Mathematical modeling and optimization increase vehicle design efficiency and productivity

Balancing fuel-efficiency and safety requirements against the market demand for greater performance—while trying to reduce design and prototyping costs—has always been a major challenge. To achieve this, automotive manufacturers are increasingly replacing traditional passive components with active systems in their vehicle designs. This has driven a dramatic increase in the number of on-board controllers—in newer model vehicles it is not uncommon to find 50 or more—where the control software determines the dynamic behavior of the system.

This automotive electronics proliferation, of course, presents its own problems: Embedded software is expensive to develop, and bug-free software even more so. In addition, in order to reduce time-to-market, component hardware is often developed in parallel with the controller. Thus engineers face developing and testing the control software without access to the real plant. As a result, the demand for better understanding of the dynamics, and the ability to produce high-fidelity mathematical (or "physical") models of vehicular systems that can be used in hardware-in-the-loop (HIL) systems to test the prototype control code, has reached a critical point for many companies.

Engineers in these companies frequently need to go back to basics and develop system models from first principles—deriving the equations that describe the system (often as systems of differential equations and algebraic differential equations), solving them, and then implementing the model in an engineering simulation tool, such as Simulink from The MathWorks.

The development of the system (or "plant") model can be a time-consuming stage, often taking up to 80% of the total project time. Even the use of tools like MATLAB and Simulink still requires significant manual manipulation of the math to get it into a form that can be used. All of this is time-consuming, costly, and error-prone.

Such hurdles are why general-purpose mathematical solving tools like Maple are used for carrying out mathematical derivations of engineering system models. Using this approach, the engineer arrives at very concise and much more computationally efficient models than models developed using more traditional approaches.

For example, something as simple as a DC Motor requires the solution of a system of two differential equations (DEs) that need to be rearranged into a form that can then be constructed using system blocks. This done, the actual construction can still be cumbersome within Simulink. With Maple, you simply enter the system of DEs and it is evaluated in a form that can be readily imported into Simulink.

View a full-size image