Analysis and Design of an Electric Vehicle using Matlab and Simulink

Analysis and Design of an Electric Vehicle using Matlab and Simulink Advanced Support Group January 22, 29

23-27: University of Michigan Research: Optimal System Partitioning and Coordination Original System: Partitioned System: Coordination:

Optimal Partitioning and Coordination Decisions in Decomposition-based Design Optimization

Application: Integrated Design of an Electric Vehicle

Vehicle Layout l e b lmax x b y b l W available battery space front control arm x b w battery traction motor pulley drive system sprung mass center rear trailing arm forward direction of travel l 3 l 1 l 2 L

Powertrain Simulation Vehicle model: backward-looking Simulink model that accounts for vehicle pitch motion and tire slip Motor model: computes power loss map from geometric design variables Battery model: Li-ion Simulink model (Fuller et al. 1994, Han 28). Battery parameters computed using artificial neural network.

Powertrain Simulation 25 2 15 1 5 5 1 15 2 25 3 35 4 time (sec) 2 15 1 5!5!1!15!2!25.4.4.4.6.8.8.92.9.6.8.6.93.9.6 1 1 2 3 4 5 6 7 1.6.4.8.4 1 velocity (m/sec) v(t) τ(t).91.91.9.92.93.93.92.93.91.8.9.9.91.4.4.6.6.9.92.92.8.4.4.8.92.91.93.94.97.95.98.96.99.91.8.92.9.93.94.97.95.98.6.99.96.91.92.4 P (t) ω(t).92.91.91.9.6 SFUDS cycle Vehicle model Motor model Battery model

Powertrain Simulation: Vehicle Model τr(t) 1/2 τb(t) Single Wheel Torque Belt Model Net Drive Torque v(t) Fa(t) Frx(t) Ffz(t) τm(t) Motor Inertia Model Aero Drag Force Net Longitudinal Force Frz(t) Vehicle Pitch Model P (t) + Frt(t) Fft(t) Motor Power Loss Map Tire Drag Model ωr(t) ωm(t) Rear Tire Slip Model Belt Model

Vehicle Pitch Model l 1 l 2 θ p z F fz static height of mass center F rz ż θ p z θ p = 1 1 k f +k r m s l 2k r l 1k f I y l 2k r l 1k f m s l2 2 kr +l2 1 k f I y c f +c r m s l 2c r l 1c f I y l 2c r l 1c f m s l2 2 cr l2 1 c f Iy z θ p ż θ p + M p I y

Tire Slip Model ω r = v(i + 1) r(v) Slip data obtained for a high efficiency tire from Bridgestone: 15 F z 1 5.2.4.1.3.2.1.1.1.2.1.2.3.1.4 15 1 5 5 1 15 F x Dynamic radius model constructed from Bridgestone data: r(v) = C t1 + C t2 v + C t3 v 2

Induction Motor Model stator R s L ls L lr output shaft V s L m R r /s rotor τ e constant flux region flux weakening region Motor Efficiency Map τ em increasing s constant V s/ω e τnet (N) ω e ω b ωm (rad/sec)

Power Demand Calculation 25 2 SFUDS Profile Power Demand History 2.5 x 14 Power Requirements battery output power mechanical power 2 1.5 velocity (m/sec) 15 1 1.5 5.5 1 5 1 15 2 25 3 35 4 time (sec) τ and ω points visited 1.5 5 1 15 2 25 3 35 4 2 4 15 6 6 1 τnet (N) 5!5!1!15!2!25!2 2!4 4!2!4!6 2!2 4!4!6 2 1 2 3 4 5 6 7 ωm (rad/sec)

Battery Simulation Li-ion Battery Construction Vehicle Range Simulation current collector separator current collector height 1 x 14 8 6 P(t) P u (t) P l (t) 4 electrode electrode power (W) 2 width 2 4 (a) Cell widings (a) cell winding (b) Flat-wound lithium-ion cell 6 2 4 6 8 1 12 time (sec) Lumped parameter dynamic model Hybrid pulse power characterization (HPPC) test computes: Polarization resistance curve Polarization time constant HHPC results modeled with a neural network

Vehicle Dynamics Simulation Quarter-car model: state-space model used to simulate vehicle comfort, roadholding, rattle space, and suspension forces Static bicycle model: analytical model used to assess directional stability Dynamic bicycle model: state-space model used to simulate steering responsiveness

Quarter-car Model z s m s /4 z us k s c s m us /4 v z k t c t d dt 2 6 4 z us z ż us z s z us ż s 3 7 5 = 2 6 4 1 4k t 4(cs +c t ) 4ks 4cs mus mus mus mus 1 1 4cs 4ks 4cs ms ms ms 3 2 7 6 5 4 z us z ż us z s z us ż s 3 7 5 + 2 6 4 1 4ct mus 3 7 5 ż

Road Profile Model Begin with random data from a gaussian distribution Apply color and moving average filters Check IRI using quarter-car model with golden parameters IRI = 4.2: driver discomfort simulation IRI = 7.37: roadholding metric.6.4 unfiltered data low pass filter moving average filter.2 Elevation (m).2.4.6.2.4.6.8 1 1.2 1.4 1.6 1.8 2 Longitudinal Position (m)

Steering Responsiveness (Step Input) Lower yaw rate (Ω) rise time more responsive handling [ ] [ vy a 3 a = 1 Ω z b3 b 1 a2 a 1 b2 b 1 ] [ vy Ω z ] + [ a4 a 1 b 4 a 1 ] δ f a 1 = m a 2 = m + 2(l 1C αf l 2 C αr ) v a 3 = 2(C αf + C αr ) v a 4 = 2C αf b 1 = I z b 2 = 2(l 2 1 C αf + l 2 2 Cαr ) v b 3 = 2(l 2 1 C αf l 2 2 Cαr ) v b 4 = 2l 1 C αf

Directional Stability Stable at speeds up to v max if: D s = L + v 2 max gk us where: K us = ( Wf W ) r C αf C αr Modeled C αf and C αr dependence on normal forces based on data from Bridgestone.

Vehicle Structure Simulation ANSYS R finite element model used to predict: bending and torsional stiffness bending and torsional stresses Surrogate model created using artificial neural network to reduce simulation time

EV Subsystem Interactions Modeling these system interactions required the flexibility of Matlab and Simulink P T Suspension parameters V D Battery mass and geometry ST Battery mass and geometry Vehicle mass and inertia Suspension forces Frame mass and inertia Vehicle mass and inertia M

Electric Vehicle Design Problem Design Objective and Constraints: minimize 1/mpg equivalent fuel consumption subject to g 1 2 motor feasibility g 3-6 time 1 sec g 4 urban range 1 mi g 5 6 battery power and capacity constraints g 7 directional stability constraint g 8 steering responsiveness constraint g 9 maximum rattle space constraint g 1 road holding constraint g 11 passenger comfort constraint g 12 geometric frame constraint g 13 14 frame stress constraints g 15 16 frame stiffness constraints g 17 18 battery packaging constraints

Electric Vehicle Design Problem Design Variables: x 1 2 x 3 x 4 7 x 8 1 x 11 12 x 13 suspension parameters pulley speed ratio motor geometry and rotor resistance battery geometry frame geometry battery position

Electric Vehicle Project Summary Developed powertrain and chassis models from scratch in Matlab and Simulink Developed structural model using ANSYS, constructed neural network model Quantified vehicle system interactions Used as a case study for system optimization research

EV Lessons Learned Modeling system interactions is difficult, but essential Requires flexible modeling environment Mass change propagation is significant Enables exploitation of synergy EV technology can provide substantial energy savings Explored tradeoffs between performance and efficiency