## European models promote fidelity

Laurent Bernardin, chief scientist and vice president of R&D, Maplesoft

Physics-based modelling – or physical modelling – for virtual prototyping of engineering products has brought about dramatic savings in time and cost over the past 20 years. Furthermore, the increasing use of controllers in engineering products has driven the use of physical modelling tools for accurate plant characterisation, which is usually the first and often the most timeconsuming stage in control system development.

Accurate prediction of the behaviour of engineering systems, through the use of powerful mathematical modelling tools, can save millions of dollars in the prototyping and production stages of a product. This has motivated many engineering organisations to invest heavily in model-based design and simulation tools.

However, it is becoming apparent that existing modelling tools fall short of what is required to do this effectively, and physical modelling of engineering systems has become a hot topic among engineers as they hit these limitations. Fortunately, a new wave of methodologies, technologies, and products is developing to address the issues faced by engineers, and one particular European initiative is emerging as the leader in this movement.

But first, a look at the limitations in current practices is required. If you consider the history of engineering modelling and simulation, you will note that the block-diagram approach employed by some tools has changed very little in more than 50 years. In our opinion, the signal-flow paradigm it uses is a legacy from the days of the analogue computer.

As pressures grow on their time, engineers are now finding this approach to physical modelling to be onerous because of the time and effort required to manually prepare the model for representation as a block diagram. The approach is also inherently weak in certain computational respects, such as poor handling of algebraic loops. If you need a powerful illustration of these limitations, try using a block-diagram approach to enter an electric circuit!

To address these issues, a new approach to physical modelling is emerging from a collaboration between several European universities, tool vendors, and industrial partners. The Modelica Association (www.modelica.org) was started in 1996 as an initiative to develop a standard model-definition language that would allow convenient, component-oriented modelling of complex engineering systems requiring the inclusion of multiple domains such as mechanical, electrical, electronic, hydraulic, thermal, control, electric power, or process-oriented subcomponents. Modelica models capture and manage all of the necessary relational, physics, and mathematical information for complex systems. Because it is better suited for handling the mathematical framework of model development, Modelica makes detailed models easier to develop.

The Modelica language allows use of an object-oriented representation that permits a very easy definition of a system model by graphically describing its topology: simply put, users connect components and define how they are related without having to worry about which signals are inputs and which are outputs. This means, for example, that an electric circuit (a classic example of a topological representation) looks like an electric circuit on a computer screen: this circuit can then be easily connected to a mechanical system model through motor models, shafts, gears, and so on.

To introduce a little jargon, this topological approach to model definition is called ‘acausal’ and lifts many of the restrictions imposed by the signal-flow, or ‘causal’, approach. This has made the mathematical formulation of system models very easy, but has led to some challenges in running simulations. Causal block-diagram tools only need to solve systems of ordinary differential equations (ODEs), but acausal modelling introduces a different class of mathematical model: Differential Algebraic Equations (DAEs). These are systems that include both ODEs and algebraic equations that are introduced by added physical constraints. Depending on the nature of these constraints, the DAE problem increases in complexity, usually indicated by an increase in the DAE ‘index’.

The development of generalised solvers for high-index DAEs is the subject of a great deal of research, and it is acknowledged by leaders in the field that symbolic computation will play a major role. My company has been actively engaged in developing DAE solvers that incorporate leadingedge symbolic and numeric techniques for solving high-index DAEs, for many years.

Until now, the use of Modelica has been largely focused within European companies that were early to adopt this new modelling methodology, and it is beginning to impact mainstream engineering there. However, word is spreading in North America: there is a growing move towards offering modelling tools that use the topological modelling approach, described above, for multidomain systems, and we’re hoping to lead that charge with the launch of a new product later this year.

One of the early proponents of Modelica, Dr Michael Tiller, VP of modelling research and development with US engineering consulting firm Emmeskay, said: ‘Modelica was started as an effort to develop a non-proprietary approach to modelling. The goal was to make modelling an open process allowing free collaboration between industry, universities, and tool vendors. As the growth of the internet has shown, open standards are much better for consumers than so-called “walled gardens”.’

After 50 years, we believe the signal-flow block diagram is coming to the end of its useful life for physical modelling. With the help of Modelica, we are addressing many of the weaknesses inherent in traditional modelling tools, as well as the challenges of advanced modelling approaches, to feed into the next generation of modelling and simulation tools.