After discussion of the design methodology and evaluation of the observer scheme, experimental results with boiling refrigerant R114 flowing upward in an electrically heated nickel tube are given.

Dynamic Process Flowsheet Simulation - An Important Tool in Process Control

Abstract Comfortable tools for control system design and evaluation have gained increasing importance as useful aids in academia and industry. The limited nonlinear simulation capabilities of existing control system design packages are not sufficient for process and control system simulations. The development of detailed dynamic flowsheet simulators and their integration in a computer-aided design (CAD) environment is required for that purpose. The outline of the general purpose dynamic flowsheet simulator DIVA (Dynamische Simulation verfahrenstechnischer Anlagen), which is currently being developed at Universitat Stuttgart is presented below. An illustrative simulation example of a chemical production plant will demonstrate the function and the possibilities offered by the simulator.