HCCI Model Adaptation

Residual Gas Temperature Correction: SI-HCCI Transition First HCCI Cycle

Based on the inspection in Sec. 3.1, any error in the combustion phasing prediction on cycle HCCI 0 of an SI-HCCI transition is attributed to the high SI exhaust temperature and low residual mass pushing the model’s charge mass and temperature calculation far outside the nominal HCCI range. Cycle HCCI 0 is thus distinct from all other HCCI cycles, where combustion phasing error will be attributed directly to error in the Arrhenius combustion phasing correlation. This policy is chosen following the results of Sec. 3.1, which suggest that the strongest source of error on cycle HCCI 0 is in the excursion of the thermodynamic state far outside the nominal HCCI range, while for the remainder of the cycles error is mostly due to nominal model error. The combustion phasing error on cycle HCCI 0 is captured by the residual gas temperature correction factor kr introduced in

Sec. 3.1.3, and the same method as in Sec. 3.2.1 is applied to backtrack from the measured θ50 to the

necessary kr value for the parameter adaptation. The Arrhenius integral inversion involved in this

method is carried out using the Arrhenius tabulation explained in Sec. 4.3.2 which allows execution in real-time. For the range of conditions examined, kr is parameterized as a linear function of θevc

as in Sec. 4.3.2, ˜ kr= aTkrΦkr (5.13) Φkr = h θevc 1 iT (5.14) Note that on cycle HCCI 0 during an SI-HCCI transition no parameter updates are executed other than the residual temperature correction, and on all other cycles the residual temperature correction update is deactivated.

Torque Model

Similar to the SI case, the HCCI N M EP calculation in the model of Sec. 2.4 mainly comes from simplified physics, with the exception of the combined thermal/combustion efficiency factor ηλ.

However, this factor is not convenient for use for adapting the torque model to match transient data, because it only accounts for the dependency of N M EP on AFR and nothing else. Thus the adaptation of the HCCI torque model is carried out following the same approach as in the SI case, where corrective parameters are introduced to account for error in the N M EP prediction:

∆τ,H = N M EP −N M EP˜ (5.15) ˜ ∆τ,H = aTτ,HΦτ,H (5.16) Φτ,S = h mf 1 iT (5.17) where ∆τ,H and ˜∆τ,H are the actual and predicted errors in the HCCI N M EP prediction. The

dependence of the torque error is simplified to be a function of fuel only, because combustion phasing is typically constrained to a smaller window in HCCI than SI and so deviations of θ50

from the optimal cannot be as large. As is apparent from the SI-HCCI transitions of Sec. 4.4, the validity of this simplification can weaken on the first several HCCI cycles of the transition due to early combustion phasing caused by high exhaust temperatures. However, the torque model is not updated on the first HCCI cycle HCCI 0 where only the kr adaptation executes, which is often

the point of earliest combustion phasing. A few early cycles may follow HCCI 0 which may not be captured properly with the simplified ˜∆τ,H parameterization, however the simplified method was

still found to provide notable improvements in torque control.

Combustion Phasing Model

As previously stated, error in the HCCI combustion phasing model on all cycles other than HCCI 0 is attributed to the model’s Arrhenius correlation Eq. 2.87. This correlation is not straightforward to work with for developing a linear parameter update method, since the integrated Arrhenius rate creates a nonlinear and implicit function. However, it can be noted that many of the dependencies in the Arrhenius correlation are parameterized into the Arrhenius threshold Kth, which is an explicit

expression that is linear in the parameters. The combustion phasing model update is thus carried out targeting the parameters of the Arrhenius threshold, while leaving the parameters np and Eawhich

are inside the nonlinear and implicit Arrhenius integral unchanged. Note that the correlation for the Arrhenius threshold Kth is taken from Eq. (A.9) for the reparameterized model in Appendix A for

the replica experimental engine, since experiments with the proposed adaptive scheme are carried out on this replica engine. A term to capture variation of in-cylinder temperature is augmented to the

Arrhenius threshold, since the dependence of the Arrhenius correlation on in-cylinder temperature enters through the Arrhenius integral and so is inaccessible

K_th∗ = Z θ∗_soc θivc 1 ωpc(θ) np_e  −Ea RTc(θ)  dθ (5.18)

θ∗_soc= (θ50− asoc,0)/asoc,1 (5.19)

pc(θ) = pivc  Vivc V (θ) nc , Tc(θ) = Tivc  Vivc V (θ) nc−1 (5.20) ˜ Kth= athΦth (5.21) Φth = 

n2_λrnsoi nλrnsoi nsoi n

2

λr nλr nTrc

1 Tivc− T_ivcmin

1 T (5.22) nλr = λr− 0 1 − 0 , nsoi= θsoi− 280 390 − 280, Trc= Trc− 600 1000 − 600 (5.23)

where θ∗_soc is the start of combustion timing to match the measured θ50. Eqns. (5.18)-(5.20) convey

that the Arrhenius threshold K_th∗ to perfectly match the measured θ50 is obtained by inverting the

θsoc to θ50 linear fit (5.19) and then running the Arrhenius integration up to the desired θsoc∗ with

the estimated pressure and temperature. K_th∗ then takes the place of the “measured” output which the model prediction ˜Kth tries to approximate, with a normalized parameterization that follows

the same form as in Eq. (A.9) with an augmented term for Tivc. The hyperbolic dependence on

Tivc is chosen to approximate the profile of the full Arrhenius correlation, which tends to have a

nonlinearly increasing slope as Tivc decreases and misfire conditions are approached. The Tivcmin

shift factor is chosen near the lower range of feasible Tivc values to increase the sensitivity of the

hyperbolic dependence in that region, but still outside the feasible Tivc range to avoid dividing by

zero. Note that the Arrhenius integration in Eq. (5.18) is evaluated using the look-up table method described in Sec. 4.3.2 to faciliate real-time execution of the adaptive law.

5.2

Experimental Results

The effects of the SI and HCCI parameter update methods described in Sec. 5.1 are examined in the SI-HCCI direction of the mode transition by augmenting the update methods to tune the parameters of the baseline SI-HCCI transition controller from Ch. 4 in online operation. The adaptive experiments are carried on the replica experimental engine from Appendix A, which also served as the experimental apparatus for the baseline controller of Ch. 4. The experimental conditions are perturbed from those in the baseline controller results of Sec. 4.4 in that a different fuel batch is used, which is a reference type fuel without any ethanol content as opposed to the 10% ethanol pump gas of Sec. 4.4. The fuel is of type Corrigan UTG 96, whose properties are listed in

Table 5.2. Despite that both the reference and pump fuel batches have the same AKI, daily check points and general SI-HCCI mode transition experimental observations indicate that reference fuel tends to increase engine knocking relative to the original pump gas. The cause for this result could not be discerned from the given information, which did not include the research and motor octane number of the pump gas, or detailed information about the pump gas aromatics, olefins, etc. One reason could be that the ethanol in the pump gas somehow provides better anti-knock properties, and/or slows the rate of coking in the combustion chamber which will reduce deposit formation and the associated combustion advancing effects. In any case, the performance of the baseline SI-HCCI transition controller from Chapter 4 suffers in some experimental trials due to higher knocking, but it will be seen that the parameter adaptation is able to restore performance and even surpass the baseline results in Sec. 4.4 in most cases. As in Sec. 4.4, the responses of two of the four cylinders which elicit anomalous torque and AFR responses are omitted.

Fuel Property Value

Specific Gravity 0.744

Vapor Pressure 9 psi

Net Heating Value 42.90 MJ/kg

Carbon Weight % 86.4 %

Hydrogen Weight % 13.6 %

Oxygen Weight % 0 %

Stoichiometric Air-Fuel Ratio (CH-based) 14.77

Anti-Knock Index 93

Sensitivity 7.9

Table 5.1: Properties of Corrigan UTG 96 gasoline used as fuel in adaptive SI-HCCI transition experiments.