New Methods for Modeling Physical Systems
Figure 1: Example of a series HEV. Images: Maplesoft
Current engineering practices create computer models that are numerical in nature to explore different design concepts and evaluate their performance. However, a more natural way to model a system is to use mathematics. In 2009, Ontario, Canada-based Maplesoft announced a partnership with the University of Waterloo, Ontario; the Natural Sciences and Engineering Research Council (NSERC), Ontario; and Toyota Corp., to produce methods for modeling physical systems.
The main goal was to develop the theory and computer algorithms necessary to automatically create engineering models in a mathematical form, which in return would speed up the system-level modeling approach for new products.
Using MapleSim, a number of multidomain system models comprising mechanical, electrical, hydraulic, and other components have now been successfully created by the research team for hybrid electric vehicle (HEV) architecture design.
Figure 1 shows a series HEV example developed by the design team, in which an internal combustion engine drives a generator, which recharges a battery, which drives two electric motors, which ultimately power the vehicle.
Using MapleSim, the team created simple and advanced controllers for the driver, the distribution of power within the system, and the electronic control. The driver model looks at a desired federal test procedure (FTP) drive cycle, compares it to the actual vehicle velocity, and then adjusts the power until the actual velocity and desired velocity match each other.
Figure 2: Schematic of the controls within the power-split hybrid electric vehicle.
Most of the components in the power-split HEV model are taken from the standard built-in MapleSim library, including all the components necessary to build a full multibody dynamic model of the vehicle, with Pacejka tires for asphalt roads, power-split device transmission, and electric motors and generators. The battery and internal combustion engine were modeled using MapleSim’s Custom Component capabilities.
A mean-value internal combustion engine model was developed, using equations available in standard engineering text books. Using the HEV model to simulate an FTP drive cycle, the desired and the actual speed of the vehicle versus time was plotted, and the state of charge of the battery viewed.