Optimal cold start calibration of spark ignition engines

Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011

Optimal cold start calibration of spark ignition engines Farzad Keynejad ∗ Chris Manzie ∗ ∗

Department of Mechanical Engineering, The University of Melbourne, Australia (e-mail: [email protected], [email protected]).

Abstract: This paper investigates optimal strategies for minimising the conflicting objectives of fuel consumption and warm up duration following an engine cold start. Using a reduced order model, parametric solutions for the optimal air-fuel ratio, valve timing, cam timing and idle speed setpoint are sought in the presence of input constraints. The results are then validated using a dynamic programming approach on a high fidelity engine model, and compared experimentally with a production calibration for an inline 6-cylinder, SI gasoline engine. The methodology used can be readily extended to other mixed objective problems, and can be a useful tool in decreasing engine calibration time. 1. INTRODUCTION Extensive calibration of spark ignition engines is required to meet both emissions legislation and to ensure smooth engine operation in a wide range of operating conditions, and represents one of the most time consuming phases of vehicle development. Consequently, there has been considerable interest in the past to use both model based (for example see Prabhakar et al. (1977); Rishavy et al. (1977); Auiler et al. (1977); Rao et al. (1979); Dohner (1981); Tennant et al. (1983); Sun and Sivashankar (1997); Kang et al. (2001); Maloney (2009)) and model free (Popovic et al. (2006)) approaches to automate the calibration process. However, this extensive body of work is largely characterised by engine-specific results and typically assumes warm engine operation only. Cold start operation is of significant interest as tailpipe emissions and fuel consumption are typically highest during this period of operation. With this in mind, recently there have been significant developments in mean value engine models that encompass a thermal aspect, as discussed in Roeth and Guzzella (2010); Manzie et al. (2009) and Keynejad and Manzie (2010*). The existence of these models allows optimal control techniques to be employed for engine calibration over cold start conditions, which is useful for several reasons - firstly, experimental calibration over the cold start region is extremely slow due to temperature soaks limiting testing to often three cold starts per day; secondly, the increased dimensionality of the problem when temperature is included in the steady state maps used in calibration (a problem that is exacerbated by the increased functionality of modern engines in terms of numbers of actuators); and thirdly, there are conflicting objectives associated with engine cold start which arise from the desire to minimise fuel consumption, but also the need for sufficient thermal performance to ensure catalyst light-off and provide heat to the cabin. The advantage of using optimal control approaches on analytic engine models is that they provide a generic 978-3-902661-93-7/11/$20.00 © 2011 IFAC

solution methodology, that can then be very quickly tuned for an individual engine using either simplified numeric techniques or reduced experimentation (or a combination of both). Here, to simplify the presentation of the methodology, the proposed calibration approach does not explicitly consider tailpipe emissions during cold start, instead assuming that these will map to temperature setpoints and constraints imposed on the engine control variables (such as spark timing and lambda during the warm up duration). Explicit consideration of emissions during cold start can be achieved by augmenting the engine model with emissions capability and an appropriate aftertreatment system model. Static approaches to emissions modelling (e.g. Hafner and Isermann (2003); Fiengo et al. (2003)) may be appropriate following light off, however models capturing catalyst dynamics (e.g. Andrianov et al. (2010)) are likely to be required to enable accurate cold start emissions optimisation. The key contribution of this work is demonstration that analytic (parametric) results for a mixed objective optimisation problem (in this case fuel and warm up time) on a general engine enable the numeric (exact) solution for a specific engine to be found quickly. The implication is that engine calibration can be made a less time consuming process through the incorporation of the methodology, leading to reduced development costs for new vehicle models. 2. ANALYTIC OPTIMISATION To obtain parametric results, a three-state model from Keynejad and Manzie (2010*) is used. This model was previously shown to be capable of capturing cumulative fuel consumption and thermal transients to within 5% of experimentally obtained data over the NEDC cycle. As they are critical to the analysis, the underlying model assumptions and equations are reproduced in this section. Assumption 1. The controllers responsible for maintaining air-fuel ratio, engine idle speed and cam timing provide perfect setpoint tracking at all times.

13022

10.3182/20110828-6-IT-1002.00300

18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

Assumption 1 decouples controller and engine dynamics to enable the best possible performance to be predicted irrespective of control structure employed. This assumption will be relaxed in the numerical analysis later, when local controllers are included. The engine inputs are constrained to limit imposed by emissions and driveability considerations. Consequently, the inputs to be analysed are air fuel ratio, β ∈ [βmin , βmax ]; spark timing, θsa ∈ [θsa,min , θsa,max ]; valve overlap, θvo ∈ [θvo,min , θvo,max ]; and idle speed setpoint, ωidle ∈ [ωidle,min , ωidle,max ]. The following two assumptions will be made about the engine indicated and volumetric efficiency for engine inputs in these allowable ranges, which characterise low- and part-load operation: Assumption 2. Indicated efficiency, ηi , increases monotonically with both spark advance, θsa , and air-fuel ratio, β. Assumption 3. Volumetric efficiency, ηvol , increases monotonically with engine speed, ωcrank , and decreases monotonically with valve overlap angle, θvo . Assumptions 2 and 3 imply a unique mapping between the engine input vector, [u, ωidle ] = [β, θvo , θsa , ωidle ] and a virtual input vector of schedulable setpoints, v = [β, ηi , ηvol , ωidle ]. 2.1 Engine model The outputs of interest when considering cold start fuel consumption are the fuel flow rate, M˙ f , and a representative engine temperature, Trep . This latter output does not model the temperature of a physical state, but instead represents a single lumped temperature that characterises of all the solid and fluid masses in the engine system. Implicitly, this represents an assumption that the temperature of any physical state is monotonically related to Trep . In Keynejad and Manzie (2010*) for example, the actual oil temperature is related to the representative engine temperature by Tˆoil = Tamb + K (Trep − Tamb ), where K was an identified constant. The internal dynamics of the reduced order model can be written in terms of three states: the intake manifold pressure Pim , a representative engine temperature, Trep , and the engine speed, ωcrank , with dynamics given by the following equations: RTamb h ˙ P˙im = Min (Tamb , Pamb , Pim , αth ) Vim i −M˙ out (Tamb , Pim , ωcrank , u) (1) h 1 T˙rep = Q˙ cyl,rep (Tamb , Pim , ωcrank , u) Crep +Q˙ f r,rep (Pamb , Pim , ωcrank , Trep ) i −Q˙ rep,amb (Tamb , Trep ) (2) h 1 ω˙ crank = τind (Tamb , Pamb , Pim , ωcrank , u) Jtotal i −τf r (Pamb , Pim , ωcrank , Trep ) − τdc (3) In (1)-(3), there are boundary conditions set by the ambient pressure and temperature, Pamb and Tamb and the drive cycle, ωdc or τdc . The time constants of the equa-

tions are given by the manifold volume and constant gas Vim properties, RT , the engine inertia, Jtotal , and the repreamb sentative temperature equivalent heat capacitance, Crep . A consequence of Assumption 1 is the throttle is adjusted so that the net torque delivered precisely tracks the defined drive cycle torque, τdc , (or equivalently, the engine speed ωcrank always approximately matches the drive cycle speed, ωdc ) irrespective of the chosen engine controls u. In effect, this means that the effective area of the throttle is an increasing function of ωdc , represented by A¯ (ωdc , ωcrank ). These simpications means (3) effectively forms a constraint equation away from idle, rather than a dynamic equation requiring treatment in the analytical optimisation to follow. Note however, that under idle conditions the crank speed can be scheduled without violating Assumption 1, meaning that ωidle remains a schedulable input to the system. N

V

s It is now useful to define K1 := cyl and K2 := RT1amb , 4π and represent the exhaust gas heat transfer as a function of engine speed, α(ωcrank ) (it can be shown using Nusselt number arguments that α is monotonic in ωcrank ). The right hand side terms of (1)-(3) can now be expressed as functions of known constants and static maps of the states and iinputs according to: M˙ in (Tamb , Pamb , Pim , αth )   p Pamb ¯ = K2 Pamb A (ωdc , ωcrank ) ψ (4) Pim M˙ out (Tamb , Pim , ωcrank , u) βηvol (ωcrank , θvo ) ωcrank Pim (5) = K1 K2 β+1 Q˙ cyl,rep = α (ωcrank ) [1 − ηi (θsa , β)] M˙ f Qlhv (6) Q˙ f r,rep (Pamb , Pim , ωcrank , Trep )

= K1 Pf me (Pamb , Pim ωcrank , Trep ) ωcrank

(7)

Q˙ rep,amb (Tamb , Trep ) = Grep,amb (Trep − Tamb ) (8) τind (Tamb , Pim , ωcrank , u) ηi (θsa , β) ηvol (ωcrank , θvo ) = K1 K2 Qlhv Pim β+1 − K1 Ppme (Pamb , Pim ) (9) τf r (Pamb , Pim , ωcrank , Trep ) = K1 Pf me (Pamb , Pim , ωcrank , Trep ) (10) While Trep is one of the outputs required, the other output of interest in the reduced order model is the fuel used. Applying Assumption 1 to the air fuel ratio controller means the instantaneous fuel flow rate follows from (5): 1 M˙ f (Pim ,ωcrank , u) = M˙ out β ηvol (ωcrank , θvo ) ωcrank Pim (11) = K1 K2 β+1 2.2 Cost function As discussed earlier, cold starting an engine may be considered a tradeoff between minimising fuel use and minimising the time to reach a desired temperature. Furthermore, the relative importance of fuel use and warm up duration may

13023

18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

∗ ∗ γ0 := wF K1 K2 ωcrank Pim ∗ ∗ K1 ωcrank Pim γ1 := Vim ∗ ∗ ∗ K1 K2 Qlhv α (ωcrank ) ωcrank Pim γ2 := Crep ∗ K1 K2 Qlhv Pim γ3 := Jtotal  

change depending on the circumstances since fuel penalties are associated with faster warmup which is unavoidable in the case of emissions, but a small fuel penalty may be tolerable if cabin heat is requested on a cold day. To capture this tradeoff, the following cost function is proposed: Z tf 2 J = wF M˙ f dt + (Tdes (tf ) − Trep (tf )) (12) 0

The constant wF represents a weight applied to the fuel use relative to the warm-up time, while Tdes (tf ) represents the desired temperature at the end of period of optimisation. In the next section, the set of virtual control variables v (and by implication the actual inputs u and ωidle ) that optimise the cost function (12), subject to the plant equations of (1) - (11) and input constraints are sought.

γ4 :=

Pamb ψ

Pamb ∗ Pim

√ Vim K2

(20) (21)

Applying the necessary conditions of (17) with the Hamiltonian of (14) leads to the following inequality which must hold for optimality: [γ0 − γ1 p∗1 β ∗ + γ2 p∗2 (1 − ηi∗ ) + γ3 p∗3 ηi∗ ]

2.3 Parametric solution for optimal cold start engine control

Substitution of (1), (2) and (11) leads to the expression of the Hamiltonian as: ηvol H(x, v, p) = wF K1 K2 ωcrank Pim (β + 1) p   Pamb p1 + K2 Pamb A¯ (ωdc , ωcrank ) ψ K2 Vim Pim    βηvol −K1 K2 ωcrank Pim β+1  p2 α (ωcrank ) (1 − ηi ) ηvol ωcrank Pim + K1 K2 Qlhv Crep β+1 +K1 Pf me (Pamb , Pim , ωcrank , Trep ) ωcrank i −Geng,amb (Trep − Tamb )  p3 ηi ηvol + K1 K2 Qlhv Pim − K1 Ppme (Pamb , Pim ) Jtotal (β + 1) i −K1 Pf me (Pamb , Pim , ωcrank , Trep ) − τdc (14)

(19)

(22)

∗ ηvol β∗ + 1

∗ ∗ + γ4 p∗1 A¯ (ωidle , ωcrank )

The Hamiltonian for the reduced order system can be expressed in terms of the states, x = [Pim , Trep , ωcrank ], Lagrange multipliers, p = [p1 , p2 , p3 ]T , and virtual inputs, v, as: H(x, v, p) = wF M˙ f + p1 P˙im + p2 T˙rep + p3 ω˙ crank (13)

(18)

≤ [γ0 − γ1 p∗1 β + γ2 p∗2 (1 − ηi ) + γ3 p∗3 ηi ] ∗ + γ4 p∗1 A¯ (ωidle , ωcrank )

ηvol β+1 (23)

This sets up four different switching conditions for each of the four virtual control inputs. These switching conditions form surfaces in the p-space, which can be derived as shown in Table 1. To aid in visualising these results, the conditions in the p1 -p2 plane for some arbitrary p3 > 0 are illustrated in Figure 1. The trajectory through the p-space is given by the solution of (16), which is nontrivial explicitly as this represents three coupled equations with time-varying coefficients. However, some important general aspects of the solution can be implied from the structure of the regions outlined in Table 1:

For the derived policy to be optimal (denoted by optimal inputs, v∗ , states, x∗ and costate vector, p∗ ), the following necessary conditions apply from Kirk (1970): x˙ ∗ (t) = ∇p H (x∗ (t) , v∗ (t) , p∗ (t) , t) (15) ∗ ∗ ∗ ∗ p˙ (t) = −∇x H (x (t) , v (t) , p (t) , t) (16) H (x∗ (t) , v∗ (t) , p∗ (t) , t) ≤ H (x∗ (t) , v(t) , p∗ (t) , t) (17) To establish the optimal policy for the virtual inputs, v, only constant idle operation will be considered in entirety due to space constraints, however a discussion of the more general case will also be included. To begin, the following quantities are defined for brevity of the proceeding arguments: 13024

• From Assumptions 2 and 3 the virtual control inputs can now be mapped back to the physical controls. Maximising indicated efficiency corresponds to maximum spark advance, i.e. running at MBT spark, and minimising indicated efficiency corresponds to maximum retard from MBT. Similarly maximising volumetric efficiency corresponds to minimising valve overlap in order to minimise internal exhaust gas recirculation. • Each of the control inputs will switch from low to high efficiency operation at different times for optimality of the solution. For realistic values of the parameters γ0 , ..., γ5 , there will be at most one switch of each control inputs. • The resulting control trajectories consist of: 1) a maximum heat production policy where the engine runs at it’s most inefficient characterised by u = [βmin , θvo,max , θsa,min , ωidle,max ]; 2) a maximum efficiency policy where the engine runs to conserve fuel with u = [βmax , θvo,min , θsa,max , ωidle,min ] ; and 3) a transition policy, which covers the switching of the control variables between the other two policies. The shape of the overall control trajectories is illustrated in Figure 2. • The weighting on fuel use, wF , is directly related to the size of the region corresponding to the maximum efficiency policy in the co-state space, since it appears in γ0 .

18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

a consequence, the engine controls will switch earlier in time.

Table 1. Switching conditions for virtual engine controls as a function of co-state variables Condition If p1 > 0

Result ∗ ωidle = ωidle,min

If p1 < 0

∗ ωidle = ωidle,max

3. IMPLEMENTATION AND RESULTS 3.1 Simulation results

If p2 >

γ3 p γ2 3

ηi∗ = ηi,max

If p2 <

γ3 p γ2 3

ηi∗

If p2 >

−γ0 +γ1 p1 βmax −γ3 p3 ηi∗ γ2 (1−ηi∗ )

∗ , β ∗ ] = [η [ηvol vol,min , βmax ]

If p2 <

−γ0 +γ1 p1 βmax −γ3 p3 ηi∗ γ2 (1−ηi∗ )

∗ , β ∗ ] = [η [ηvol vol,max , βmin ]

!idle,max

!idle,min

To validate the optimality of the results via simulation, a high-order engine model (also from Keynejad and Manzie (2010*)) is used along with local PI controllers on each of the actuators. A modified dynamic programming algorithm was used to determine the optimal control trajectories given the cost function (12) with the modification Trep = Tcoolant , as the coolant temperature is a state in the higher order model. Two cases were considered, the first being an optimal fuel policy with no consideration of temperature (i.e. wF >> 1) while the second case uses a balanced policy that attempts to match the engine coolant temperature of the modelled engine at idle after 300 seconds running using the production engine calibration, (i.e. Tcoolant (300) = 325K), with the weight on total fuel use set to wF = 100.

= ηi,min

"max #vol,min "min

Maximum efficiency region

p

2

p2 = $3p3 / $2

#vol,max

The resulting state and output trajectories are shown in Figure 3, where it is clear that there is a significant fuel penalty relative to the best possible to meet the temperature requirement implied by the production temperature setpoint after 300 seconds.

#i,max #i,min

0

Maximum heat production region

0

p1

Fig. 1. One two-dimensional segment (for arbitrary p3 > 0) of the decision planes for the virtual engine controls in the co-state space

The importance of this validation is that once the control problem is formulated, a reduced computation numerical optimisation can be performed to either:

7-1*,-26' 5,"16$0-1' +-2$/3' !"#$%&%'()"*'' +,-.&/0-1'+-2$/3' βmin θvo,max θsa,min ωidle,max

The inputs to achieve these state trajectories are in Figure 4 and it is seen the analysis in Section II holds. For the fuel optimal case, the engine operates at maximum efficiency at all points in time. Meanwhile, when a balanced objective is desired, the engine starts off running inefficiently and the control variables switch at different points in time. Although not shown explicitly here, small perturbations about the derived strategy result in higher cost calculated using (12). This provides some further validation that the developed policies are at least locally optimal for the given problem formulation.

(1) Search for the p(0) that satisfies the boundary conditions ∀t ∈ [0, tf ] and develop the control policy using (15)-(16) and Table 1, or alternatively; (2) Search only for the switching times of each of the control variable using a dynamic programming approach.

βmax θvo,min θsa,max ωidle,min

!"#$%&%')4/$)1/3' '+-2$/3'

3.2 Experimental results

5$%)'

Fig. 2. General optimal cold start strategy for a SI engine If non-idle operating conditions are considered, the same general results eventuate, although the progression of the co-state variables in time is clearly different. This is completely intuitive, as running the engine away from idle will naturally generate more heat, leading to less need to generate heat by running the engine a low efficiency. As

To obtain experimental validation of the results, a 4.0l, inline 6-cylinder production engine was connected a 460kW transient engine dynamometer and the production calibration was adjusted via an ATI Vision interface. The production engine has no actuation authority of the cam at low temperature so only three engine control inputs were used. An optimal fuel policy was derived by minimising (12), with the temperature under the production calibration (which meets legislated emissions levels) used to set the reference level after 300s. For comparison purposes, an

13025

18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

The engine was run for 300 seconds at constant idle conditions, using each of the three (two optimal and one production) policies. The results for measured temperatures and fuel consumption are show in Figure 5.

%(!"

%%!"

),+1,23452,"-670""

%$!"

Coolant temperatures (solid)

%#!" -670""

340   Fast warm up policy

%!!"

330  

$&!" !"

#!!"

$!!"

%!!"

)*+,"-.,/0""

!

140

120

Minimum fuel policy

320  

310   [°K]    

Temperature  [°K]    

Oil temperatures (dashed)

$'!"

Production calibration

300  

290  

80

60

[g]

Fuel use [g]

100

280   0  

100  

40

200  

300  

Time  [sec]    

 

  20

140  

0 0

100

200

300

120  

Fast warm up policy

Time [sec]

100  

Spark angle [CA]

20

80  

Minimum fuel policy

[g]    

Fuel  use  [g]    

Fig. 3. Simulation results at idle for minimum fuel policy (grey lines) and faster warm up policy achieving Tcoolant (300s) = 325K (black lines).

60  

40  

Production calibration

0 -20 -40

20   0

100

200

300

0   0  

AFR/AFRs

1. 1

200   Time  [sec]    

1. 0

300    

0. 9 0. 8

Cam angle [CA]

100  

0

100

200

Fig. 5. Experimental results at constant idle operation under the three policies. (Top) Coolant (solid) and oil (dashed) temperatures, (Bottom) Cumulative fuel consumption.

300

30 20 10

additional balanced policy that achieved 10K higher temperature at the final time was also sought.

The faster warm up policy represented by the black line in Figures 5 (and which can be considered as representative of tighter emissions constraints) also clearly demonstrates

Engine idle speed [rpm]

Fig. 4. Optimal idle engine inputs obtained numerically from simulation for minimum fuel policy (grey lines) and faster warm up policy achieving Tcoolant (300s) = 325K (black lines).

Not surprisingly, when the production calibration and the optimal fuel consumption policy are compared in Figure 5 the overall results differ only marginally. The oil and coolant temperatures at the end of the interval match well, validating the use of a single representative engine temperature state in the analysis. Similarly, the cumulative fuel use under both policies is very similar, although the derived optimal policy has only marginally better fuel consumption. This closeness of solutions is not unexpected since given the development effort typically associated with engine calibration it is reasonable to assume that the outcome will be at least very close to locally optimal. This result provides some real world validation of the derived policy.

0 -10

0

100

0

100

200

300

200

300

1600 1200 800 400

Time [sec ]

13026

18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011

that there is an associated fuel penalty. Although not shown here due to space constraints, testing was also conducted over the NEDC drive cycle. Under this scenario, the fuel penalty associated with the higher temperature setpoint is less pronounced, because additional heat available when running the engine at higher speeds and loads facilitates an earlier transition from the maximum heat policy to the maximum efficiency policy. Finally, it is worth noting is that the time to develop the faster warm up policy using the methodology outlined in this paper is significantly shorter. Thus once the development time associated with calibrating the engine models is invested, it is relatively straightforward to generate new policies to suit any desired objective. This implies that different optimal policies can be generated for different conditions (e.g. when the cabin heater is requested, it may be desirable to sacrifice some initial fuel to achieve faster warm up) and the look up tables in existing engine controllers automatically populated. In essence, this is similar in spirit to explicit model predictive control approaches. 4. CONCLUSIONS AND FURTHER WORK The proposed approach to engine cold start calibration is to use a low order model to develop parametric strategies, which can then be used to reduce the computational burden associated with numerical approaches on higher fidelity engine models. Of course, it is possible that the calibration time associated with the development of the models may be significant, and thus exact identification of the optimal strategy may be significant. In this instance, there may be benefits in incorporating both a model based approach to optimal calibration that uses less accurate engine models that are faster to define, and coupling this with model free optimisation approaches (such as Popovic et al. (2006); Nesic et al. (2010a) or Nesic et al. (2010b)) that can fine tune the solution to find a local optima. Further extensions include with augmenting the reduced order model with static maps representing engine-out emissions and modelling the three-way catalyst thermal and chemical dynamics in a control oriented fashion. The augmented model can then be used to set additional explicit constraints when optimising the cost function (12). ACKNOWLEDGEMENTS The authors acknowledge the ARC funding of Linkage Project LP0453768 and the in-kind support provided by the Ford Motor Company of Australia. Furthermore, the resources within the ACART research centre (http://www.acart.com.au) were instrumental to the experimental work. REFERENCES Andrianov, D., Keynejad, F., Dingli, R., Voice, G., Brear, M., Manzie, C., 2010. A cold-start emissions model of an engine and aftertreatment system for optimisation studies (SAE Paper 2010-01-1274). Auiler, J. E., Zbrozek, J. D., Blumberg, P. N., 1977. Optimization of automotive engine calibration for better

fuel economy – methods and applications. SAE Paper 770076. Dohner, A. R., 1981. Optimal control solution of the automotive emission-constrained minimum fuel problem. Automatica 17 (3), 441–458. Fiengo, G., Glielmo, L., Santini, S., Serra, G., 2003. Control oriented models for TWC-equipped spark ignition engines during the warm-up phase. In: American Control Conf. Hafner, M., Isermann, R., 2003. Multiobjective optimization of feedforward control maps in engine management systems towards low consumption and low emissions. Trans. Inst. of Measurement & Control 25, 57–74. Kang, J. M., Kolmanovsky, I., Grizzle, J. W., 2001. Dynamic optimization of lean burn engine aftertreatment. Journal of Dynamic Systems Measurement and Control, Transactions of the ASME 123 (2), 153–160. Keynejad, F., Manzie, C., 2010*. Cold start engine modelling of spark ignition engines. Submitted to Control Engineering Practice in May 2010. Kirk, D. E., 1970. Optimal Control Theory: An Introduction. Prentice-Hall. Maloney, P., 2009. Objective determination of minimum engine mapping requirements for optimal SI DIVCP engine calibration. SAE Paper 2009-01-0246. Manzie, C., Keynejad, F., Andrianov, D., Dingli, R., Voice, G., 2009. A control-oriented model for cold start operation of spark ignition engines. In: IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling, (E-CoSM ’09). Nesic, D., Mohammadi, A., Manzie, C., 2010a. A systematic approach to extremum seeking based on parameter estimation. In: IEEE Conf. on Decision and Control. Nesic, D., Tan, Y., Moase, W. H., Manzie, C., 2010b. A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives. In: IEEE Conf. on Decision and Control. Popovic, D., Jankovic, M., Magner, S., Teel, A., 2006. Extremum seeking methods for optimization of variable cam timing engine operation. IEEE Transactions on Control Systems Technology 14 (3), 398–407. Prabhakar, R., Citron, S., Goodson, R., 1977. Optimization of automotive engine fuel economy and emissions. ASME Journal of Dynamic Systems, Measurement and Control 99 (2), 109–17. Rao, H. S., Tennant, J. A., Van Voorhies, K. L., Cohen, A. I., 1979. Engine control optimization via non-linear programming. SAE Paper 790177. Rishavy, E. A., Hamilton, S. C., Ayers, J. A., Keane, M. A., 1977. Engine control optimization for best fuel economy with emission constraints. SAE Paper 770075. Roeth, J. A., Guzzella, L., 2010. Modelling engine and exhaust temperatures of a mono-fuelled turbocharged compressed-natural-gas engine during warm-up. Proc. IMechE Part D-Journal of Automobile Engineering 224 (D1), 99–115. Sun, J., Sivashankar, N., 1997. An application of optimization methods to the automotive emissions control problem. In: American Control Conf. pp. 1608–1612. Tennant, J. A., Cohen, A. I., Rao, H. S., Powell, J. D., 1983. Computer-aided procedures for optimization of engine controls. International Journal of Vehicle Design 4 (3), 258–269.

13027