Thermodynamic Based Modeling for Nonlinear Control of Combustion Phasing

in HCCI Engines

J.B. Bettis, J.A. Massey and J.A. DrallmeierDepartment of Mechanical and Aerospace Engineering

Missouri University of Science and TechnologyJ. Sarangapani

Department of Electrical and Computer EngineeringMissouri University of Science and Technology

Oak Ridge National LaboratoriesJune 23, 2010

– Background– State-Space Methods– Specific Objective– Experimental Setup– Model Development– Results– Extension to Other Fuels– Conclusions

Outline

– Unlike SI or CI engines, HCCI requires advanced control strategies for proper control of combustion phasing.

– A model which captures the key dynamics of the HCCI process is essential to achieve this control.

– Modeling the onset of combustion is difficult due to its dependence on chemical kinetics through reactant concentrations and temperature (Yao et al.)

– Control-oriented models must remain as simplistic as possible while still capturing the key dynamics of the process.

– Previous models of this nature have been developed, most of which utilize linearization in order to achieve effective control (Shaver, Roelle et al).

Background

State-Space Methods for Control• Strategy used for advanced control

– Can handle multiple input-multiple output nonlinear systems• Represented by a discrete system of the form:

– xk+1 = F(xk,uk) (i.e. T1,k+1 = F(T1,k, αi,k, θ23,k, Tin,k, αe,k, αe,k-1))– Current state is determined by previous state and input– F is typically nonlinear– Control input is inside the nonlinearity

• Linearization essentially simplifies the control problem, but comes with a price– F becomes linear – xk+1 = Axk + Buk– Reduced operating range and loss of some nonlinearities

• This model developed with nonlinear control in mind– Significant challenges in control, but more accurate– Motivation for a discrete state engine model

The specific objective of this work is to develop a nonlinear control-oriented model of the HCCI process which provides a platform for

nonlinear controller development.Methodology:1. Use a five state ideal thermodynamic cycle to develop a

discrete model.2. Investigate the engine cycle to determine where it

should begin for control.3. Investigate HCCI combustion timing models to

determine which one best balances accuracy and simplicity.

Specific Objectives

Experimental Setup• Hatz 1D50Z CI engine operating in HCCI mode• Existing preliminary data taken by Scott Eaton and Jeff Massey at

ORNL.• Varied intake temperature using resistance heater to vary timing• Run using a 96RON Unleaded Test Gasoline (UTG96)• Sister engine being set up at MS&T

Model Development

• Five state thermodynamic cycle– Adiabatic, constant pressure induction– Isentropic compression– Constant volume combustion– Isentropic expansion– Isentropic blowdown to an adiabatic, constant

pressure exhaust• Stoichiometry modeled using C/H = 7/16

– Gasoline-type fuels (exhibit little low temperature heat release (LTHR))

– Extension to other fuels possible

Model Development

Engine cycle begins with compression.

Model Development (Combustion Timing)

• Integrated Arrhenius Rate model (Shaver)– Relates timing to reactant concentrations and

temperature– Evaluate integrand at TDC– Modified integration limits

Threshold calculated at one setpoint and held constant at all others.

Model Development (Combustion Timing)• Variable Δθ

– Real combustion event is not instantaneous

– Exp. data shows relation to SOC – Developed correlation from

exp. data• Related to chemical kinetics

(Chiang, Stefanopoulou) • Residual fraction

– Effects combustion through temperature and dilution.

– Introduces cyclic coupling– Utilized correlation from the

literature (Waero)

• Definitions for control– State variables

• Temperature at IVC• Residual fraction

– Inputs• Intake temperature• External EGR fraction• Fueling rate

– Outputs• Peak pressure• θ23

Model Development (Control)

6 gpm UTG96Tin=495K

9 gpm UTG96Tin=463K

Results - ValidationPressure Evolution

• Simple model captures pressure evolution

• Single threshold captures drop in peak pressure

Results - ValidationSOC Tracking

Fdes evaluated using 9 gpm fueling rate at Tin=463K.

Trends are most important for control.

9 gpm UTG96

6 gpm UTG96

Results - ValidationModel θ23 vs. Exp. CA50

Variable Δθ has significant impact.

Constant Δθ representative of linearization.

9 gpm UTG96

6 gpm UTG96

Results

Heat transfer effects.Unburned Hydrocarbons.

UTG96

UTG96

socPPPRR 3

EfficiencyPressure Rise Rates

EnergyFueligW

ResultsHCCI Operating Range

9 gpm fueling rateUTG96

Excessive pressure rise rates

Late combustion results in significant

cyclic variationsLimits effectively captured by model.

ResultsHCCI Operating Range

9 gpm fueling rateUTG96

Excessive pressure rise rates

Late combustion resulting in significant

cyclic variations

Future control objective: Maximize efficiency while minimizing PRR.

Preliminary ResultsClosed-Loop Control

• Optimal Neural Network controller tracks a desired θ23.– Possible future control objectives are also shown

Preliminary ResultsClosed-Loop Control

• Controller based on previous work done at MS&T for lean SI engines.

• Nonlinear NN controller. • Controller learns how the

model behaves and then tracks a desired θ23.

• Noise added to states

Extension to Other Fuels

Experimental data reveals that all fuels behave similarly as intake

temperature is varied.

How can we explain the shift seen in the experimental data as

the fuel is varied?

Similarities between HCCI auto-ignition and SI knock suggest that RON and

MON may be responsible.

Extension to Other Fuels• Due to differences in engine

operating conditions, RON and MON alone cannot fully describe HCCI ignition (Kalghatghi)

• It turns out Octane Index (OI) does a good job of predicting HCCI auto-ignition (Kalghatghi) Combines RON and MON values Accounts for engine operating

conditions

67.31135.000497.0where 15

compTK

KSRONOI

Oxygenates

Gasoline-Type

Hydrocarbons and alcohols exhibit different behavior.

PG

UTG

TRF

UTG

TRF

E50

E50

E85

Extension to Other Fuels• Physical relationship between OI and Ea

• Resistance to auto-ignition vs. energy required for reactions to occur

• Developed an experimental correlation between OI and activation temperature (Ea/Ru)• Based on experimental combustion timing

E85E50TRF

UTG96

PG

• Using the same threshold value, the activation temperature was modified to account for different fuels

• Separate model developed for alcohols based on E85 stoichiometry• Same general form as previous model

• Accounting for OI allows the model to predict ignition timing for various fuels

Extension to Other Fuels

Gasoline-Type Oxygenates

Conclusions– A control-oriented model of the HCCI process was

developed in the form of a nonlinear discrete time system for state space control.

– This model was validated against experimental HCCI data and was able to accurately predict trends.

– The model displays an operating range similar to that seen in experiment.

– The model displays high sensitivity to intake temperature, similar to what is seen in the literature (Yao et al.)

– Extension to other gasoline-type fuels is possible by modifying the activation temperature to reflect changes in OI.

AcknowledgmentsFunding for this project was provided by the

National Science Foundation under grant ECCS-0901562. Also, thanks to Dr. Bruce Bunting of

ORNL for allowing data collection from the Hatz engine.

Questions?

State Space Methods

• Model results in a non-affine nonlinear discrete system.– xk+1 = F(xk,uk, uk-1)– yk = H(xk,uk-1)

• Control input is inside the nonlinearity• F and H are not accurately known, so how can

we linearize it?• Significant challenges in control due to MIMO

non-affine system.

350 360 370 380 390 400 410 420 430 440 450 460 470350

360

370

380

390

400

410

420

430

440

450

460

470

Theta23 (i), (CAD)

Thet

a23

(i+1)

, (C

AD

)

Theta23 Return Map for Varying Intake Temperatures (alphae = 0)(9 gpm fuel rate)(Tegr = 300)(Variable dtheta)

Temp = 410Temp = 430Temp = 450Temp = 470Temp = 490

ResultsOutput Sensitivity

• Gave random 1% perturbations to Tin

• Observed effects on control outputs

Ignition does not occur for intake temperatures less than 430 K, which is also seen in the experimental data.

9 gpm fueling rateNo EGR

0 5 10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25

30

35

40

45

50

55

60

65

Peak Pressure (i), (bar)

Pea

k P

ress

ure

(i+1)

, (ba

r)

Peak Pressure Return Map for Varying Intake Temperatures (alphae = 0)(9 gpm fuel rate)(Tegr = 300)(Variable dtheta)

Temp = 410Temp = 430Temp = 450Temp = 470Temp = 490

Sensitivity increases as temperature decreases.Outputs much more sensitive to temperature than dilution.

Preliminary ResultsClosed-Loop Control

9 gpm fueling rateTin = 463 K

Control switched ON

Controller effectively rejects noise.

Cyclic variability is significantly reduced when control is switched on.

Preliminary ResultsClosed-Loop Control

Optimal controller results in a tradeoff between tracking Theta23

and energy expended (via Tin).

Intake temperature required to track Theta23.

The faster we make the Tin actuator, the faster we can track Theta23.

Preliminary ResultsClosed-Loop Control