Let's get physical

Why the automotive industry needs new tools for design and development.

Physics-based modelling - or physical modelling - and simulation have become an essential part of the automotive design process.

Powerful mathematical modelling tools and the accurate prediction of the behaviour of engineering systems can save millions of dollars in the prototyping and production stages of a product. This has motivated many companies to invest heavily in model-based design and simulation tools.

The number of controllers in vehicle systems has also dramatically increased over the last 20 years: from power-train management through to modern cars, which can have more than 20 controllers. This has driven the use of physical modelling tools for accurate plant characterisation, which is usually the first stage in control system development, and typically the most time-consuming.

Falling short

It is becoming apparent that existing modelling tools fall short of what is required to do this effectively. If we consider the history of engineering modelling and simulation, we see that the block-diagram approach employed by tools like Simulink from MathWorks has changed little in over 50 years.

The signal-flow paradigm it uses is a legacy from the days of the analogue computer. Busy engineers are now finding this approach for physical modelling is onerous because of the effort required to manually prepare the model for representation as
a block diagram.

It is also computationally weak in certain respects, such as poor handling of algebraic loops. For a powerful illustration of these limitations, just ask a Simulink user to try entering an electric circuit.

But the issues are not restricted to electric circuits. What if you want to connect that circuit to an electric motor, which is in turn connected to a transmission and drive train, including pneumatic tyres, so that the effect of a change to the circuit on the dynamic behaviour of a vehicle can be determined?

Creating physical models over multiple domains is notoriously difficult, but the challenges of automotive development demand the inclusion of many different domains, including hydraulics, thermal, gas-flow and chemical reactions. This will only increase the complexity of physical models to the point where traditional tools are woefully inadequate.

New approach

The good news is that a new approach to physical modelling is beginning to emerge. This uses an object-oriented representation that lends itself to very easy definition of the system model by graphically describing its topology: simply put, how components relate to each other by connecting them together, without having to worry about how signals flow between them. For example, an electric circuit looks like an electric circuit on the computer screen.

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 it has introduced a different class of mathematical model: differential algebraic equations (DAEs). These are systems of ordinary differential equations with algebraic equations that are given by added physical constraints in the system.

The development of generalised solvers for complex 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. For this reason, Maplesoft is actively engaged in developing solvers that incorporate leading-edge symbolic and numeric techniques for solving high-index DAEs.

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