physics-based modeling and control of homogeneous charge compression ignition (hcci) engines

Physics-based Modeling and Control of Homogeneous Charge Compression Ignition

(HCCI) Engines

Gregory M. Shaver

Dynamic Design Lab

May 6th, 2005

Department of Mechanical Engineering

Stanford University

Stanford UniversityPhysics-based Modeling and Control of Homogeneous Charge Compression

Ignition (HCCI) Engines

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Outline

What is residual-affected HCCI? What are its benefits?

Hurdles to practically implementing HCCI Lack of combustion trigger Cyclic coupling

Dynamic modeling of HCCI

Making HCCI practical with feedback control

Conclusions and future work



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What is Residual-Affected HCCI?

Residual-Affected Homogeneous Charge Compression Ignition Advanced combustion strategy for piston engines

Combustion due to uniform auto-ignition using compression alone

Hot exhaust gases reinducted using Variable Valve Actuation (VVA)

Main benefits 1. Increased efficiency compared to SI

2. Modest compression ratios

3. Drastic reduction in NOx emissions (i.e. smog)



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HCCI with Variable Valve Actuation



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Reactants (fuel & air) & previously exhausted gases (residual) inducted



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Compression of mixture



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Compression of mixture causes auto-ignition uniform, fast & uncontrolled



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Useful work from expansion



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Hot combustion products exhausted



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Hot combustion products exhausted, portion reinducted



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Valve motions from VVA determine: inducted gas composition amount of compression



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Sudden rise in pressure combustion initiation



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Sudden rise in pressure combustion initiation

Work output: PdVW



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HCCI with VVA -Challenges

Goal: achieve desired combustion timing & work output

Challenges No direct initiator of combustion Cycle-to-cycle coupling through exhaust gas

Significantly complicate transient load operation



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HCCI with VVA -Challenges

Goal: achieve desired combustion timing & work output

Challenges No direct initiator of combustion Cycle-to-cycle coupling through exhaust gas

Significantly complicate transient load operation To date – HCCI impractical!!



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Research Goals

Make HCCI practical through closed-loop control Stabilize process & control work output

Modeling Objective: Simple physical models that capture behavior most relevant for control Cyclic coupling Combustion timing In-cylinder pressure evolution (work output)

Control Objective - Control of: Combustion timing – make combustion sure happens! Work output – the key output of the engine

efficiency & reduced emissions come as result of process



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Previous Work – Simulation Modeling

Ogink and Golovitchev 2002, Babajimopoulos et al. 2002 Multi-zone modeling of HCCI

Kong et al. 2002 Multi-dimensional CFD models using detailed chemistry

Many others

Complex flow and chemical kinetics models Capture general steady state behavior

Ignore cycle-to-cycle coupling

Exhibit long run times - ~12 hours per engine cycle



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Contributions – Simulation Modeling

Developed a simulation model of residual-affected HCCI that:

Captures the cyclic couplingPredicts behavior during steady state & transients

Captures ignition via kinetics with a simple, intuitive model runtimes: ~ 15 seconds per engine cycle (amenable to

use as a control testbed)



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Previous Work - Control

Agrell et al. 2003, Haraldsson et al. 2003, Bengtsson et al. 2004, Olsson et al. 2001, Matthews et al. 2005, others Various approaches to control combustion timing or work

output

In all cases: controller hand-tuned or synthesized from black-box models



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Contributions - Control

Physics-based control model of HCCI The first physics-based approach to control of HCCI

Generalizable Enables use of control engineering tools:

Theoretical control designStability analysis

Control strategies for:Combustion timingPeak pressure or work output



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Outline - Modeling Strategies

Simulation model Gain some intuition of the process

What are key features?What are relevant control inputs & outputs?

Control model Need a slightly simpler physical description for synthesis The launching point for developing control strategies

…..making HCCI practical!!



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Experimental Apparatus

Single cylinder engine With VVA

Fuel used: Propane

Compression ratio Variable: 13-15.5

Engine speed Fixed: 1800 rpm

In-cylinder pressure transducer Combustion timing Peak pressure Work output



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1st law analysis of cylinder and exhaust manifold

HCCI Simulation Model



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1st law analysis of cylinder and exhaust manifold Steady state 1D compressible flow relations




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Heat transfer In-cylinder (modified Woschni)

Ref: Chang et al. 2004 Exhaust manifold




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Combustion model Wiebe function What do we use as a combustion trigger?




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Combustion model Wiebe function What do we use as a combustion trigger?

Resulting Model – 9 nonlinear ODEs




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Temperature Threshold

Assume HCCI occurs at a threshold temperature A fit at one temperature…



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Temperature Threshold

Assume HCCI occurs at a threshold temperature Fit at one temperature… doesn’t hold at others!

Increasing residual



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What Happened?

Simulation model: earlier timing for increasing residual More residual means mixture temperature Higher temperature leads to early timing

Experiments show more constant timing

Is some physical effect missing? Yes! Concentration of reactants More residual means lower reactant concentration



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Integrated Arrhenius Rate Equation

Simple model for start of combustion Integrated Arrhenius rate

Constant threshold, a, b and Ea from published experiments

Contributions from temperature & reactant concentration captured

dOHCRTEAK ba

VC ath

th

283/exp

thK



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Integrated Arrhenius Rate

Set threshold at one operating point…



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Set threshold at one operating point… …and pressure, timing & work output at all points is captured

Increasing residual




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Note: can vary composition without much change in timing

Increasing residual



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Steady state behavior with propane captured

What about transients?Changes in load

Can the model capture these?

Simulation Model: Can it be extended?



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Simulation Model: Transients

1st operating point has higher steady state temperature than 2nd

The elevated exhaust temperature advances combustion process during transition

As exhaust temperature decreases, behavior reaches new steady state

Cycle 1

Cycle 2

Cycle 6

EVC 180IVO 70EVC 185

IVO 50

Valve Profiles1 2-6

Experiment



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Simulation Model: Transients

Simple model captures the coupling and ignition behavior during transition

Cycle 1

Cycle 2

Cycle 6

Cycle 1Cycle 2Cycle 6

EVC 180IVO 70EVC 185

IVO 50

Valve Profiles1 2-6

Simulation

Experiment



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Results from Simulation modeling

Aspects most relevant for control captured with simple simulation model: Cyclic coupling & combustion timing In-cylinder pressure evolution

Approach can handle: Steady-state behavior Transients

A valuable virtual testbed for control



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Motivation for Control Model

Simulation model has a lot of benefits

Still, too complex for synthesizing control strategies

Motivates a simpler dynamic model1. Enabled through additional physical assumptions

2. Discretizing the process (induction, compression, etc.)

3. Linking processes



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Control Model Assumptions

Assumptions: Induction: atmospheric pressure Isentropic compression & expansion HCCI is fast: constant volume combustion In-cylinder heat transfer:% of combustion energy



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Control Model Assumptions



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A Simple Control Model



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Step through process to develop model of dynamics



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Step through process to develop model of dynamics

dynamics



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Peak Pressure Dynamics

The peak pressure dynamics takes the form:

Fairly complex nonlinear dynamic model



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Fairly complex nonlinear dynamic model Can see dependence on:

Control inputs



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Control inputsCyclic coupling



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Control inputsCyclic couplingCombustion timing



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Control inputsCyclic couplingCombustion timing

How do we model initiation of combustion, comb



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Combustion Timing Dynamics

Recall the integrated Arrhenius rate model:

dOHCRTEAK ba

ath

th

vc283/exp



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Integrand takes on largest value at TDC

dOHCRTEAK ba

ath

th

vc283/exp



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Integrand takes on largest value at TDC Simplify: begin integration at TDC with values at TDC

dOHCRTEAK ba

ath

th

vc283/exp



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dOHCRTEAK b

TDC

a

TDCTDCath

th

TDC283/exp

~



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TDCthb

TDC

a

TDCTDCa

b

TDC

a

TDCTDCath

OHCRTEA

dOHCRTEAKth

TDC

283

283

/exp

/exp~



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Integrand takes on largest value at TDC Simplify: begin integration at TDC with values at TDC Algebraic expression exists for each variable

TDCthb

TDC

a

TDCTDCa

b

TDC

a

TDCTDCath

OHCRTEA

dOHCRTEAKth

TDC

283

283

/exp

/exp~



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Integrand takes on largest value at TDC Simplify: begin integration at TDC with values at TDC Algebraic expression exists for each variable

TDCthb

TDC

a

TDCTDCa

b

TDC

a

TDCTDCath

OHCRTEA

dOHCRTEAKth

TDC

283

283

/exp

/exp~

),,,,,( 1,,1,11, kvckvckcombkkkkcomb Pf



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Control Model

Peak pressure and combustion timing dynamics together give:

A nonlinear 2-state, dynamic, discrete system model

),,,,,(

),,,,,(

1,,1,11,

1,,1,11

kvckvckcombkkkkcomb

kvckvckcombkkkpk

Pf

PfP



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Control Model Validation

Control model captures Steady state & transient

Peak pressure Combustion Timing

Captures Cyclic coupling Ignition via kinetics



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Control Modeling Summary

HCCI is difficult to control: Cyclic coupling No direct combustion trigger

Control model captures these phenomena!! Simple model tells us how dynamics are affected by

control inputs Is a launching point for:

Synthesizing control strategiesAssessing system stability

Generalizable



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Outline of Control Implementations

From control model

1. Peak-pressure control at constant combustion timing

2. Work output control at constant combustion timing

3. Simultaneous peak pressure and combustion timing control

Many other approaches possible



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Peak Pressure Control w/ Constant timing

Fix final valve closure

Vary composition to control peak pressure A “static” approach to controlling timing

A large number of control approaches can be utilized

),,,,,(

),,,,,(

1,,1,11,

1,,1,11

kvckvckcombkkkkcomb

kvckvckcombkkkpk

Pf

PfP

),,( 11 kkkk PfP



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Peak Pressure Control w/ Constant timing Linear Controller Synthesis

A common control approach is to linearize the system model Linearizing about an operating point yields:

Simple linear control laws can be synthesized

kk

k

k

k

cP

c

c

c

cP

c

~

1~00~

20

22

1

1

20

21

20

23

P

PPkk kk

~where:

,P



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Peak Pressure Control w/ Constant timing

In closed-loop:

Controller synthesized from linearized version of model

Is controller stable in closed-loop with nonlinear model?



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Peak Pressure Control w/ Constant timing Nonlinear Stability Analysis

Using: Lyapunov

stability theory Convex

optimization

Shows: Simple linear

controller stabilizes entire operating regime



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Peak Pressure Control w/ Constant timing Experimental Implementation

Accurate control of peak pressure Mean tracking Fluctuation reduction

Increases robustness

Little change in phase

What about direct control of work output (IMEP)?



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Experimental Work Output Control

Rapid mean tracking & fluctuation reduction

We can control work output, while keeping timing roughly constant



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Experimental Work Output Control

Positive and negative load transients

What about simultaneous control of combustion timing and work output?



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Combustion Timing & Work Output Control

Add other control input: final valve closure Significant control knob for combustion timing

Simple approach Separate linear controllers for peak pressure and timing



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Decoupled Peak Pressure and Phase Control

Maintain cycle-to-cycle peak pressure controller, vary phase more slowly



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Approach works

Simultaneous control of timing and peak

pressure

Experiments with Decoupled Control



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Comments on Control Experiments

Simple physics-based controllers works well Implementation is straightforward Mean tracking & fluctuation reduction of

peak pressure work output

Combustion timing fairly constant

Independent control of peak pressure & combustion timing

Many others possible



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Conclusion

HCCI has a promising future as a cleaner, more efficient strategy Hurdle: controlling the process No combustion initiator & cycle-to-cycle coupling

The good news: HCCI is amenable to model-based control Key behaviors captured in both simulation and control models

Simulation & control models capture: Steady-state Transients

Physics-based control of: Peak pressure Work output Combustion timing



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Future Work

Study different control approaches

Control of multi-cylinder HCCI engines Results to date with single-cylinder engines

Cylinder-to-cylinder dynamics now play a key role!

Change the world!



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Acknowledgments

Chris Gerdes

The Dynamic Design Lab

Partners in crime: Matt Roelle & Nikhil Ravi

A great sponsor – Robert Bosch Corporation Jean-Pierre Hathout, Jasim Ahmed, Aleks Kojic & Sungbae Park

The defense Committee Chris Edwards, Sanjay Lall, Matt Franchek & Steve Rock

Stanford University

physics-based modeling and control of homogeneous charge compression ignition (hcci) engines

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