Physics-based modelling - or physical modelling - and simulation have become an essential part of the automotive design process. Through the use of powerful mathematical modelling tools, accurate prediction of the behaviour of engineering systems can save millions of dollars in the prototyping and production stages of a product development. This has motivated many companies to invest heavily in model-based design and simulation tools.
Furthermore, the number of controllers in vehicle systems has dramatically increased over the last 20 years. From power-train management through to stability control, modern cars can have upwards of 20 controllers. This has driven the use of physical modelling tools for accurate plant characterisation; usually the first stage in control system development, and typically the most time-consuming.
However, 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 existing tools has changed little in over 50 years. As pressures grow on their time, engineers are now finding this approach onerous because of the effort required in preparing the model manually 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, one need only try asking a user of a present-day modelling tool to enter an electric circuit! But the issues are not restricted to entering electric circuits. What if one wishes to connect that circuit to an electric motor, which is in turn connected to a transmission and drive train, including pneumatic tyres, so that one can determine the effect of a change to the circuit on the dynamic behaviour of a vehicle?
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 serve to increase the complexity of physical models to the point where traditional tools are woefully inadequate.
Good news
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. In other words, 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 leaders in the field agree 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.
Through the collaboration between Toyota and Maplesoft all areas of engineering development such as engines, transmissions, suspensions, braking systems, climate control systems, and in-vehicle electronics stand to gain from the use of the new set of modelling tools.
As part of the partnership, Maplesoft and Toyota have formed a Physical Modeling Consortium, which brings together leaders in the automotive industry to share ideas and advance the development of rapid plant modelling methodologies based on symbolic computation. To find out more about this initiative, please contact pmc@maplesoft.com.
- Paul Goossens is director, commercial markets, at Maplesoft