Title: Software for modeling and simulation of hybrid systems

Partners

• Slovak University of Technology in Bratislava, Faculty of Chemical and Food Technology, Department of Inform. Eng. and Process Control (M. Kvasnica, M. Herceg)
• ETH Zurich, Automatic Control Laboratory (M. Morari)
• ABB Switzerland

Project duration: 2007-2009

Objectives, project description, background, proposed research

Mathematical models of dynamical systems are subject of studies in scientific and engineering communities. In general, there are two kinds of models. The first one is based in physics/chemistry and the second one on empirical results. Mathematical models based on physical, and chemical relations (material and enthalpy balances, thermodynamics, kinetics of chemical reactions) are often used in optimisation and optimal control. These models are attractive as the general model can be precisely tailored to a concrete application. On the other side, empirical models are advantagenous in cases where it is difficult to recover a precise physical model of the plant, either because it is too complicated, or because it is not possible to estimate the values of the model parameters with enough precision.

Other division of models than theoretical and empirical can be linear or non-linear, static or dynamic, lumped or distributed parameters, continuous or discrete, etc. A relatively new class of mathematical models is represented by the class of hybrid models, which are also referred to as hybrid systems. These models combine the elements of continuous dynamics with discrete logic. As an example one can imagine a chemical reactor whose behaviour is described by continuous differential equations, but where certain input variables can either take discrete values, such as active/inactive cooling, or stirring performed in several discontinuous steps (e.g. 3 levels of stirring speed). Hybrid mathematical models are also very well suited to capture the elements of decision-taking, which includes sequences of operations described by IF-THEN-ELSE conditions. This allows one very efficiently to capture the behaviour of non-linear plants by utilizing the concepts of multiple linearizations, where each linearized model has a precisely determined domain of validity. It is worth noting that despite the fact that hybrid models, in general, belong to the class of non-linear systems, the optimal control design for the class of hybrid systems is much less complicated compared to control design based on general non-linear models. It is so due to the fact that the problem of minimizing a performance function subject to the hybrid dynamics can in fact be solved as a mixed-integer problem. Several off-the-shelf efficient solvers exist which are capable of solving this class of problems efficiently.

The tool HYSDEL (HYbrid Systems DEscription Language, http://control.ee.ethz.ch/~hybrid/hysdel/) aims at obtaining mathematical models of hybrid systems. This modelling language uses a syntax simillar to the C-language and offers the users a comfortable, yet powerful way of describing behavior of systems which include continuous and discrete variables, IF-THEN-ELSE conditions and analog-to-digital and digital-to-analog converters. The ABB corporation located in Switzerland, one of the main users of HYSDEL, uses this tool to create mathematical models of cement-producing plants, watter turbines and voltage converters. One of the main drawbacks of the current HYSDEL implementation is the lack of support for vector and matrix variables, which renders the modelling of complex plants a time-consuming job.

This project is aimed at extending the HYSDEL language such that modeling of complex hybrid systems can be performed in an easy and efficient way. The language will be extended to allow to create compositional hybrid systems (i.e. systems which consist of several sub-modules). Moreover, the user will have the possibility to create such composition graphically by joining selected blocks in the MATLAB/SIMULINK envirnoment.