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# Model Based CalibrationOPEN ACCESS

A Case Study for Calibrating Control Systems for Downsized Boosted Engines

[+] Author Notes
Yue-Yun Wang

Technical Fellow Propulsion Systems Research Lab General Motors Company

Mechanical Engineering 137(12), S19-S21 (Dec 01, 2015) (3 pages) Paper No: ME-15-DEC-10; doi: 10.1115/1.2015-Dec-10

## Abstract

This article describes calibration of control systems for downsized boosted engines. Model-based design of powertrain and aftertreatment control systems includes plant modeling and controller synthesis. The article illustrates the typical work flow of the model-based calibration process for an engine. In the process, the first step is the design of experiment. The experiment design should cover a multisurface space. That guides the next step to collect data from an engine or powertrain at critical operating points. Once the data are collected, an engine system model is built along with its designed controller models, then the operation of the control systems and controller parameters are optimized or calibrated based on the plant models. With these initial values of the calibrations handy, one can either download the calibration into the production ECU or use a rapid prototyping controller to conduct a full validation or final fine tuning of the engine powertrain control system in test cells or on vehicles.

## Article

Model-based design of powertrain and aftertreatment control systems includes plant modeling and controller synthesis. On the other hand, calibration or optimization of control system parameters is a major important step during the implementation of the powertrain control systems into products.

A well designed control system based on the knowledge of a plant model and carefully chosen control methods can effectively deal with system uncertainties, nonlinearities, couplings between the multi-variable inputs and outputs, and, therefore, reduce the calibration effort to the minimum. Furthermore, control system calibration requires large amounts of effort involving enormous engineering time, dynamometer test and vehicle test time. Reducing calibration complexity, time and effort have become the top priority for an automotive company to reduce material cost and deliver its products to market quickly.

In reality, due to various new engine programs under development and new model year vehicles brought to the market, test cell time is fully utilized for almost 24 hour operation a day. It is impossible that an engineer can tune all calibration parameters from the initial try to the final finishing in a test cell. Therefore, model based calibration methodology is vital to help speed up the calibration process and minimize test cell time. With the help of plant models, a calibration engineer can simulate the plant responses or behavior and tune the control system parameters off-line or in a desktop environment. A plant model can help the engineer obtain initial calibration parameters that are suboptimal solutions to the actual systems merely subject to modeling errors. Starting from those best initial guesses, the engineer can spend minimum time to fine-tune calibrations in the test cell and on vehicles. In the next section, we will present a case studythat shows howto use the model-based calibration method to optimize the operation of a two-stage turbocharged engine for fuel economybenefit and fast torque acceleration.

## Model based calibration

Figure 1 shows a typical work flow of the model-based calibration process for an engine.

Figure 1 Model-based calibration process.

In the process, the first step is the design of experiment. The experiment design should cover a multi-surface space. That guides the next step to collect data from an engine or powertrain at critical operating points. Once the data are collected, an engine system model is built along with its designed controller models, then the operation of the control systems and controller parameters are optimized or calibrated based on the plant models. With these initial values of the calibrations handy, one can either download the calibration into the production ECU or use a rapid prototyping controller to conduct a full validation or final fine tuning of the engine powertrain control system in test cells or on vehicles.

To illustrate this process, let us look at a case study. The goal is to replace a single stage turbocharged diesel engine with a two-stage turbocharged engine in order to achieve better fuel economy, faster torque acceleration while keeping engine emissions under control. The hardware configuration of the system is shown in Figure 2.

Figure 2 Series-connected two-stage turbocharged engine.

In this engine, the inputs of the air path system include high pressure (HP) turbine by-pass valve, high pressure turbine VGT position, low pressure (LP) turbine wastegate, high pressure EGR valve, low pressure EGR valve, intake air throttle, variable valve actuators and high pressure compressor by-pass valve.

The controlled outputs are boost pressure or the outlet pressure of the HP stage compressor, EGR% or EGR fraction, and AFR (air fuel ratio). This is a highly nonlinear multi-input multi-output system.

In [1], a first principle based physics model was built for the two-stage turbocharged engine. The governing nonlinear differential equations for the system describe the turbocharger dynamics for both high and low pressure stage turbo, which determines the boost pressure through power balance. The intake manifold model describes the manifold pressure dynamics in relation with fresh air flow, EGR flow and cylinder charge flow. The intake O2 concentration dynamics describe transient and steady-state relations between EGR and AFR. The model structure is shown in Figure 3.

Figure 3 Airpath model of a two-stage turbocharged engine.

The model is built in MATLAB/Simulink, which includes two series connected turbocharger models. The high pressure turbine has a modulated by-pass valve, and the high pressure compressor has a passive by-pass valve. The low pressure turbine has a by-pass valve, which is often called a wastegate. The Simulink model also includes intake and exhaust manifold dynamics models, the EGR valve, EGR cooler and EGR by-pass models, the charge air cooler model and the intake air throttle model. Additionally a combustion and torque model is provided. In particular, Figure 4 and Figure 5 showthe data validation of the turbocharger compressor models. It can be seen that both models for the low pressure compressor and high pressure compressor are accurate. The overall modeling errors for the boost pressure and fresh air flow are controlled within 5∼10%.

Figure 4 Validation of LP compressor model.

Figure 5 Validation of HP compressor model.

With this model ready, our objective is to optimize the control system over the engine speed and torque operation map, such that the engine will achieve better power and fuel consumption through the optimization of operating LP and HP stage turbochargers and HP-bypass valve collaboratively.

This is a challenging calibration problem which, if performed in a test cell, would waste time and fuel cost in order to search the combination of the operation between the two-stage turbochargers. This search can be translated into an optimization problem [2][2,[3]3].

In [3], the cost function is defined as:Display Formula

(1)
$J=w1pIMrefpIM2+w2PMEPPMEPref2+w3zEGRzEGRref−12 ,$

with design spaceDisplay Formula

$000T≤xVGTxEGRxBPT≤10070100T ,$

where pIMref, pIM are the desired or reference intake manifold pressure and the actual pressure, PMEP, PMEPref are engine delta pressure and its reference, zEGR and zEGRref are EGR fraction and its desired reference. The reference values are obtained from the same type of engine with a single stage turbocharger. In the design space, xVGT is the HP stage turbo VGT position, xEGR is the EGR valve position, xBP is the HP stage turbo by-pass valve position. The optimization is subject to the constraints of the plant model and limits of the system parameters including:

• EGR ratio set points

• AFR limits to prevent excessive smoke

• Maximum pressure in the intake (3.5 bar) and exhaust manifolds (5 bar)

• Compressor outlet temperature (288̊C) and turbine inlet temperature (871ｱ/2C)

• Turbo speed limit (170 krpm)

The weights in the cost function are defined asDisplay Formula

$w1=α,w2=1−α,w3=10, α∈01 .$

In [3], 15 key operating points are selected for the optimization study, which consist of 6 points on the peak torque curve; 3 points on FTP cycle; 6 points on mode switching region (see Figure 6, where x-axis is the engine speed and y-axis is the engine torque).

Figure 6 Selection of optimization points.

To illustrate the effectiveness of the optimization, the optimization result for point 3 at max torque@l8ooRPM is shown in Figure 7. For the six plots in Figure 7, the first plot in the first row shows the optimized HP VGT and EGR valve positions and by-pass valve position when the weighting factor a sweeps from 0 to 1.At this operating point, the by-pass valve is always closed. As a increases, the VGT position and the EGR valve turn to close further. For a more complete reference to the optimization results, the second and the third plots in the first row show the changes of the engine delta pressure (delta-P) and EGR fraction with respect to different actuator positions. In the second row of Figure 7, the first plot shows the changes of air-fuel ratio, and the second and third plots show the changes of the engine exhaust pressure and the compressor pressure ratio with respect to different actuator positions. When the weighting factor a sweeps from 0 to 1, the EGR fraction level is maintained as specified in the optimization cost function. The references for the engine delta pressure and boost pressure (or compressor pressure ratio) optimized for the same engine but equipped with a single stage turbo system are given in red dashed lines in the corresponding plots. Now with two-stage turbo-charging, if we choose a=0.4 for example, adjust the VGT and the EGR valve positions based on the optimization results accordingly, we can achieve higher boost pressure and less engine delta-P than those produced by the engine equipped with the single stage turbocharger (see Figure 7f and Figure 7b). This means the two-stage turbocharged engine can achieve less fuel consumption and provide higher acceleration torque with more air to reduce smoke as well. The model-based calibration clearly shows the benefits of how to operate the two-stage turbocharger.

Figure 7 Optimization results at max torque curve and 1800 RPM. Subplots (a) actuator positions, (b) engine delta pressure, (c) EGR fraction, (d) air-fuel ratio, (e) exhaust pressure, (f) compressor pressure ratio. FF—feedforward desired set points from the single stage turbocharged engine. PSO – optimized results for the two-stage turbocharged engine using particle swarm optimization (PSO) algorithm.

Based on overall optimization, the operation of the two-stage turbocharger is calibrated as shown in Figure 8. By looking at the torque speed based map in Figure 8b, at low and middle engine speed, the blue circles show that the turbo control should only use HP stage turbo VGT. The green circle region shows to operate both turbochargers by modulating the HP stage turbo by-pass valve. This area is very limited, merely as a transition to operating the turbochargers at high engine speed and load, where the by-pass valve is required to fully open and only low pressure stage turbo is in operation. Similarly, these operational results are presented in the fueling versus engine speed based map in Figure 8a, if a calibration engineer prefers to use such a map. Through this exercise, it shows that the two-stage turbo system increases the benefits for fuel economy, fast acceleration torque and lower emissions. It also demonstrates the benefits of model-based calibration methods. With its help, a calibration engineer can find the sub-optimal solution for the actuator positions that optimize the overall system to achieve the optimal value of the cost function target. Those suboptimal solutions are subjected to modeling errors only. This could save significant test cell calibration time, and help deliver products to market faster.

Figure 8 Model-based calibration/optimization results for two-stage turbo operation using particle swarm optimization (PSO). Subplots (a) optimization results on speed and fuel based map, (b) optimization results on speed and torque based map.

In addition to the example shown here, developing on-line and off-line model based calibration tools by utilizing computer power can also reduce the calibration complexity. One good example is presented in another literature [4], where a model based method to tune PID gains is programmed into a graphic user interface (GUI). If a linear model of the airpath system is identified, with the given desired robustness margins of a control channel, such as classic gain and phase margin, the GUI can calculate the PID gains based on the system model in seconds.

To conclude, the trend from road to lab to math by using model-based virtual environment to help powertrain control system calibration will gain more attention in industry applications.

## References

M. Canova, F. Chiara, G. Rizzoni and Y.Y. Wang, “Design and validation of a control-oriented model of a diesel engine with two-stage turbocharger”, SAE International Journal of Fuel and Lubricants, 2 (2) pp.387– 397, 2010.
Q. Zhang, C. Brace, S Akehurst, R Burke, G Capon, L Smith, S Garrett and K Zhang, “Control strategy study of the series sequential turbocharging using 1-D simulation”, Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, 2013, San Antonio, Texas, USA
Y. Liu, J. Zhou, L. Fiorentini, M. Canova, and Y.Y. Wang, “Model-based calibration: a case study for calibrating control systems of downsized boosted engines”, American Control Conference, Tutorial Session, Chicago, 2015.
Y.Y. Wang, I. Haskara and O. Yaniv, “Model-based quantitative feedback control of air and boost pressure for turbocharged diesel engines”, Control Engineering Practice, 19, pp. 626– 637, 2011.
View article in PDF format.

## References

M. Canova, F. Chiara, G. Rizzoni and Y.Y. Wang, “Design and validation of a control-oriented model of a diesel engine with two-stage turbocharger”, SAE International Journal of Fuel and Lubricants, 2 (2) pp.387– 397, 2010.
Q. Zhang, C. Brace, S Akehurst, R Burke, G Capon, L Smith, S Garrett and K Zhang, “Control strategy study of the series sequential turbocharging using 1-D simulation”, Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, 2013, San Antonio, Texas, USA
Y. Liu, J. Zhou, L. Fiorentini, M. Canova, and Y.Y. Wang, “Model-based calibration: a case study for calibrating control systems of downsized boosted engines”, American Control Conference, Tutorial Session, Chicago, 2015.
Y.Y. Wang, I. Haskara and O. Yaniv, “Model-based quantitative feedback control of air and boost pressure for turbocharged diesel engines”, Control Engineering Practice, 19, pp. 626– 637, 2011.

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