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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.

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.

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.

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.

It is imperative to have accurate tire models when trying to control the trajectory of a vehicle. With the emergence of autonomous vehicles, it is more important than ever before to have models that predict how the vehicle will operate in any situation. Many different types of tire models have been developed and validated, including physics-based models such as brush models, black box models, finite element-based models, and empirical models driven by data such as the Magic Formula model. The latter is widely acknowledged to be one of the most accurate tire models available; however, collecting data for this model is not an easy task. Collecting data is often accomplished through rigorous testing in a dedicated facility. This is a long and expensive procedure which generally destroys many tires before a comprehensive data set is acquired. Using a Vehicle Measurement System (VMS), tires can be modeled through on-road data alone.

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.

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.

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.

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.

A compact sized vehicle that has a narrow track could solve problems caused by vehicle congestion and limited parking spaces in a mega city. Having a smaller footprint reduces the vehicle's total weight which would decrease overall vehicle power consumption. Also a smaller and narrower vehicle could travel easily through tight and congested roads that would speed up the traffic flow and hence decrease the overall traffic volume in urban areas. As an additional benefit of having a narrow track length, a driver can experience similar motorcycle riding experience without worrying about bad weather conditions since a driver sits in a weather protected cabin. However, reducing the vehicle's track causes instability in vehicle dynamics, which leads to higher possibility of rollovers if the vehicle is not controlled properly. A three wheel personal vehicle with an active tilting system is designed in MapleSim.

The optimum driving dynamics can be achieved only when the tire forces on all four wheels and in all three coordinate directions are monitored and controlled precisely. This advanced level of control is possible only when a vehicle is equipped with several active chassis control systems that are networked together in an integrated fashion. To investigate such capabilities, an electric vehicle model has been developed with four direct-drive in-wheel motors and an active steering system. Using this vehicle model, an advanced slip control system, an advanced torque vectoring controller, and a genetic fuzzy active steering controller have been developed previously. This paper investigates whether the integration of these stability control systems enhances the performance of the vehicle in terms of handling, stability, path-following, and longitudinal dynamics.

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.

A two-passenger all-wheel drive urban electric vehicle (AUTO21EV) with four direct-drive in-wheel motors and an active steering system has been designed and developed at the University of Waterloo. A novel fuzzy slip control system is developed for this vehicle using the advantage of four in-wheel motors. A conventional slip control system uses the hydraulic brake system in order to control the tire slip ratio, which is the difference between the wheel center velocity and the velocity of the tire contact patch along the wheel plane, thereby influencing the longitudinal dynamics of a vehicle. The advantage of the proposed fuzzy slip controller is that it acts as an ABS system by preventing the tires from locking up when braking, as a TCS by preventing the tires from spinning out when accelerating.

The vision for the future automotive chassis is to interconnect the lateral, longitudinal, and vertical dynamics by separately controlling driving, braking, steering, and damping of each individual wheel. A major advantage of all wheel drive electric vehicles with four in-wheel motors is the possibility to control the torque and speed at each wheel independently. This paper proposes a traction controller for such a vehicle. It estimates the road's adhesion potential at each wheel and adjusts each motor voltage, such that the longitudinal slip is kept in an optimal range. For development and validation, a full vehicle model is designed in ADAMS/View software, in co-simulation with motor and control elements, modeled in MATLAB/Simulink.

A real-time control-oriented mean value engine plant model that includes engine thermals and cold starts is developed for a Toyota Prius 2015 plug-in hybrid engine in Modelica and MapleSim and validated experimentally. The model consists of an engine block model, intake and exhaust manifold models, and a throttle model. An advantage of the engine block model is the ability to compute the frictional Mean Effective Pressure during engine cold starts from calculated air, oil, and coolant temperatures at various locations in the engine block. Traditionally, engine thermals are modelled utilizing thermal resistances and capacitors. The proposed model utilizes linear graph theory with terminal equations to study the topology of the different components that affect engine thermals, including engine head, liner, coolant, and oil sump.

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.