1. Electric Vehicle Modeling Utilizing DC Motor Equations Clay S. Hearn, Damon A. Weeks, Richard C Thompson, and Dongmei Chen 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics July 6 – 9, 2010, Montreal, Quebec

2. Introduction Previous electric and hybrid electric vehicle modeling experience and demonstrations at UT-CEM PSAT modeling toolbox and motor models Acausal modeling Steady state efficiency maps Development of causal electric vehicle model Account for transient dynamics and other constraints Requires feed-forward control design

3. Vehicle Modeling at UT-CEM Plug-In Hybrid Fuel Cell Shuttle Bus On road evaluations 3 different routes PSAT models matched energy consumption data to within 5% Columbia ParCar utility vehicle conversion Upgrading with 8.5 kW fuel cell and ultracapacitor energy storage PSAT modeling used in design process Base vehicle modeling with DC motor used for model development

4. Advantages and Limitations of PSAT Large library of component models derived from testing for engines, motors, batteries, etc… Quickly evaluate different component options and hybrid configurations Development of supervisory control strategies Acausal modeling techniques Static power converters with efficiency transfers power between batteries, motors, and auxiliaries Steady state efficiency maps used for motors and engine models Validity of efficiency map Loss of transient dynamics Loss of other limitations such as current limits or thermal limits Inaccuracies in transient dynamics and performance limitations

5. Model Development Base vehicle model is ParCar SUV-LN 48V lead acid batteries 12.9 kW DC motor Model vehicle with DC motor equations and causal modeling techniques Bond graph and equation formulation Develop control strategies for route following Feed-forward Torque demand estimation Field and armature voltage control

6. Bond Graph Model Development Bond graph tracks power flow and causality Idealized DC converters modeled as transforming elements Nonlinearities included in motor constant

7. Derived Equations from Bond Graph Model Battery SOC is a quasi-state based on Voc – R battery model Main model states If = field current Ia = armature current V = Linear velocity Controls m = field current duty cycle n = armature current duty cycle Back EMF EM Torque Motor Friction Drag Grade and Roll Resistance

8. DC Motor Control Separately wound DC motors allow active control of field and armature current Below base speed: field current held constant and armature voltage controlled for constant torque Above base speed: field current is weakened to increase motor speed at constant power

9. Driver Model Driver model estimates required torque to move vehicle along given velocity profile Feed forward controller design Linearize and invert vehicle equations Feedback PI controller included to add additional corrections to reference speed

10. Feed Forward Control Design Linearize vehicle motion equations about a specified V0 and solve for steady state EM torque Derive and invert transfer function from linearized equations. Inverted TF yields dynamic EM torque output, but requires low-pass filter Set filter pole ~100X left of pole location Steady state torque minus V0 torque requirement is added to dynamic estimation (above)

11. DC Motor Current Requirements Vehicle model uses separate PI controllers for armature and field loops (m and n duty outputs) Translate torque estimates from driver model to field and armature current demands Constant torque regime Constant field current at 10 amps Solve for the armature current Field weakening regime Solve for the steady state field and armature currents from initial state equations Solution based on the motor speed demand

12. Field Weakening Current Estimate Steady state expression for armature current demand Steady state expression for field current demand Substitution yields quadratic equation that can be used to find required currents Above base speed, PI motor current controllers solve for these reference currents Current limits are set at 400 A for armature and 40 A for field

13. Simulink Model Overview

14. Route Following Response

15. Comparisons to PSAT Performance

16. Summary Presented a causal model of an electric vehicle driven by separately wound DC motor Developed driver models and vehicle control algorithms Level of modeling will include transient dynamics as well as specified constraints Current limitations Addition of thermal modeling will allow current limits due to thermal constraints ParCar SUV-LN is now at UT-CEM for testing and retro-fit