The Simulation Tool for Mission-Optimized System Design

The Simulation Tool for Mission-Optimized System Design Tianlei Zhang, Jeremiah Shepherd, Jijun Tang, Roger A. Dougal Dept of Electric Engineering, Dept of Computer Science, University of South Carolina–Columbia, USA ([email protected], [email protected], [email protected], [email protected])

Keywords: co-optimization process, 3D multibody modeling, mission-optimization, gaming environment Abstract A method for optimizing system design, considering control strategies, is developed. The method is numerically analyzed for the design of a simple buck converter but then is more generally applicable for mission-optimized design of large and complex systems. We develop the particular simulation tool by combining gaming-oriented methods with the Virtual Test Bed multi-disciplinary simulation software. We further illustrate the method by applying it to design of a hybrid electric vehicle. The method involves use of high-level simulation models to abstract the system architect from the discipline-specific nuances of individual component behaviors. To this end, we also include some description of the related 3D multibody mechanics modeling of a vehicle system in resistive companion form. The methods proven in this simple case can be extended to study more sophisticated electromechanical systems, such as electric ship system. 1.

INTRODUCTION Early consideration of different control strategies may drive a system to different optimum configurations, yet the tools for optimal design of systems generally do not consider the effect of control strategies on the optimal design outcome. We describe here the strong effect that the choice of control strategy has on optimal configuration or parameterization of a system, and illustrate by application to design of a buck converter. We further expand by applying it to a hybrid electric vehicle (HEV) system and then show how the system model can be used in three ways: 1) given several choices of control strategy for an energy storage system, how does the choice of control strategy affect the “best” system for a given mission; 2) given a system optimized for one mission, what is the best operating strategy to achieve a different mission; 3) given a system optimized for some mission, how should recharging stations be located to fulfill a different mission. The mission-optimized system design is implemented in the gaming environment [1] combined with the engineering design software, Virtual Test Bed (VTB). The gaming environment facilitates our process by enabling the simulation of vehicle system as it travels a route that is

extracted from external software, such as Google Earth. The vehicle system is realized by assembling the basic vehicular components together with a propulsion system that includes hybrid energy storage subsystems. The system performance such as the state of charge of the power source, the traveling distance and speed etc, be visualized and evaluated. Since the vehicle is maneuvered through the gaming controller by the player, we can obtain the direct relationship of energy consumption based on different driving scenarios. We have chosen an electric vehicle as the application example because: firstly, a complete vehicle system depicts a typical three dimensional (3D) structure that has not been previously modeled with the Resistive Companion Method (RCM), hence this modeling method can be generalized into other more sophisticated areas, such as electric ship design; secondly, few publication actually explained proper mathematical expressions of 3D vehicle system for people not in the mechanical field, like electrical engineers or cyber-game developers, even if automotive dynamics are widely studied in major simulation software products. Our modeling approach is articulated in a total mathematical manner despite the diversity of simulation software [3]-[4]. Different from the published literatures, firstly we define the vehicular parts at the system level of detail for a reasonable compromise between easy comprehension and model accuracy; secondly we employ a standard scalar coupling interface to realize the vector joints in mechanics, rather than enrich the interface library to complicate multi-disciplinary usage. In comparison to our approach, references [10]-[12] introduce a sophisticated vehicle library in Dymola for multi-disciplinary research but it displays limits in electromechanical systems due to the counterintuitive interface definition; ADAMS software is powerful in mechanical modeling [7][9][13], but requires external software linkage to accomplish the electrical engineering simulation. None of them are mission-objected. Lu [14] offers the physical equations for 3D vehicle movements but does not cover the multibody application and establishment of standard interfaces; furthermore, some of Lu’s modeling assumptions and coordinate transformation cannot be generalized for universal purposes.

2.

EFFECT OF CO-OPTIMIZATION ON THE OPTIMUM SYSTEM DESIGN Normally, an optimal design configuration is found by firstly considering the physics of the system. After the optimal choices of hardware are found, the system controls are developed in order to meet the performance requirements. But, in fact, the optimal configuration of a system actually depends on the chosen control strategy. Given some cost function for a system, hardware cost and the system performance cost are always included as criteria to define an optimum design point. And they are related by certain weights. To demonstrate the effect of control strategy choices on the optimal design configuration, we propose a simple case of buck converter design and quantitatively evaluate it by two processes. Process I, also known as the standard industrial design process, determines the system hardware values by finding the local minimum point of the hardware cost, and then chooses the control strategy for the lowest performance cost. In contrast, Process II tries to identify both the hardware design and the control strategy simultaneously in order to find the global minimum design point of overall system cost, thus Process II is also called co-optimization process. It is noted that when it comes to the control strategy choice, it refers to deciding both control method, e.g. PID control, fuzzy logic control, sliding mode control, model predictive control etc, as well as control parameters for the methods. To simplify the analysis presented here, we specify a PID controller and only consider the parameter optimization of Kp, Ki and Kd. We define the cost function in Equation (1). Provided that all the power switch devices (e.g. MOSFETs, diodes) at the same power level have negligible cost differences, the coefficients of inductance L and capacitance C largely determine the relationship between size and financial cost of our product. There are three items defined in the evaluation of system performance, which are also related to the financial cost by certain weights: ev is the load voltage error from a step response; t1 is certain period of time in which we are interested in measuring the system dynamics, and here we choose 1ms; ∆iL is the inductor current ripple and ∆vC is the output voltage ripple, both of which are implicitly related to the hardware cost. CF  hardware cost  control performance cost

C   2L    7 1  10 5   1  10





t (1)  01 ev2 dt  100  Δi L  1  10 5  Δv c The operating parameters and design requirements of this buck converter is listed in Table 1 as Schelle [2] used in his design case. LIR is the ratio of inductor current ripple peak magnitude to the current average value. And OVO is measured when the peak energy stored in the inductor is suddenly switched to the load capacitor in the worst case.

Table 1. Design information of buck converter Operating Parameters Input Voltage (Vin) 7V-24V DC Bus Voltage (Vout) 2V Output Max Current (Ioutmax) 7A Switching Frequency (fs) 300kHz System Design Requirements Inductor-Current Ratio (LIR) 0.3 Output Voltage Overshoot (OVO) 100mV 2.1. Simulation Realization of Process I In Process I, the minimum hardware cost can be directly obtained from the specifications that meet the lowest requirements [2]. L and C are chosen to be 2.8μH and 560μF, respectively. Their values also determine the current and voltage ripples expressed in the performance cost function through equation (2). Thus we employ Matlab Optimization Toolbox only to tune the PID controller for the optimum operating behavior in terms of load step response. Vg  V D i L vC  i L  (2) 8 Cf s 2 Lf s





Figure 1. The block diagram of voltage regulator system small-signal model of buck converter in Matlab/Simulink The block diagram of the Buck converter small-signal continuous conduction mode system is built in Matlab/Simulink, as shown in Figure 1. Neglecting the variations of input voltage and control reference, we add the step change on the output current at the system steady state. And then in Matlab Script, we apply the command lsqnonlin for solving the least squares of function (3), which is the discretized form of the integral of error square in equation (1). Finally we substitute the optimized result of F and hardware values into equation (1) to attain the partial and entire system cost.

F   ev2 t i  n

i 0

(3)

2.2. Simulation Realization of Process II Process II uses the same system model in Simulink as Process I, but applies different optimization method in Matlab script because the objective function is no longer equation (3) but the complete expression of equation (1). The multiple variables, including L, C, Kp, Ki and Kd, are evaluated simultaneously under the constraints that L and C must be larger than the values determined in Process I, hence the command fmincon is implemented to find the minimum of the objective function with the optimizing method of PID controller nested in it. Table 2. The optimized prototypes of buck converter design Process I Process II 2.8 3.6 L (𝜇H) 560 562 C (𝜇F) Kp 11.12 13.24 Ki 0.50 10.70 Kd 2.38×10-4 4.18×10-4 Hardware Cost 112.00 128.18 Control Cost 240.37 206.66 Cost Function 352.37 334.84 2.3. Comparison between Process I and Process II The optimum results from the two design processes are numerically exhibited in Table 2. Though it only reflects the particular case of buck converter design, there are at least four remarkable conclusions that we can generalize into the universal industrial design applications: 1) Process I always guarantees the local minimum of hardware cost expression because it only considers meeting the minimum design criteria under investment budget, as indicated from our case that Process II costs 14% more in hardware due to its selection of larger L and C compared with Process I; 2) Since the optimum control strategy in Process I is obtained under the limits of the lowest hardware performance, the control efficiency cannot be considered as the highest operating level that the original design goals can essentially achieve, as revealed from 16% higher in the compromise of system performance from Process I than that in Process II; 3) As demonstrated by our simulation results, Process II does improve the overall design goals and system capability by partially compromising on hardware costs. In fact, the cost difference in two cases is highly dependent upon the system properties, complexity and the definition of cost function. As far as our design case is concerned, for such a small system, once the cost weight of hardware in equation (1) is increased by 10 times, the new optimum states will result in about 20 times cost difference between Process I and Process II. Therefore, the deeper insight on this topic will be studied in our future work;

4) Compared with the step-by-step design in Process I, the biggest disadvantage of Process II is that the complete system needs to be established at the evaluation moment. As a result, Process II brings much heavier burden to the simulation capability of the current software, especially for the design of very large and complex systems (VLCS). 3.

PROBLEM DESCRIPTION Taking the design of HEV system as an example, at present people have to separately implement the related research work, including vehicle dynamics study, energy storage system design, property improvement of clean energy sources and motor control topologies and so on, without being able to consider the practice of cooptimization for the best outcome. On one hand, when it comes to the complex multidisciplinary system, like the 3D electromechanical systems, currently available software usually requires expertise within each involved discipline. Since the mechanical interfaces carry their own specific motion restrictions related to the spatial dimensions, most software, such as Dymola and ADAMS, introduce particular types of joints, such as spherical, revolute, cylindrical, prismatic and even user-defined joints [11][13][19]. Nonetheless, this solution complicates the rapid construction of mechanical prototype that need to be used by electrical engineers because the interface concepts have to be understood before one can decide where and how to use it. In Section 4, we develop a streamlined modeling practice of multibody vehicle system by applying the 1D universal power coupling interface into modeling any type of 3D mechanical joint. This method for the first time enables the application of RCM into 3D mechanical modeling. This vehicle mechanism can reflect 3D dynamics in different road conditions through the assembly of four classes of autonomous components: chassis, suspension, wheel and ground friction, as well as be extended for more features. Since the interconnection among components is intuitively developed to be manageable by different levels of users, the modeling of other VLCS, such as ship structure, can be done in the future. On the other hand, currently few simulation softwares can be regarded as mission-oriented design tools. Cooptimization has to be implemented according to specified missions. For example, given several options of control topology, in designing the best one for a mountainous terrain mission, it is necessary for power engineers to easily generate electrical system, mountain terrain and vehicle structure in the same simulation environment. In addition, it should be easy to instantaneously manipulate the vehicle according to the road orientation and driving manners. Therefore, it is required to have a simulation tool that can provide the complexity of system assembly at proper level and communicate information with the real world.

In Section 5, we describe a vehicular gaming environment that utilizes the engineering simulation software, namely VTB, to develop a HEV-related missionoptimized design process. Our tool can load terrain conditions from Google Earth and study the HEV dynamics from the point of view of energy control design. 4.

MULTIBODY VEHICLE MODELING

4.1. Establishment of 3D Natural Coupling Interface Any system that can be expressed through differential equations can be analyzed by applying the RCM through the network theory of nodal analysis [8]. Two types of ports are commonly defined in VTB: Natural Port and Signal Port. Each natural coupling interface, also named Natural Port, refers to a node at which a pair of through and across variables is subject to energy conservation laws. (through, across), their product equals the transmitted power at the connection point. The units of through and across can be defined in multi-disciplines, for instance, in mechanical domain, through represents the force or torque while the across represents the velocity or angular velocity. A Signal Port enables unidirectional data flow from one component to another. The direction is explicit and the direction is defined by use of different icons for input and output. Signal Ports are usually employed for data transmission and logic design [18], but they are also useful in the mechanical domain for conveying properties such as temperature or composition of a flow stream. Our achievement is establishing the dimensional mechanical coupling interface straightforwardly as specific numbers of Natural Ports, which indicates the decomposed power flow in the fixed Global Coordinate System (GCS). In other words, one Natural Port is for 1D power flow, two for 2D and three for 3D. As long as people can express the dynamic equations of the coupled components with through and across at the interface, people can model any joint type with respect to each coordinate direction in the Body-fixed Coordinate System (BCS) individually using standard natural coupling interface. This method is implemented by Euler Angles, also known as the RPY transformation [20], into the transformation between two coordinate systems. X O GCS Y Z

 y, j  x, i

BCS

 z, k

Figure 2. The Definition of the GCS and BCS in the vehicle mechanism The GCS evaluates the motions in the absolute inertial space. Both the origin and the orientation of the Cartesian coordinate system are destined, fixed and time-independent,

shown as the axes X, Y, Z in Figure 2. Through and across are defined with respect to the GCS for the best understanding. The BCS, shown as the axes x, y, z in Figure 2, is established as a rotation frame of reference at the center of gravity (CG) of each component. The orientation of the axes instantaneously follows the angular motions of the entity and reflects the pitch, roll and yaw angles. Since the BCS constantly aligns with the principal axes of an entity, for the best convenience, the moment equations can be developed about each axis in the BCS independent from each other. Our method transforms the BCS and the GCS implicitly in each component, so that we do not need any component specially added to handle the vector calculations as is used in Dymola [11]. Transformation of across values is provided in equation (4) while transformation of through values is in (5). ϕ, γ and φ are roll, pitch and yaw angles, respectively, obtained from the angular motions of chassis and distributed among components by the Signal Ports. v X  v x   X   x          (4)  vY   ΨΓΦ v y  , Y   ΨΓΦ  y   v Z   v z   Z   z   Fx   FX  T      F y   ΨΓΦ   FY  ,  Fz   FZ  0 1  Φ  0 cos 0 sin  cos  Ψ   sin   0

0    sin   cos 

 sin  cos 0

0  0 1 

Tx  T X  T     T y   ΨΓΦ  TY  Tz  TZ   cos  Γ  0  sin 

(5)

sin    0  0 cos  0

1

(6)

4.2. Modeling of the Chassis Component Approximating the chassis as a rigid prism, we represent this component in six degrees of freedom: three linear motions along the axes in the BCS and three angular motions around them. The momentum change and angular motion with respect to the rotating BCS are expressed in equation (7) and (8), respectively [20]. dv F m  ω I (7) dt where F, ω and I represent the vector of net force, angular speed about the axes and momentum, respectively. dω T m  ω M (8) dt where T and M represent the vector of net torque and angular momentum with respect to the principal axes, respectively. The torque with respect to each axis is

depicted in Figure 3 and mathematically expressed through equation (9)-(11). 4

4

n 1

n 1

Tx   Fzn y e ,n   Fyn z e ,n

(9)

4

4

4

n 1

n 1

n 1

T y   Fxn z e ,n   Fzn xe ,n   Tn 4

4

n 1

n 1

(10)

Tz   Fyn xe ,n   Fxn ye ,n

(11)

The two subscripts are consistently applicable through the paper. Firstly, n, taking values of 1 through 4, represents the four wheels numbered following the sequence: the front left, the front right, the rear left and the rear right; secondly, e indicates the effective value, which is the coordinate distance from the axis where the torque is measured to the point where the force is applied. As labeled in Figure 3, xn, yn are the fixed coordinates of the top joint of the suspension with the chassis. zn is the instant length of the suspension. y1 , y 3

x x1 , 2

x3 , x 4

y2 , y4

x Pitch

Y

X

Roll

y

G z

G

z1

ze,1

Fx4

Fy2

Fx2

z2

T2

4.4. Modeling of the Wheel Component The drive axles are simplified as two individual natural coupling interfaces on the wheel component to represent the torque coupling with the powertrain and the force coupling with the suspension. Both the linear motion and spin motion of a wheel component are developed according to Figure 5.



Fzn

Gwheel zn Kt ztn

N

Tn

r

Fxn

y

Fyn

Ffyn

x

Ffx z

n

Figure 5. the force diagram of the wheel

Z

Fy1

Fz 2

z

ze,1

T4

Z

expressions. Therefore, we adopt this stereotype in equation (12) for the best compromise among the modeling accuracy, simulation efficiency and people’s comprehension. F  F1  F2  K s z1  z 2  C d v1  v2  (12) where Ks, Cd are the spring constant and damping coefficient, respectively,. ∆z and v are the vertical response and velocity at the end of system, respectively.

F z1

Fz2

Fz4

(a) the front view

(b) the right side view x1 , x2

y2 , y4

y1 , y3

x3 , x4

X Yaw

x

y

Y

Fx2

Fy2

(c) the top view Figure 3. The force diagrams of the vehicle system 4.3. Modeling of the Suspension Component Chassis

 z1

v1

F1 Cd

Ks

F2 z 2

v2 Wheel

Figure 4. The structure of the spring-damper suspension The design of suspension ensures the ride comfort and accurate vehicle handling. Nonetheless, Sharp [21] pointed out that the passive spring-damper model in Figure 4 bears the most suitable complexity for deriving analytical

The wheel exhibits 3D translational motions, angular motion about its center of wheel and steering motion around its vertical axis in the BCS by neglecting the camber angle. The pneumatic characteristic is embodied by an upright spring between the wheel center and ground. The linear motions on the x-y plane can be obtained in equation (13) by containing both axle driving force Fn and tractive force Ffn; ωx, ωy have to be removed because the wheel only generates yaw angle; ωzn reflects the algebraic sum of the yaw rate of chassis and the steering rate from the driver’s command. dv Fn  F fn  m  ω I (13) dt We corrected the equations in [14] based on the signs following the BCS orientation. The vertical response of the pneumatic wheel can be calculated from equation (14). (14) Fzn   N n  K t z n  z tn  where Kt is the spring constant of the air pressure; ∆zn, ∆ztn are the vertical response at the center of wheel and the measurement of terrain roughness, respectively. Since the axle driving torque only acts about the y-axis in the BCS, the acceleration can be evaluated by equation (15). (15) J w n  rF fx,nTn where Jw is the moment of inertia of a rotating wheel; r is the instant radius of wheel.

4.5. Modeling of the Ground Friction Component Pacejka’s friction model [15] is widely employed because it matches well the experimental data of steadystate friction. Here “steady-state” refers to constant vehicle traveling speed and constant wheel angular speed. However, in most studies, it is essential to run the vehicle at arbitrary speed. Then it is not possible to predict and adjust the friction model instantly for every moment. In this paper, then, we apply the LuGre friction model [14][16], because it is capable of precisely describing both transient and steady-state frictions in most cases. This model is implicitly speed dependent and reflects the dynamics more precisely than Pacejka’s model [22]; on the other hand, this model is based upon real physical insight of the power conversion by measuring the instantaneous deformation of notional “bristles”, and hence can be more suitably implemented by the natural coupling interface than the data-fitting equation of Pacejka’s model. The friction coefficient µ is given in equation (17) as the function of internal deflected state of rubber element η which satisfies equation (16) .  0 Vr d η   Vr    t  (16) dt g Vr 

   0 t    1

d t    2Vr dt  Vr     s

   

(17)



(18) g Vr    k   s   k e where Vr is the relative velocity at the wheel-ground contact surface; σ0, σ1 and σ2 are the parameters of rubber characteristics; g(Vr) is a speed dependent sliding function representing the transitions between the static and kinetic friction coefficients. µk is the parameter reflecting kinetic friction force, µs is the parameter reflecting static friction force, υs is Stribeck speed, and δ is Stribeck exponent typically valued between 0.5 and 2. Since the bristle deflection affects merely little from each other in different directions [17], we modify the left side of equation (16) into (19).     d η   x i   y j   x   zn y i   y   zn x j (19) dt



 

 

Vr  Vrx2  Vry2



as indicated in equation (23). F fx   x N n

F fy   y N n

(23)

5.

DEMONSTRATION OF MISSION-OPTIMIZED SYSTEM DESIGN The complete multibody vehicle system can be obtained through the coupling way shown in the multibody vehicle subsystem in Figure 6 in VTB 2009 simulation environment, which provides the mature version of multidisciplinary Component Library and the simulation Work Space for building systems.

Figure 6. The schematic configuration of a HEV system with energy storage strategy in VTB The powertrain can be easily assembled with any type of power sources, energy control topology and valid motor control subsystem as shown in Figure 6. The vehicle dynamics has been validated in acceleration, steering maneuver and driving on rough road. In order to couple the simulation together with a gaming environment, two pieces of software are constructed: a utilitarian simulation server and a gaming environment client, as illustrated in Figure 7. The idea is to separate the simulation from the gaming environment, so that each can perform relevant specific tasks without interference between the worlds. For the server, its main task is to run the simulation and constantly update vital information. These values are then streamed to the gaming environment client where the visual component will update its values. Also the gaming environment is in charge of displaying predefined viewables of each component, such as the state of charge (SOC) of the battery.

(20)

where for acceleration Vrx  r  v xn ,

Vry  v yn

for braking Vrx  v xn  r

Vry  v yn

(21)

(22) It is noted that we correct the sign of lateral relative velocity from the Lu’s expression [14]. It should be negative to follow the coordinate definition. To conclude, it is straightforward to obtain the tractive forces by multiplying the normal force, Nn, on each wheel,

Figure 7. Coupling method of simulation server and gaming client

Even though this worked for the most part, it is not enough just to change these values at each time step, because everything in the gaming environment is assumed to run in real-time. Since this assumption cannot be made with such a complex simulation, an interpolative algorithm is created to fill in the gaps of information. By linear interpolation between the states, an estimated position can be found. However, some conflicts will arise between the simulation’s values and the gaming environment values. Whenever these conflicts occur it is always assumed that the server is correct. The gaming environment client not only visualizes the simulation, but it also streams user input to the simulation. Either from a mouse click, a key press, or a button press on a gaming controller, this information is processed and streamed to the simulation server. From there, the server will take the user input and dispatch it to the pertinent components. Some of this information is included, the percentage the accelerometer is pressed, and amount of brake being applied, and also the steering angle. In order to illustrate our co-optimization method into energy storage design, we simulate the vehicle system in Figure 6 in the coupled gaming environment. Different driving route is loaded from the Google Earth to represent the missions. Different control strategies as reviewed in [23] are substituted in the power source subsystem. The view of the simulation in the gaming environment is shown in Figure 8. By considering the battery SOC and velocity values graphically shown on the screen, the performance of different system structures can be compared in the same driving route; or a selected control strategy can be evaluated in different driving routes. The quantitative co-optimization results will be presented in our future work.

Figure 8. The simulation of HEV system in the gaming environment 6.

CONCLUSION Through the co-optimization process that we developed in the buck converter design, its significance in the multidisciplinary VLCS design is proposed. This method considers the effect of control strategy choice on the optimal

configuration of a system, and thus optimizes the overall system cost in terms of certain mission objectives. Compared with other multi-disciplinary simulation software, our simulation tool significantly facilitates the mission-optimized design process because: firstly, we developed the interface modeling method for universal coupling applications among 3D mechanical components to facilitate rapid virtual prototyping; secondly, we infused the gaming methods into normal engineering simulation software and developed the features of loading real environment conditions into simulation process. We apply the hybrid electric vehicle design into our simulation tool and illustrate three possible mission-optimized processes for people’s reference. Our simulation tool makes the design concept of co-optimizing VLCS possible, in a ship system, for example, if one were to size a flywheel energy storage system, the best size of that system would be able to be obtained depending on how it is controlled to supply power during times of peak usage. 7.

ACKNOWLEDGMENT The authors acknowledge support from the US Office of Naval Research under contract # N00014-07-0686. References [1] Shepherd, J., Shi, J., Zhang, T., Tang, J., and Dougal, R, “Application of multiplayer computer gaming paradigm to engineering Design Tools,” 2008 Summer Simulation Multi-conference, Grand Challenges in Modeling and Simulation, Edinburgh, Scotland. [2] D. Schelle, J. Castorena, “Buck-converter design demystified,” Power Electronics Technology, June 2006. [3] Andres Kecskemethy, Manfred Hiller. “Object-oriented programming techniques in vehicle dynamics simulation” Mathematics and Computers in Simulation 39 (1995): 549-558. [4] Schiehlen, Werner. “Computational dynamics: theory and applications of multibody systems.” European Journal of Mechanics. A, Solids, Jul. – Aug. 2006, Vol.25 Issue 4: 566-594. [5] J. J. McPhee. “On the use of linear graph theory in multibody system dynamics,” Nonlinear Dynamics, 1996, Vol. 9 No. 1-2: pp. 73-90. [6] Paredis, C. J. J., Calderon, A. D., Sinha, R., and Khosla, P. K.,“Composable Models for Simulation-Based Design,” Engineering with Computers, 2001, Vol. 17 No. 2: pp. 112–128. [7] L. Sass, J. McPhee, C. Schmitke, P. Fisette, and D. Grenier. “A comparison of different methods for modelling electromechanical multibody systems,” Multibody System Dynamics, OCT 2004, Vol. 12 Issue 3: 209-250.

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Biography Tianlei Zhang received his Bachelors in Electrical Engineering from Xi’an Jiaotong University, China in 2006. He is currently working on his Ph.D. in Electrical Engineering in the University of South Carolina, Columbia. His research experience includes modeling of VLCSs, designing energy control strategies and vehicle-related control problems. His research is now involved in the topic of infusion of a gaming paradigm into computer-aided engineering design tools, as well as studying the effect of control strategy choices on optimal design configuration. Jeremiah J. Shepherd received his Masters in computer science from University of South Carolina, Columbia in 2009. He is now working on his Ph.D. in computer science by performing research in serious video games. Some games that he has created have been used to teach foreign languages, train medical professionals, and aid in system engineering. Also He has given several lectures about the importance of serious video games, and also teaches video game design at USC along with several high schools around the state. Prof. Jijun Tang received his Ph.D. in Computer Science from University of New Mexico, in 2004. He is currently an Associate Professor in Department of Computer Science and Engineering, University of South Carolina. He leads a research lab of eight graduate students and has has diversified research interests on high performance algorithm development, computer game research, engineering simulation and computational biology. During the past five years, His research has been supported by ONR, NSF and NIH. Prof. Roger A. Dougal received his Ph.D. in electrical engineering from Texas Tech. University, Lubbock, in 1983. He is currently the Thomas Gregory Professor of Electrical Engineering at the University of South Carolina, where he leads the Power and Energy Systems group. He is a Director of the Electric Ship R&D Consortium, which is developing electric power technologies for the next generation of electric ships, he is Site Director of the NSF Industry/University Cooperative Research Center for Gridconnected Advanced Power Electronic Systems, and he leads development of the Virtual Test Bed --- a computational environment for simulation-based-design and virtual prototyping of dynamic, multidisciplinary systems. His research interests include power electronics, hybrid power sources, and simulation methods.