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Engine Calibration: A Model-Based Approach

David J. M. Sampson Letitia A. D. Sheridan

1 Introduction

Vehicle customers continue to demand ever-improving performance and economy, while govern-ment regulators impose ever-tightening restrictions on engine emissions. In response, enginedevelopers have turned to increasingly complex control systems that provide great exibilityto trade off these conicting objectives and optimise operation through a wide variety of con-ditions. Complex combinations of powertrain actuator technology variable inlet and exhaustvalve timing, exhaust gas recirculation, variable geometry turbochargers, direct injection systems

with multiple injection events per cycle, swirl control valves are becoming common on modernproduction series engines. However, as engine complexity increases, the time and cost neededto calibrate engines (that is, to optimise the control system settings) using traditional methodsbecomes impractical.

Model-based calibration refers to the process of using modern design of experiments, sta-tistical modelling and optimisation techniques and tools to dene a methodology for efficientlyproducing high quality calibrations for complex engine applications. Model-based calibrationprovides a way to break down the calibration process into manageable subtasks. This paper il-lustrates the approach using two typical example applications: a gasoline engine for a passengercar, and a diesel engine for a heavy-duty off-road vehicle. Spin-off benets that can be leveragedby engineers involved in vehicle simulation, controller software design and component testing are

also detailed, and future applications for model-based calibration techniques are also discussed.

2 Gasoline engine application

2.1 Problem denition

The rst example application involves a 2.2 litre gasoline engine with dual independent variablevalve timing. This is a representative engine type for modern passenger cars. The calibrationengineers problem is to nd the best settings of spark, intake cam and exhaust cam as a functionof engine speed and load; best settings means balancing engine power, fuel consumption andemissions to meet customer requirements, government regulations and hardware constraints.

2.2 Design of experiments

This application is challenging for two reasons: there are a large number of possible inputcombinations (spark, cam timings, speed and load) to explore, and the engine responses (torque,fuel consumption and emissions) vary in a complex way with those inputs.

Design of experiments techniques can be used to give an efficient set of test combinationsto make best use of engine dynamometer time. The Model-Based Calibration Toolbox providescalibration engineers with a range of design types, from classical to space-lling to optimal,depending on the application and a priori engine knowledge. Space-lling designs are suitable

The MathWorks, Matrix House, Cambridge Business Park, Cambridge CB4 0HH, UK


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Figure 2: Torque and exhaust temperature model slices for the gasoline engine application.Both the torque model (N.m) and exhaust temperature model (degrees Celsius) are shown as afunction of spark timing (degrees) and engine speed (rpm).

functions and neural networks, and a range of visualisation and validation tools to assist withassessing model quality and selecting between candidate models.

For this application, models were built for torque and exhaust temperature. A two-stagemodelling approach was used. This involved tting a local model to each spark sweep, andthen building a global model of how the parameters of the local model vary in speed, load,inlet cam timing and exhaust cam timing. The two-stage approach has numerous advantagesover the one-stage approach (building models as a single function of all the variables) includingmore appropriate treatment of factors caused by unregulated environmental conditions (e.g.,temperature and humidity), easier outlier identication, and a more natural, step-by-step modelreviewing process for tool users. Two-stage modelling also provides scope for choosing modelsbased on engineering knowledge of underlying physical processes or previous experience. For thetorque response, the best local model (torque versus spark) was a quadratic polynomial spline,while the best global model to predict the spline parameters was found to be a radial basisfunction with a multiquadratic kernel. For the exhaust temperature, a quadratic local modelwas sufficient, while the global model selected was a hybrid radial basis function with a quadraticpolynomial part. The average difference between model and data was 0.7% for torque and 1.2%for exhaust temperature. A range of statistical metrics including the overall error (RMS), theoverall prediction error (RMS) and the small-sample Akaike information criteria were used tocompare candidate models. Slices of models for torque and exhaust temperature are shown ingure 2.

2.4 OptimisationOptimisation techniques can be used to specify objectives and constraints to achieve an trade-off between performance, economy and emissions. The Model-Based Calibration Toolbox providescalibration engineers with exible tools to specify and solve optimisation problems and to popu-late calibration tables with the results. A scripting interface also allows engineers to use advancedalgorithms from the Optimization Toolbox and the Genetic Algorithm and Direct Search Tool-box.

For this application, the objective was to maximise torque by selecting optimal settings of spark, inlet cam timing and exhaust can timing, subject to constraints on exhaust tempera-ture (to ensure a safe operating temperature for the catalyst). A boundary model constraint,representing the feasible operating region, was also included. The optimisation was carried out


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Figure 3: Optimisation results for the gasoline engine application.

Figure 4: Optimised tables for the gasoline engine application, as a function of speed (rpm)and load (dimensionless). Clockwise from top left: spark timing (degrees), intake cam timing(degrees), torque (N.m), exhaust cam timing (degrees).

using a gradient-based (steepest descent) method at fteen important speed-load combinations.The results are summarised in gure 3. The optimal spark and cam timing results were theninserted into tables, with the remaining remaining table values lled by using a smoothing spline

to interpolate and extrapolate. Illustrations of the resulting tables for spark and cam timingsare shown in gure 4. The best torque values found by the optimisation were also used to ll atorque estimator table. (In addition to lling tables used for control, ECUs often employ tablesfor estimation, thereby saving on the cost of including expensive sensors.)

3 Diesel engine application

3.1 Problem denition

The second example application involves a 9.0 litre diesel engine with cooled EGR and a variablegeometry turbocharger. This is a representative engine type for modern heavy-duty off-road

applications. The calibration engineers problem is to nd the best settings of injection timing,


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Figure 5: Experimental design for the diesel engine application.

fuel quantity, fuel pressure, EGR and turbo rack position as a function of engine speed andtorque; best settings again means balancing engine power, fuel consumption and emissions withinhardware constraints.

3.2 Design of experiments

For this application, a V-optimal design based on an underlying quadratic model was used.The V-optimal class of optimal designs is used to produce a model that has good predictivequalities (see [1] for a detailed comparison of optimal design types) and is most suitable forengine calibration applications. The quadratic model was selected after reviewing existing testdata from a similar engine. The design featured 65 points in speed, injection timing, fuel quantity,

fuel pressure, EGR and turbo rack position. Constraints on reasonable injection timing, fuelquantity, fuel pressure and turbo rack position as a function of speed were included, again basedon data from a similar engine and engineering judgement.

The data was generated using a WAVE model, running on a four-processor cluster andcontrolled by a Simulink/Stateow test harness. The total simulation time required was 2.4 days(9.6 processor days, 3.5 hours per sweep) for 30 engine cycles per point.

3.3 Modelling

Two-stage models were built for the relevant responses: torque, NOx, exhaust temperature andpeak cylinder pressure. In all cases, quadratic models were used at the local level and hybridradial basis functions (with quadratic polynomial parts) were used at the global level. Theaverage difference between model and data was 1.0% for torque, 0.9% for NOx, 0.2% for exhausttemperature and 0.4% for peak cylinder pressure. Slices of models for torque and NOx are shownin gure 6.

3.4 Optimisation

For this application, the objective was to minimise brake specic fuel consumption by selectingoptimal settings of injection timing, fuel quantity, fuel pressure, EGR and turbo rack position,subject to constraints on turbo speed and peak cylinder pressure (to ensure reliable operation).The optimisation was again carried out using a steepest descent method, at seven of the eight


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Figure 6: Torque and NOx model slices for the diesel engine application. The torque model (N.m)is shown as a function of injection timing and turbo rack position. The NOx model (mg/s) isshown as a function of injection timing and engine speed.

Figure 7: Optimisation results for the diesel engine application.

points in the current U.S. eight-mode off-road drive cycle (idle was neglected). The results aresummarised in gure 7. The optimal results were inserted into tables which are shown in gure 8.

4 Other applications

While the applications described have been control problems (e.g., populating tables for bestspark timing and best injection timing), the model-based approach is equally useful for estimation problems (e.g., lling tables for air charge determination) [1, 2].

The model-based calibration methodology and tools described have also been applied success-fully to a range of additional complex engine calibration applications, including on-road dieseland gasoline direct injection engines. Organisations have achieved signicant reductions in de-velopment time and improvements in calibration quality from using a model-based approach,compared to traditional methods, for these complex applications.


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Figure 8: Optimised tables for the diesel engine application, as a function of speed (rpm) andtorque (N.m). Clockwise from top left: injection timing (degrees), fuel pressure (MPa), EGRvalve position (mm), turbo rack position (mm).

5 Future directions

Sophisticated tools for design of experiments, modelling and optimisation are enabling produc-tivity improvements throughout the engine development process.

The model-based calibration approach, coupled to physics-based engine simulation packages,is enabling engineers to produce initial ballpark calibrations, even before production enginehardware is available for dynamometer testing. The same technology is also allowing engineersto simulate the effects of unexpected engine hardware changes.

High-delity, fast-running statistical engine models (such as those generated using the Model-Based Calibration Toolbox) can be of great value to ECU software designers, who can prototypetheir algorithms conveniently and rapidly on the desktop using simulation tools (e.g., Simulinkand Stateow).

At the other end of the development process, the same statistical engine models can enablevalidation of production ECU hardware and software, for example, in the area of fault detectionand management. This is achieved by deploying the engine model to a real-time system (e.g.,xPC Target or dSPACE) and connecting to a candidate production ECU for hardware-in-the-loopsimulation.

Design of experiments and modelling tools, coupled to increasingly exible test automationsystems, enable robust test automation and reduced test time. In future, calibration engineerswill be able to program systems that adjust a design on the y when infeasible operating regionsare encountered, or that collect data until a specied level of model accuracy is reached [3].

Acknowledgements

Thanks to the following colleagues at The MathWorks for their involvement in the modellingand optimisation: Ian Noell, Tanya Morton, Paul Kerr-Delworth, Russell Goyder, Richard Lang,Richard Alcock, Jon Cherrie and Jos Martin (Cambridge, UK) and Pete Maloney (Novi, USA).

Thanks also to Gamma Technologies for use of their GT-POWER software for the gasolineengine example, and to Ricardo for use of their WAVE software for the diesel engine example.


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References

[1] Model-Based Calibration Toolbox Users Guide . The MathWorks, Inc., Natick, MA, USA,2004.

[2] P. J. Maloney. Embedded torque estimator for diesel engine control application. In Electronic Engine Controls , number 2004-01-1371 in SP-1822. SAE, Warrendale, PA, USA, 2004.

[3] T. M. Morton, R. D. Connors, P. J. Maloney, and D. J. M. Sampson. Model-based optimalcalibration of a dual independent variable valve-timing engine. In K. R opke, editor, Design of Experiments (DOE) in der Motorenentwicklung , pages 7785. expert verlag, Renningen,Germany, 2003.

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