NSERC-Toyota-Maplesoft Industrial Research Chair in
Mathematics-Based Modeling and Design

In June 2009, Maplesoft entered into a partnership with the University of Waterloo, the Natural Sciences and Engineering Research Council (NSERC), and Toyota Corporation to produce new methods for modeling physical systems. The Industrial Research Chair was granted to Dr. John McPhee, from the Department of Systems Design Engineering at the University of Waterloo, and then Executive Director of the Waterloo Centre for Automotive Research (WatCAR).

Project Goals

Current engineering design uses computer models to explore different product concepts and evaluate their performance. Unfortunately, most existing models are numerical, hiding the physics behind reams of data. A more natural way to model a system is to use mathematics, and the main goal of this research is to develop the theory and computer algorithms necessary to create engineering models in a mathematical form that can be easily viewed and shared between colleagues. This will speed up the "model-based design" of new products, an approach that is being embraced by the automotive industry as it strives to become more efficient and responsive to consumer demands. Dr. John McPhee and his team are collaborating with computer experts at Maplesoft and engineers at Toyota to develop these math-based models and computer simulations, with a focus on automotive applications such as vehicle dynamics, powertrains and hybrid electric vehicles.

The results of this ground-breaking work is being shared with the engineering community through published research papers and shared models.

Research Papers and Models


Below you will find many of the research results from this project. Often, the models themselves are included.  Note that these models were developed using the version of MapleSim available at the time the research was done, and they have not been tested in the current release of MapleSim. 

LICENSE: You may use the models for internal, non-commercial research and development purposes. However, we encourage you to contact Maplesoft if you are interested in using these applications in your own activities, as we may have updated and/or expanded versions of these models available.


  Symbolic Sensitivity Analysis of Math-Based Spark Ignition Engine with Two-Zone Combustion Model
2014 SAE International

  Efficient Control-oriented Combustion Modelling of Internal Combustion Engines
H. Adibi Asl, R. Fraser, J. McPhee
Proceedings of Combustion Institute – Canadian Section Spring Technical Meeting

  Parameter Identification of a Quasi-Dimensional Spark- Ignition Engine Combustion Model
2014 SAE International

  Internal Combustion Engine Modelling with Multibody Dynamics and Cycle-by-cycle Spark Ignition
H. Adibi Asl, R. Fraser, J. McPhee
Proceedings of The Canadian Society for Mechanical Engineering International Congress 2014, CSME International Congress 2014

  Mean value engine model including spark timing for powertrain control application
2013 SAE International
Download Model. Created in MapleSim 4.

Torque Converter

  Math-based torque converter modelling to evaluate damping characteristics and reverse flow mode operation
International Journal of Vehicle Systems Modelling and Testing, 2014, Vol. 9, No. 1 pp. 36 – 55

  Math-Based Modeling and Parametric Sensitivity Analysis of Torque Converter Performance Characteristics
2011 SAE International

  Modeling Torque Converter Characteristics in Automatic Drivelines: Lock-up Clutch and Engine Braking Simulation
A. Asi, N. Asad, J. McPhee, 2012
Proceedings of the 14th International Conference on Advanced Vehicle Technologies (AVT)

Download Model. Created in MapleSim 4.


  Physics-Based Models, Sensitivity Analysis, and Optimization of Automotive Batteries
2014 SAE International

  Comparison of Optimization Techniques for Lithium-ion Battery Model Parameter Estimation
2014 SAE International

  A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation
Journal of Power Sources 256 (2014) 410–423

  Mathematical Modeling and Symbolic Sensitivity Analysis of Ni-MH Batteries
2011 SAE International

  Simplification and order reduction of lithium-ion battery model based on porous-electrode theory
Journal of Power Sources 198 (2012) 329– 337
Download Model. Created in MapleSim 4.5

  Dynamic modeling of electrochemical systems using linear graph theory
Journal of Power Sources 196 (2011) 10442– 10454
Download Model. Created in MapleSim 4.5

Electric and Hybrid Electric Vehicles

  A Comparative Analysis of Route-Based Power Management Strategies for Real-Time Application in Plug-In Hybrid Electric Vehicles
M. Vejedi, A. Taghavipour, N. L. Azad, J. McPhee
Proceedings of the 2014 American Control Conference

  Design and evaluation of a real-time fuel-optimal control system for series hybrid electric vehicles
International Journal of Electric and Hybrid Vehicles, 2012 Vol.4, No.3, pp.260 - 288

  Predictive Power Management Strategy for a PHEV Based on Different Levels of Trip Information
Proceedings of the 2012 IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling

  Symbolic Math-Based Battery Modeling for Electric Vehicle Simulation
Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
Download Model. Battery model created in MapleSim 4.5. Electric vehicle model created in MapleSim 3

  Mathematics-Based Modeling of a Series-Hybrid Electric Vehicle
Proceedings of the 5th Asian Conference on Multibody Dynamics 2010

  Development of a High-Fidelity Series-Hybrid Electric Vehicle Model using a Mathematics-Based Approach
2011 SAE International
Download Model. Created in MapleSim 4.5

  High-fidelity modeling of a power-split plug-in hybrid electric powertrain for control performance evaluation
A. Taghavipour, R. Masoudi, N. L. Azad and J. McPhee, 2013
Proceedings of the ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference

Download Model. Created in MapleSim 4.5


  A three-dimensional musculoskeletal driver model to study steering tasks
Engineering Conference

  Optimal disturbance rejection control design for Electric Power Steering systems
2011 IEEE Conference on Decision and Control and European Control Conference

  Study of Human Steering Tasks using a Neuromuscular Driver Model
N. Mehrabi, M. S. Shourijeh, and J. McPhee
Proceedings of 11th International Symposium on Advanced Vehicle Control (AVEC '12)

Model Reduction

  Reduction of vehicle suspension models to single-degree-of-freedom equivalent kinematic joints
Proceedings of the ECCOMAS Thematic Conference Multibody Dynamics 2013

  Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization
Archive of Mechanical Engineering. Volume LX, Issue 1, Pages 23–35

  Using Gröbner bases to generate efficient kinematic solutions for the dynamic simulation of multi-loop mechanisms
Journal of Mechanism and Machine Theory 52 (2012) 144–157

Dr. John McPhee, Professor, Systems Design Engineering, University of Waterloo, and NSERC/Toyota/Maplesoft Industrial Research Chair, Mathematics-based Modeling and Design
Dr. John McPhee's main area of research is multibody system dynamics, with principal application to the analysis and design of vehicles, mechatronic devices, and biomechanical systems. He has won many awards, including a Premier's Research Excellence Award and the I.W. Smith Award from the Canadian Society of Mechanical Engineers. He completed his term in 2009 as the Executive Director of the Waterloo Centre for Automotive Research, spending a sabbatical year at the Toyota Technical Center in Ann Arbor, Michigan. He holds a Ph.D. in mechanical engineering from the University of Waterloo, Canada.