�

24th American Control Conference

June 8-10, 2005

Diesel Engines

� Offer superior fuel economy, albeit at higher cost and complexity of the aftertreatment system

� Achieved remarkable passenger car market penetration in Europe and growing presence in North America� Thanks to advances in technology and controls, diesel engines

are no longer sluggish nor spewing clouds of black smoke

� Used also in commercial heavy vehicles, off-road, construction, marine and power generation applications� Constitute more than 90 percent of “prime movers”

�

24th American Control Conference

June 8-10, 2005

Modern Diesel Engines

� Compression Ignition DI

� Variable Geometry Turbocharged (VGT)

� Operate lean and require lean aftertreatment system

� Use high EGR rates

� Fueling rate is a primary actuator for torque management

� Fuel rate shaping and multiple injections for torque, noise and emission control

VGT

�

24th American Control Conference

June 8-10, 2005

Mean-Value Modeling� Intake manifold dynamics

• density, pressure, composition

� Exhaust manifold dynamics• density, pressure, composition

� Turbocharger dynamics• turbocharger speed, turbine and

compressor mass flow rates

� Engine cylinder block • Cylinder flow, temperature rise

and torque

� EGR flow model� Engine speed dynamics

VWWW

i

cylegrc

i

−+=ρ�

( )( )���

�

�

���

�

�

−−+−+=cQ

TWTWTWVPp

iicylECTeegrcc

ii

TR �

� εεγ1

,ρRPT

i

ii=( )

VWFFWF

Fii

egrieci

i ρ−+

= −�

VWWW

e

egrte

e

−−=ρ�

( )V

WFFFee

eene ρ

−=�

���

�

�

���

�

�

−−−=cQ

TWTWTWVPp

eeegretenge

ee

R ��

γ

,ρRPT

e

ee

=

�

24th American Control Conference

June 8-10, 2005

Turbocharger ModelingTurbine sub-model

),( vgtx

et

e

et P

Pf

TP

W χ=

)( tetpt TTWc −=Π

Compressor sub-model

T/C rotational dynamics

ex

e

e

t

e

tctet T

PP

PP

TN

TT ⋅���

�

�

���

�

�

���

����

�−⋅

��

�

�

��

�

�−=

−γ

γ

η

1

1,

),( 1

amb

tc

ambc

amb

ambc

TN

PP

fTP

W =

)( ambccpc TTWc −=Π

���

�

�

���

�

�

−���

����

�⋅

��

�

�

��

�

�+=

−

1

,

1

1

1

γγ

η amb

ambamb

tcc

ambambc P

P

PP

TN

TTT

��

���

�

Π−Π=

30π

tctc

cttc

NJN�

surge region

choke region

�

24th American Control Conference

June 8-10, 2005

Engine Cylinder Block

Torque production Temperature rise

Cylinder flow

)N()N,P,P()F,,N,W( friciepumpifind ττδττ ++= ),,,,( δicylfriseie FWWNTTT ∆+=

),,,,(120

NTTPPPRTNV

W eieivolii

dcyl η⋅⋅= (+engine cycle

delays)

�

24th American Control Conference

June 8-10, 2005

Exhaust Gas Recirculation(EGR) Model

EGR valve flow model Exhaust flow and composition

)(30

,)(

303

}1,)()(

)1)(()()(min{)(

)()()(

21

21

211

21

tNt

tNt

ttWttW

ttWttWttFtF

ttWttWtW

fcyl

sfcylin

fcyle

=⋅=

−+−+Φ−+−−

=

−+−=( )

( )

( )( )

���

����

�

+���

����

�

+

���

����

�

+−−

+

−+

≤=

>��

���

� −−

=

���

����

�=

12

12

12

1121

21

112

12

γγγ

γγγ

γγ

γγ

γγ

γγ

γ

χ

rrf

rrf

PP

fW

egr

egr

e

iegr

e

eegrdegr

rr

RTPC

for

for

�

24th American Control Conference

June 8-10, 2005

Model Validation

Fuel Steps VGT Steps

�

24th American Control Conference

June 8-10, 2005

Diesel Model Summary

� Higher order than for gasoline engines� Contains significant nonlinearities� Contains delays � Using physics-based characterizations is advantageous� Sub-models becomes parts of the control strategy� Analysis goals may necessitate additional modeling

� Crank angle resolved cylinder-by-cylinder behavior� Uncertainties due to part-to-part variability, aging, operating

conditions� Aftertreatment system

24th American Control Conference

June 8-10, 2005

Static Subsystem Interactions

MAP – Manifold Air Pressure

MAF – Compressor Mass Air Flow

“b” – nominal operating point:

(Maximizes burnt gas fraction subject to constraint on AFR)

iP=

cW=

�

24th American Control Conference

June 8-10, 2005

Static Subsystem Interactions (cont’d)

Coordinated EGR/VGT ControlInstability Caused by Gain Reversal and Incorrect Set-

Points

��

24th American Control Conference

June 8-10, 2005

Dynamic Interactions

� Engine dynamics become slower with EGR valve opening

� Non-minimum phase behavior for a usual selection of outputs

� Non-intuitive optimal transient VGT operating strategies

� Decentralized architecture for EGR/VGT control may not be optimal in transients

��

24th American Control Conference

June 8-10, 2005

Sensor and Controller Configuration Selection

� Steady-state sensitivity to uncertainties� Relative degree & non-minimum phase behavior

considerations� Relative Gain Array (RGA)� Optimal control� I/O Screening� µ analysis� Feedback architecture interplay with the need to

operate at steady-state optimal set-points

��

24th American Control Conference

June 8-10, 2005

Coordinated EGR/VGT Control Approaches

� Linear gain scheduled and gain switching control

� Nonlinear Lyapunov-based control� Feedback passivation� Sliding mode control� Model predictive control� Feedback on estimates� Adaptation

��

24th American Control Conference

June 8-10, 2005

PI Control With Transient Set-Point Governing

A/F response to fuel increase for decentralized PI and TSPG

•Decentralized PI feedback architecture: MAP VGT pos., MAF EGR valve pos.

• “Automatic” gain scheduling based on inverse of plant DC gain

• Transient governor to modify set-points

��

24th American Control Conference

June 8-10, 2005

Nonlinear Lyapunov-based Control

2,

32,

22,

1 )(2

)(2

)(2

µµdiideedcc PP

cPP

cWW

cV −+−+−=

uxgxfx ⋅+= )()(� )(xgxV

uT

��

���

�

∂∂−= γ

� Basic approach (applied to a reduced order model):

��

�

�

−−−⋅−+−−−⋅−

−=��

�

�

)())(()()())((

,22,1

,23,22,1

,

,

deedcc

diideedcc

ct

cegr

PPkcWWbc

PPkcPPkcWWacW

W µµ

γ

� Flow controller:

� Invert EGR valve and turbine flow models to calculate EGR valve and VGT positions

��

24th American Control Conference

June 8-10, 2005

Nonlinear Lyapunov-based Control (cont’d)� Controller response to fuel steps:

Air-fuel ratio

EGR rate

VGT position (percent open)

EGR valve position (percent open)

��

24th American Control Conference

June 8-10, 2005

Composition Estimation and Fuel Limiting

� Problem: Estimate cylinder flow and oxygen concentration in the cylinder flow

� Limit fuel rate according to fresh air charge amount

��

24th American Control Conference

June 8-10, 2005

Cylinder balancing� Problem: Balance individual cylinders to produce equal torque� Approach: Adapt individual cylinder fuel quantity according to

an indication of cylinder imbalance e.g., based on crankshaft acceleration

� Process passage time between two teeth on the tooth-wheel:

)()(

,

12

1

NtNtT

TTI

i

iii

−=−= −

� An alternative measure which is closer related to acceleration and also scales automatically with engine speed is:

)(25.0

,)(60

,12

112

031

1

0

NNN

kN

NNk

TTT

kk

I tot

toti

iii −

=−=−⋅= −

�

24th American Control Conference

June 8-10, 2005

Aftertreatment Control

� Selective Catalytic Reduction (urea)� Lean NOx Trap� Diesel Particulate Filters� Active Lean NOx Catalyst� Combinations of the above

�

24th American Control Conference

June 8-10, 2005

Implementation Considerations

� Automotive microcontrollers are limited in terms of chronometrics and memory

� Control algorithms must be calibratable and designed concurrently with calibration procedures

� Requirements and system interactions (including in abnormal conditions) need to be fully understood

� Portability to different powertrain configurations and maintainability are important