Maplesoft, partners develop new methods for modeling physical systems

  • 06-Mar-2013 09:19 EST

A schematic representation of a lithium-ion battery model is shown.

Seeking new, more efficient methods for modeling physical systems, Maplesoft and the University of Waterloo are researching—with support from the Natural Sciences and Engineering Research Council (NSERC) and Toyota—ways to develop the theory and computer algorithms necessary to automatically create engineering models in a mathematical form.

As a result of this research, engineers are now able to build more complex, nonlinear, and high-fidelity models that provide more insight into the actual physics, while also accelerating system-level modeling of new products.

In collaboration with experts from Maplesoft and Toyota, Dr. John McPhee, Executive Director for the Waterloo Centre for Automotive Research (WatCAR), and his research team have used MapleSim to create a number of multidomain system models comprising mechanical, electrical, hydraulic, and other components. MapleSim will be demonstrated at the company’s SAE 2013 World Congress booth (T1) April 16-18 in Detroit, MI.

McPhee and team member Dr. Sam Dao modeled a power-split HEV in MapleSim, with simple and advanced controllers created for the driver, power distribution, and electronic control. The driver model looks at the desired federal test procedure (FTP) drive cycle, compares it to the actual vehicle velocity, and adjusts the power until the actual and desired velocity overlap.

Many of the power-split HEV model’s components were taken from the 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, electric motors, and generators.

“If we want to look at the underlying equations for any of these components, we can easily do so. On the other hand, we don’t need to take the time to assemble any of the component-level equations into the system-level equations. MapleSim takes care of that grunt work for us,” McPhee said.

Because of their complexity, the battery and the internal-combustion engine (ICE) models were developed directly using MapleSim’s Custom Component capabilities.

2-D models of the battery were created, where the response of the system was governed by partial differential equations that model the concentration of solid and liquid ions within the battery. The completely chemistry-based battery model was then converted into a MapleSim Custom Component by taking the mathematical models and directly entering them into a Maple worksheet to define the governing equations for the component.

When compared with existing physical experiment results for the discharge/charge of a battery, the results of the chemistry-based battery model matched very well.

A mean-value ICE model was developed using equations available in standard engineering textbooks. The engine model includes a throttle body, where the input is a throttle valve angle, connected to an intake manifold, which connects to the engine itself where the combustion takes place, followed by a driveshaft.

In the full HEV model, the mean-value engine model connects to the power-split planetary gear set, as do two motor/generators that are powered by the lithium-ion battery pack and controlled by an electrical controller. The output then drives the vehicle model.

When the hybrid vehicle model is used to simulate an FTP drive cycle, the desired and actual speed of the vehicle vs. time are compared, and state of charge of the battery is also plotted. Results showed that during heavy braking maneuvers, the state of charge of the battery increased as a result of energy being recovered from regenerative braking.

“With MapleSim, the model development and analysis time of our power-split HEV model was drastically reduced,” McPhee said. “MapleSim gives you complete flexibility and openness for complex multidomain models, letting you create, analyze, and run system-level models in a fraction of the time it takes with other tools.”

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