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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.

A two-passenger all-wheel-drive urban electric vehicle (AUTO21EV) with four in-wheel motors and an active steering system has been designed and developed at the University of Waterloo. In order to evaluate the handling and performance of such a vehicle in the design stage and analyze the effectiveness of different chassis control systems before implementing them in the real vehicle, the simulation of a large number of different open-loop and closed-loop test maneuvers is necessary. Thus, in the simulation environment, not only is a mathematical vehicle model needed for every test maneuver, but a driver model must also be designed to simulate the closed-loop test maneuvers. The role of the driver model is to calculate the control inputs required to successfully follow a predefined path.

A two-passenger, all-wheel-drive urban electric vehicle (AUTO21EV) with four direct-drive in-wheel motors has been designed and developed at the University of Waterloo. An advanced genetic-fuzzy active steering controller is developed based on this vehicle platform. The rule base of the fuzzy controller is developed from expert knowledge, and a multi-criteria genetic algorithm is used to optimize the parameters of the fuzzy active steering controller. To evaluate the performance of this controller, a computational model of the AUTO21EV is driven through several standard test maneuvers using an advanced path-following driver model. As the final step in the evaluation process, the genetic-fuzzy active steering controller is implemented in a hardware- and operator-in-the-loop driving simulator to confirm its performance and effectiveness.

A two-passenger, all-wheel-drive urban electric vehicle (AUTO21EV) with four direct-drive in-wheel motors has been designed and developed at the University of Waterloo. A 14-degree-of-freedom model of this vehicle has been used to develop a genetic fuzzy yaw moment controller. The genetic fuzzy yaw moment controller determines the corrective yaw moment that is required to stabilize the vehicle, and applies a virtual yaw moment around the vertical axis of the vehicle. In this work, an advanced torque vectoring controller is developed, the objective of which is to generate the required corrective yaw moment through the torque intervention of the individual in-wheel motors, stabilizing the vehicle during both normal and emergency driving maneuvers. Novel algorithms are developed for the left-to-right torque vectoring control on each axle and for the front-to-rear torque vectoring distribution action.

This paper outlines the state-of-the-art of approaches for automated design synthesis of ground vehicle suspensions. Conventionally, design synthesis of suspensions has been based on trial and error approaches, where designers iteratively change the values of design variables and reanalyze until acceptable performance criteria are achieved. This is time-consuming and tedious. With stringent requirements for vehicles, design synthesis undergoes fundamental changes. This puts much attention on the potentials of an automated process. This process is based on the following techniques: effective modelling and simulation methods, realistic formulation approaches, and appropriately selected optimization algorithms. These techniques are reviewed and an automated design synthesis methodology is briefly introduced.

This paper presents math-based models of automotive torque converters in the MapleSim1 modeling environment, which has a multi-domain nature. The created models can be easily connected to models of other vehicle components from different domains (mechanical, electrical, and hydraulic) developed in the same package. The proposed model is a math-based dynamic model of a torque converter, based on the paper by Hrovat and Tobler, which includes both transient and steady state behavior of the torque converter. The dynamic model of a torque converter can be used as an essential element to investigate vehicle longitudinal dynamics, drive quality, emission, and fuel consumption during gear shifting and throttle stepping. A sensitivity analysis is used to evaluate the effects of the torque converter's parameters, such as radius, blade angles, and inertias, on the model's behavior.

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.

Because of its widespread use in almost all the current electric and hybrid electric vehicles on the market, nickel metal hydride (Ni-MH) battery performance is very important for automotive researchers and manufacturers. The performance of a battery can be described as a direct consequence of various chemical and physical phenomena taking place inside the container. To help understand these complex phenomena, a mathematical model of a Ni-MH battery will be presented in this paper. A parametric importance analysis is performed on this model to assess the contribution of individual model parameters to the battery performance. In this paper the efficiency of the battery is chosen as the performance measure. Efficiency is defined by the ratio of the energy output from the battery and the energy input to the battery while charging. By evaluating the sensitivity of the efficiency with respect to various model parameters, the order of importance of those parameters is obtained.

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.

Mean value engine models (MVEMs) are intermediate-level internal combustion (IC) engine models which include more physical details than simplistic linear transfer function models, but significantly fewer details than large complex cylinder-by-cylinder models [1]. The MVEM is well-known as a suitable plant model for model-based control applications. The combinations of physics-based component models, which allow the physical parameter effects to be evaluated and controlled, and look-up table models, with fast response, make the MVEM suitable for control applications. A mean value engine model based on mathematical and parametric equations has recently been developed in the new MapleSim software. The model consists of three main components: the throttle body, the manifold, and the engine. The model is developed in the MapleSim environment which takes advantages from both Maple's powerful symbolic mathematical tool and Modelica's modern equation-based language.

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.

This paper presents a math-based spark ignition (SI) engine model for fast simulation with enough fidelity to predict in-cylinder thermodynamic properties at each crank angle. The quasi-dimensional modelling approach is chosen to simulate four-stroke operation. The combustion model is formulated based on two-zone combustion theory with a turbulent flame propagation model [1]. Cylinder design parameters such as bore and stroke play an important role to achieve higher performance (e.g. power) and reduce undesirable in-cylinder phenomenon (e.g. knocking). A symbolic sensitivity analysis is used to study the effect of the design parameters on the SI engine performance. We used the symbolic Maple/MapleSim environment to obtain highly-optimized simulation code [3]. It also facilitates a sensitivity analysis that identifies the critical parameters for design and control purposes.

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.