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Ardalan VahidiAnd Students: Ali Borhan, Chen Zhang, Dean Rotenberg

Mechanical Engineering, Clemson UniversityClemson, South Carolina

2008 American Control ConferenceSeattle ‐ June 11, 2008

Modeling and Control of Hybrid Electric VehiclesTutorial Session

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The Tutorial Session

• Overview on Modeling and Control of Hybrid Electric Powertrains (Ardalan Vahidi, Clemson University)

• Understanding Opportunities for Energy Management Control in HEVs through Degree‐of‐Freedom Analysis (Tony Phillips and Ming Kuang, Ford Motor Company)

• Configuration, Sizing and Control of Power‐Split Hybrid Vehicles (Huei Peng, University of Michigan)

• The Role of System Theory in Reducing Energy Losses in Hybrids (Lino Guzzella, ETH, Zurich) 

• Design and Control of a Renewable Energy‐Based Eco‐System With Plug‐In/V2GHybrid Electric Vehicles (Georgio Rizzoni, Ohio State University)

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Overview

• Why Hybrids Improve Fuel Economy 

• Configurations of a Hybrid Powertrain

• How Systems and Controls Help

• Supervisory Control Strategies

• Some Recent Trends

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Different Types of Hybrids

• Main Propulsion: Gasoline or Diesel Engines, Fuel Cells

• Assist Propulsion: Motors, Generators, Hydraulic Pumps

• Energy Storage: Batteries, Ultracapacitors, Flywheels, HydraulicAccumulators

• The main focus of this talk is on gasoline engine‐electric hybrid electric vehicles with battery/ ultracapacitor storage with the purpose of improving fuel economy.

• Main Configurations: Series, Parallel, Powersplit

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Well to Wheel Efficiencies

Available Online: http://www.toyota.co.jp/en/tech/environment/hsd/pdf/a_guide_to_hsd.pdf

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How Does Hybridization Help?

• Reducing braking losses through regeneration

• Possibility of clutch‐less operation thus reduced losses 

• Potential for downsizing the engine

• Enabling operation of the propulsion system at its more efficient operating regions

• Allowing engine shut‐down during idle

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Role of Control Engineering

• Engine downsizing, removing the clutch, and hybrid system configurations are mainly design considerations (system engineering perspective is still necessary).

• Regenerative braking is free energy, so no sophisticated high‐level control needed. Low‐level control still needed to optimize regeneration of electrical machine.

• Control engineering is critical in determining when to run the engine and at what power split ratio. The problem is very complex due to its dynamic nature and uncertainty about future driving conditions.

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Engine Fuel Consumption and Efficiency

Engine

 Max. Eff

iciency

 Curve

Lower Fuel Rates

Higher Fuel Rates

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Series Configuration of HEVs

• The engine and the driveline are decoupled. Drawbacks: electrical path losses; motor/generator should be sized for max power.

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Parallel Configuration of HEVs

• Engine power (or torque) can be decoupled from demand power.  The engine speed is determined by the vehicle speed (and the transmission).

• Less power conversion loss compared to series and therefore less power losses.

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Power‐Split or Series‐Parallel Configuration

• Combines advantages of parallel and series configuration,   the output power can be delivered from both electrical and mechanical paths.• Degrees of freedom are battery power and engine speed or torque.

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The Challenge of Energy Management

• In an ideal world where the electrical path had an efficiency of 1, then– the battery could be thought of a free buffer and charged/discharged at any 

time.

– The fuel economy optimization problem would be simplified to running the engine at most efficient line + charge sustaining considerations.

• In reality each charge/discharge results in losses:– Battery should be used conservatively and predictively. 

– Running the engine at most efficient line is NOT equivalent to running the hybrid most efficiently!

– Another concern is battery’s life which is sensitive to cycling and depth of discharge. (less of a problem for an ultracapacitor).

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The Control Objective

• Minimize fuel use and/or reduce emission without compromising the drivability of the vehicle. 

• Additional Limits: Charge sustaining is needed for vehicle certification. Cycling of the energy storage should be limited to prolong battery life. 

SOC

Velocity

Tdemand

Gear

Power Management

Strategy

Tmotor

Tengine

Tbrake

Tgenerator

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Backward Looking or Quasi‐Static Models (Non‐Causal)

EngineDrivelineVehicle

Electric Machine

ωeng

Ttraction Tengine

ωmotor TmotorFroad

Parallel Hybrid Example:

Current

Voltage

vcycle

ωwheel

Battery + Inverter

ADVISOR uses a backward simulation model.

SOC

Fuel rate

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Forward Looking or Dynamic Models (Causal)

EngineDrivelineVehicle

Electric Machine

ωeng

vTtraction Tengine

ωmotor TmotorFroad

Parallel Hybrid Example:

Current

Voltage

ωwheel

Battery + Inverter

PSAT uses a forward simulation model.

SOC

Fuel rate

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Models of Hybrid Powertrain Components

EngineDrivelineVehicle

Electric Machine

ωeng

vTtraction Tengine

ωmotor TmotorFroad

Parallel Hybrid Example:

Current

Voltage

ωwheel

Battery + Inverter

Fuel rate statically mapped from torque and speed.

Torque dynamics fast and can be ignored.

Efficiency statically mapped from torque and speed.

Torque dynamics fast and can be ignored.

torque/speed couplers:Static modeling okay.

torque converter: Speed dynamics important in transients.

Power electronics: No need to model dynamics.

Battery: State of charge should be modeled as a dynamic state.

In forward looking approach velocity is modeled as a dynamic state.

SOC

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Energy Management

• Control strategies used:– Rule‐based

– Fuzzy Logic/Neural Network

– Dynamic Programming

– Analytic Optimal Control 

– Variable Structure Control (Sliding optimal control)

– ECMS, Adaptive ECMS

– Model Predictive Control

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Rule‐Based Methods: An Example

Low optimal curve

Pure Electric Region

Medium optimal curve

High optimal curve

Run in Pure Electric Mode

Run the engine at next higher optimal curve, charge the battery

Assist Mode: Run Motor + Engine

The “pure‐electric” threshold is made a function of SOC for charge sustaining.

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Pros and Cons of Rule‐Based

• Intuitive

• Simple to implement

• Fuel economy sensitive to threshold curves

• Charge sustaining is cycle dependent

• Fundamentally the optimal curve will depend on FUTURE charging/discharging conditions

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Optimization‐Based Method

The goal is to determine the power split that minimizes fuel use over an 

entire cycle, i.e. find Pbatt that minimizes:

Ensuring that the charge is sustained:

subject to the system dynamics. When SOC is the only state:

and several inequality constraints, for example motor and engine

torque limits.

dtmJ ft

t f∫=0

0( ) ( )fSOC t SOC t=

2 42

oc oc batt batt

batt batt

V V R Pd SOCdt C R

− −= −

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Dynamic Programming

• Assumes known drive cycle and solves the fuel minimization problem backwards‐in‐time based on Bellman’s optimality principle.

time

tk tk+1t0 tft1

State of Charge

0.7

0.8

0.6

minimum fuel path

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DP is Non‐Causal

• Unfortunately future driving conditions are normally highly uncertain:– Driver behavior

– Road profile

– Traffic conditions

• Still DP can be used to:– Evaluate an upper bound to fuel economy potential of a hybrid

– Learn from and extract rules for real‐time control

– When future driving cycle can be estimated using telematics or for vehicles that have repeatable cycles.

• Stochastic DP has also been proposed with a probablistic driver model.

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Optimal Control: Let’s Simplify

• Find u=Pbatt that minimizes J. Without inequality constraints, the Hamiltonian is:

and

In the case of a battery, this renders a constant λ. The constant optimal λ is the onethat ensures charge sustaining. AGAIN DEPENDENCE ON FUTURE CYCLE!

A constant estimate λ0 can be obtained by inferring the driving conditions; but fuel economy and final charge very  sensitive to this choice.

dtmJ ft

t f∫=0

2 42

oc oc batt batt

batt batt

V V R Pd SOCdt C R

− −= −

2 4( , ) ( )

2oc oc batt batt

fbatt batt

V V R PH u t m t

C Rλ

⎛ ⎞− −⎜ ⎟= + −⎜ ⎟⎝ ⎠

( , ) 0d H u tdt SOCλ ∂= − =

∂

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Equivalent Consumption Minimization Strategies: ECMS

• Instead of the charge sustaining constraint, use of electrical energy is directly penalized in an instantaneous cost function using a fuel equivalence function Ф:

• The challenge is approximating the equivalence function which depends on energy conversion efficiencies in the future.

• One popular approach is evaluation of Ф based on the average energy paths from fuel to storage of electrical energy and vice‐versa.

( )f LHV battJ m H Pϕ= +

f LHV battJ m H s P= + ×

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Model Predictive Power Management• Minimize

Subject to system dynamics and several constraints. Use a receding 

horizon approach. 

Can be translated to a: Nonlinear program, dynamic program or   

simplified to a quadratic or linear program.

MPC suitable for handling complexity of next generation hybrids:– Multiple degrees of freedom requires more systematic optimization

– Pushing system components to their limits: constraints

– More far‐sighted than ECMS still causal and real‐time implementable

– Ease of integration of future road data

( )221 2 0min

i P

fu k i

J Q m Q SOC SOC+

=

⎡ ⎤= + −⎣ ⎦∑

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MPC: Preliminary Results

Sponsored by Ford Motor Company

Dean shows reduction in fuel use with MPC over his rule-based algorithm

for an ultracapacitor parallel hybrid. (Results presented earlier.)

Ali shows a more flexible and systematic control design with MPC for multi-

DOF hybrids. (Results to appear next year.)

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Still a Next Step: Use of Future Road Information

Sponsored by Intermap Technologies

Preliminary Results: Chen shows up to 4% additional reduction in fuel use when future road grade known in highway driving, depending on the terrain. A modified rule-based was used.(Details in the next ACC)

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Ultracapacitor Assisted Powertrains

D. Rotenberg, A. Vahidi, and I. Kolmanovsky, “Ultracapacitor Assisted Powertrains: Sizing, Modeling and Control, and The Impact on Fuel Economy” 2008 ACC.

BMOD0140 Maxwell ultracapacitor module:Capacitance: 140F Voltage: 48 Volts Mass~13kgEnergy: Only 160 kJ Power: Up to 30~60kW instantaneously

Demonstrated up to 15% reduction in fuel use for city cycle with 2 ultracapacitor modules shown above and a 40kW induction motor.

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Finally My Favorite Hybrid: The Electric Bicycle

mgh

Question: How much of the potential energy can be recovered by regeneration?

Undergrads: Maria, Carl, and Seneca riding the E‐Bike.

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Main References

• L. Guzzella, and A. Sciarretta, Vehicle Propulsion Systems, Springer 2005.

• M. Ehsani, Y. Gao, S. Gay, and A. Emadi, Modern Electric, Hybrid Electric, and Fuel Cell Vehicles, CRC Press 2005.

• J. Larminie, and J. Lowry, Electric Vehicle Technology Explained, Wiley 2003.

• And several technical papers.