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A method to improve the computational efficiency of analyzing wheeled vehicle systems on three-dimensional (3-D) roads has been developed. This was accomplished by creating a technique to incorporate the tire on a 3-D road in a multibody dynamics model of the vehicle with an approach that formulates the governing equations using symbolic formulation. For general handling analysis performed on the vehicle, the tire forces and moments are determined using a tire model that represents the tire as a set of mathematical expressions. Since these expressions need numerical values to determine the forces and moments, a symbolic solution does not exist. Therefore, the evaluation of the tire forces and moments needs to be done during simulation. However, symbolic operations can be used when the governing equations are formulated to develop an efficient method to evaluate these forces.

System identification is an important aspect in model-based control design which is proven to be a cost-effective and time saving approach to improve the performance of hybrid electric vehicles (HEVs). This study focuses on modeling and parameter estimation of the longitudinal vehicle dynamics for Toyota Prius Plug-in Hybrid (PHEV) with power-split architecture. This model is needed to develop and evaluate various controllers, such as energy management system, adaptive cruise control, traction and driveline oscillation control. Particular emphasis is given to the driveline oscillations caused due to low damping present in PHEVs by incorporating flexibility in the half shaft and time lag in the tire model.

Torque converters are used as coupling devices in automobile powertrains involving automatic transmissions. Efficient modeling of torque converters capturing various modes of operation is important for powertrain design and simulation, (Hroval and Tobler 1, Ishihara and Emori 2) optimization and control applications. Models of torque converters are available in various commercial simulation packages, Hadi et. al. 3. The information about the effect of model parameters on torque converter performance is valuable for any design operation. In this paper, a symbolic sensitivity analysis of a torque converter model will be presented. Direct differentiation (Serban and Freeman 4) is used to generate the sensitivity equations which results in equations in symbolic form. By solving the sensitivity equations, the effect of a perturbation of the model parameters on the behavior of the system is determined.

Dynamic modelling of the contact between the tires of automobiles and the road surface is crucial for accurate and effective vehicle dynamic simulation and the development of various driving controllers. Furthermore, an accurate prediction of the rolling resistance is needed for powertrain controllers and controllers designed to reduce fuel consumption and engine emissions. Existing models of tires include physics-based analytical models, finite element based models, black box models, and data driven empirical models. The main issue with these approaches is that none of these models offer the balance between accuracy of simulation and computational cost that is required for the model-based development cycle. To address this issue, we present a volumetric approach to model the forces/moments between the tire and the road for vehicle dynamic simulations.

This paper discusses modeling of a power-split hybrid electric vehicle and the design of a longitudinal dynamics controller for the University of Waterloo’s self-driving vehicle project. The powertrain of Waterloo’s vehicle platform, a Lincoln MKZ Hybrid, is controlled only by accelerator pedal actuation. The vehicle’s power management strategy cannot be altered, so a novel approach to grey-box modeling of the OEM powertrain control architecture and dynamics was developed. The model uses a system of multiple neural networks to mimic the response of the vehicle’s torque control module and estimate the distribution of torque between the powertrain’s internal combustion engine and electric motors. The vehicle’s power-split drivetrain and longitudinal dynamics were modeled in MapleSim, a modeling and simulation software, using a physics-based analytical approach.

Parameter identification of a math-based spark-ignition engine model is studied in this paper. Differential-algebraic equations governing the dynamic behavior of the engine combustion model are derived using a quasi-dimensional modelling scheme. The model is developed based on the two-zone combustion theory with turbulent flame propagation through the combustion chamber [1]. The system of equations includes physics-based equations combined with the semi-empirical Wiebe function. The GT-Power engine simulator software [2], a powerful tool for design and development of engines, is used to extract the reference data for the engine parameter identification. The models is GT-Power are calibrated and validated with experimental results; thus, acquired data from the software can be a reliable reference for engine validation purposes.

In this paper, a new solution method is presented to study the effect of wave propagation in engine manifolds, which includes solving one-dimensional models for compressible flow of air. Velocity, pressure, and density profiles are found by solving a system of non-linear Partial Differential Equations (PDEs) in space and time derived from Euler’s equations. The 1D model includes frictional losses, area change, and heat transfer. The solution is traditionally found by utilizing the Method of Characteristics and applying finite difference solutions to the resulting system of ordinary differential equations (ODEs) over a discretized grid. In this work, orthogonal collocation is used to solve the system of ODEs that is defined along the characteristic curves. Orthogonal polynomials are utilized to approximate velocity, pressure, sound speed, and the characteristic curves along which the system of PDEs reduce to a system of ODEs.

Due to rising fuel prices and environmental concerns, Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs) have been gaining market share as fuel-efficient, environmentally friendly alternatives. Lithium-ion batteries are commonly used in EV and HEV applications because of their high power and energy densities. During controls development of HEVs and EVs, hardware-in-the-loop simulations involving real-time battery models are commonly used to simulate a battery response in place of a real battery. One physics-based model which solves in real-time is the reduced-order battery model developed by Dao et al. [1], which is based on the isothermal model by Newman [2] incorporating concentrated solution theory and porous electrode theory [3]. The battery models must be accurate for effective control; however, if the battery parameters are unknown or change due to degradation, a method for estimating the battery parameters to update the model is required.

Physical rig testing of a vehicle is often undertaken to obtain experimental data that can be used to ensure a mathematical model is an accurate representation of the vehicle under study. Kinematics and Compliance (K&C) testing is often used for this purpose. The relationship between the hard point locations and compliance parameters, and K&C characteristics of a suspension system is complex, and so automating the process to correlate the model to the test data can make the exercise easier, faster and more accurate than hand tuning the model. In this work, such a process is developed. First, the model parameters are adjusted, next a simulation is run, before the results are read and post processed. This automation processed is used in conjunction with an optimization procedure to carry out the K&C correlation.

The recent increase in oil prices and environmental concerns have attracted various research efforts on hybrid electric vehicles (HEVs) which provide promising alternatives to conventional engine-powered vehicles with better fuel economy and fewer emissions. To speed up the design and prototyping processes of new HEVs, a method that automatically generates mathematics equations governing the vehicle system response in an optimized symbolic form is desirable. To achieve this goal, we employed MapleSimTM, a new physical modeling tool developed by Maplesoft Inc., to develop the multi-domain model of a series-HEV, utilizing the symbolic computing algorithms of Maple software package to generate an optimized set of governing equations. The HEV model consists of a mean-value internal combustion engine (ICE), a chemistry-based Ni-MH battery pack, and a multibody vehicle model. Simulations are then used to demonstrate the performance of the developed HEV system.

An electric vehicle model has been developed with four direct-drive in-wheel motors. A high-level vehicle stability controller is proposed, which uses the principles of fuzzy logic to determine the corrective yaw moment required to minimize the vehicle sideslip and yaw rate errors. A genetic algorithm has been used to optimize the parameters of the fuzzy controller. The performance of the controller is evaluated as the vehicle is driven through a double-lane-change maneuver. Preliminary results indicate that the proposed control system has the ability to improve the performance of the vehicle considerably.