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MODELING OF TURBOCHARGED SPARK IGNITED ENGINE AND MODELPREDICTIVE CONTROL OF HYBRID TURBOCHARGER

By

KANG RONG

A THESIS PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCE

UNIVERSITY OF FLORIDA

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c 2014 Kang Rong

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Special thanks to everyone that helped!

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ACKNOWLEDGMENTS

I am very grateful to my advisor Dr. Carl Crane for letting join the CIMAR group

and providing me with such a precious opportunity to work on this excellent project.

Special thanks to Olugbenga Moses Anubi and Darsan Patel for their wonderful

instruction, selfless help and great support to me on this research. This work could

not be completed without your help.

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TABLE OF CONTENTS

page

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

CHAPTER

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.1 Introduction of Conventional Engine Charging Method . . . . . . . . . . . 12

1.2 Introduction of Hybrid Turbocharger . . . . . . . . . . . . . . . . . . . . . 131.2.1 How Hybrid Turbocharger Works . . . . . . . . . . . . . . . . . . . 13

1.2.2 Why Use Hybrid Turbocharger. . . . . . . . . . . . . . . . . . . . . 141.3 Problem Formulation and Thesis Outline. . . . . . . . . . . . . . . . . . . 15

2 BATTERY MODELING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1 Battery Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Battery Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Mathematical Equations of Battery Discharging and Charging . . . 18

2.2.1.1 State of Charge . . . . . . . . . . . . . . . . . . . . . . . 182.2.1.2 Discharging Mode . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1.3 Charging Mode. . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Simulink Battery Modeling and Validation . . . . . . . . . . . . . . . . . . 192.3.1 Simulink Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 TURBOCHARGED SI ENGINE MODELING. . . . . . . . . . . . . . . . . . . . 22

3.1 Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Model Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.2 Model States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.3 Model Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Compressor Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Pressure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.2 Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 Mass Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.4 Efficiency Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Intercooler Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.1 Pressure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2 Mass Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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3.3.3 Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.4 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Throttle Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.1 Mass Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.2 Throttle Pressure Model . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4.3 Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.5 Intake Manifold Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 Combustion Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7 Exhaust Manifold Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.7.1 Mass Flow Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 343.7.2 Pressure Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.7.3 Temperature Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 353.8 Turbine Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.8.1 Mass Flow Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 353.8.2 Pressure Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.8.3 Temperature Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 373.8.4 Efficiency Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.9 Exhaust System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.10 Wastegate Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.11 Turbocharger Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40


4 HYBRID TURBOCHARGER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1 Hybrid Turbocharger Simulink Model . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 DC Motor Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . 444.1.2 Hybrid Turbocharger Modeling. . . . . . . . . . . . . . . . . . . . . 44

4.2 Advantages of Hybrid Turbocharger . . . . . . . . . . . . . . . . . . . . . 464.2.1 Comparison with Conventional Turbocharger . . . . . . . . . . . . 46

4.2.2 Comparison with Naturally Aspirated Engine. . . . . . . . . . . . . 474.3 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 INTRODUCTION TO MODEL PREDICTIVE CONTROL . . . . . . . . . . . . . 49

5.1 Why Use MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 MPC Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 MPC Derivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


6 MODEL PREDICTIVE CONTROL OF HYBRID TURBOCHARGER. . . . . . . 54

6.1 Model Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.2 Model Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.3 MPC Implementation In Matlab . . . . . . . . . . . . . . . . . . . . . . . . 596.4 MPC With Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.4.1 Overview of MPC with Constraints . . . . . . . . . . . . . . . . . . 626.4.2 Add Constraints to the System . . . . . . . . . . . . . . . . . . . . 63

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6.5 Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.6 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

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LIST OF TABLES

Table page

2-1 Battery Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3-1 Model Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233-2 Model States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3-3 Model Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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LIST OF FIGURES

Figure page

1-1 Turbocharged SI engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1-2 Scheme of hybrid turbocharger workflow. . . . . . . . . . . . . . . . . . . . . . 152-1 Battery model validation in discharge mode . . . . . . . . . . . . . . . . . . . . 20

2-2 Battery model validation in charge mode. . . . . . . . . . . . . . . . . . . . . . 21

3-1 Validation of the compressor temperature model . . . . . . . . . . . . . . . . . 25

3-2 Validation of the compressor mass flow model . . . . . . . . . . . . . . . . . . 26

3-3 Validation of the intercooler temperature model . . . . . . . . . . . . . . . . . . 28

3-4 Validation plot for Q-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3-5 Validation of throttle mass flow model . . . . . . . . . . . . . . . . . . . . . . . 30

3-6 Validation of volumetric efficiency model . . . . . . . . . . . . . . . . . . . . . . 32

3-7 Validation of torque model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3-8 Validation of exhaust manifold temperature model . . . . . . . . . . . . . . . . 36

3-9 Validation of turbine mass flow model . . . . . . . . . . . . . . . . . . . . . . . 37

3-10 Validation of turbine temperature model . . . . . . . . . . . . . . . . . . . . . . 38

3-11 Validation of turbine efficiency model . . . . . . . . . . . . . . . . . . . . . . . . 39

3-12 Validation of exhaust system mass flow model . . . . . . . . . . . . . . . . . . 39

3-13 Turbocharged SI engine model . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4-1 Hybrid turbocharged SI engine model . . . . . . . . . . . . . . . . . . . . . . . 45

4-2 Turbo lag elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4-3 Engine downsizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6-1 Validation of linearized mass flow model . . . . . . . . . . . . . . . . . . . . . . 57

6-2 Validation of linearized engine torque model. . . . . . . . . . . . . . . . . . . . 58

6-3 Fuel consumption before and after optimization . . . . . . . . . . . . . . . . . . 64

6-4 Engine toruque tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6-5 Required battery voltage input . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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6-6 Required wastegate opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

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Abstract of Thesis Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of the

Requirements for the Degree of Master of Science

MODELING OF TURBOCHARGED SPARK IGNITED ENGINE AND MODEL

PREDICTIVE CONTROL OF HYBRID TURBOCHARGERBy

Kang Rong

May 2014

Chair: Carl CraneMajor: Mechanical and Aerospace Engineering

The idea of a hybrid turbocharger is demonstrated in this thesis. First a battery

model and a turbocharged spark ignited(SI) engine is modeled using Simulink. The

hybrid turbocharger is obtained by replacing the turbo shaft with a battery, which is

connected to the turbine through a generator and to the compressor through a motor.

The main idea of the hybrid turbocharger is that the compressor is driven by the battery

and the battery is charged by the generator, which is driven by the turbine.

Comparisons of the performance of the hybrid turbocharger to the conventional

turbocharger and the naturally aspirated engine has been made in a few aspects. The

comparison to the naturally aspirated engine shows that the hybrid turbocharger plays a

significant role in engine downsizing. In comparison to the conventional turbocharger, it

shows that the hybrid turbocharger eliminates the turbo lag.

The last step is applying model predictive control (MPC) to the hybrid turbocharger

model to minimize the fuel consumption. This is achieved by controlling two inputs of the

system. First is controlling the battery output voltage in order to change the compressor

speed and influence the air mass flow into the engine. Second is the control of the

open angle of the waste gate in order to improve the turbine efficiency and decrease

emissions.

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CHAPTER 1INTRODUCTION

1.1 Introduction of Conventional Engine Charging Method

The most common type of engine is the naturally aspirated engine. In a naturally

aspirated engine, air for combustion (diesel cycle in a diesel engine, or specific types of

Otto cycle in gasoline engines namely gasoline direct injection), or an air/fuel mixture

(traditional Otto cycle petrol engines) is drawn into the engines cylinders by atmospheric

pressure acting against a partial vacuum that occurs as the piston travels downwards

toward bottom dead center during the intake stroke. Most automobile petrol engines, as

well as many small engines used for non-automotive purposes, are naturally aspirated.

A supercharged engine is an engine that uses an air compressor as the supercharger

to increase the pressure or density of air supplied to an internal combustion engine.

This gives each cycle of the engine more oxygen, letting it burn more fuel and do

more work, thus increasing power. Power for the supercharger can be provided

mechanically by means of a belt, gear, shaft, or chain connected to the engines

crankshaft. Superchargers (and turbochargers) have been widely applied to racing

and production cars, although the superchargers technological complexity and costhave largely limited it to expensive, high-performance cars.

When power is provided by a turbine powered by exhaust gas, a supercharger is

known as a turbosupercharger typically referred to simply as a turbocharger or just

turbo. A large amount of work has already been done on the design and control of

the turbocharged engine, as described in , , , . The working principal of the

turbocharger is utilizing the high pressure and temperature of the exhaust gas to drive

the turbine, which is connected to the compressor through a shaft, in order to drive

the compressor to increase the air flow rate into the engine. A turbocharged engine is

more powerful and efficient than a naturally aspirated engine because the turbine forces

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more air, and proportionately more fuel, into the combustion chamber than atmospheric

pressure alone.

Figure 1-1 shows the workflow of how a conventional turbocharger works.

Figure 1-1. Turbocharged SI engine

1.2 Introduction of Hybrid Turbocharger

1.2.1 How Hybrid Turbocharger Works

A hybrid turbocharger is an electric turbocharger consisting of an ultra high speed

turbine-generator and an ultra high speed electric air compressor. The turbine and

compressor are high-speed aeromachines, as in a conventional turbocharger. The

electrical motors run at speeds in excess of 120,000 rpm and when used as generators,

generate electricity at up to 98.5% electrical efficiency. High electrical efficiency is

paramount, because there is no mechanical link between the turbine and compressor. In

other words, hybrid turbocharger refers to a series hybrid setup, in which the compressor

speed and power are independent from the turbine speed and power. This design

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flexibility leads to further improvements in turbine and compressor efficiency, beyond a

conventional turbocharger.

Discharging Mode. When the driver depresses the throttle, the HTT initially acts

like an electric supercharger. The compressor motor is powered from the energy storage

medium, which in this thesis is the battery, allowing it to accelerate to full operating

speed in approximately 500 ms. During this transient stage, the engine control unit

(ECU) on a standard turbocharged engine uses a combination of sensors such as

lambda sensors and air mass flow sensors to regulate the fuel flow rate. In an HTT

equipped engine the ECU can deliver the precise fuel flow rate for complete combustion

more accurately. This is achieved by directly controlling the air flow rate and boost

pressure via control of the compressor speed.

Charging Mode. When the state of charge(SOC) of the battery drops to some

certain level, the generator starts to charge the battery until the SOC returns to a

fixed level. The discharging and charging mode will repeat again and again during

the working process to keep the battery in a good working mode, so as to keep the

compressor speed at a high level to supply sufficient air to the engine.

Figure 1-2 shows the main idea of the hybrid turbocharger and how it works.

1.2.2 Why Use Hybrid Turbocharger

Even though turbo charging technology has already been fully developed and the

turbocharger shows excellent performance in engine downsizing and increasing engine

power, it still has inevitable shortcomings. The most obvious one is the turbo lag, which

means it takes a very long time for the vehicle to reach the required speed after the

driver depresses the gas pedal.

The idea of the hybrid turbocharger solves this problem. Since the compressor is no

longer connected directly to the turbine, the turbo shaft inertia is not important any more.

The compressor is driven by the battery, and is able to reach full operating speed in less

than 0.5s. This rate of acceleration eliminates the turbo lag significantly.

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Figure 1-2. Scheme of hybrid turbocharger workflow

On the other hand, the hybrid turbocharger keeps the advantage in engine

downsizing with respect to the naturally aspirated engine. The engine with the hybrid

turbocharger installed can have a smaller size than ordinary ones to provide even more

power due to the increased air flow rate and higher combustion efficiency.

1.3 Problem Formulation and Thesis Outline

Two problems have been solved in this thesis.

The first one is the modeling of the SI engine with the hybrid turbocharger installed.

Comparison with the naturally aspirated engine and with the turbocharged SI engine

will be made to show that the hybrid turbocharger does play an important role in engine

downsizing and eliminating the turbo lag.

The second one is to apply Model Predictive Control (MPC) to the system to

minimize the fuel consumption and in the meantime prevent the generated engine

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torque deviating too much from the required torque. This is achieved by controlling the

voltage output of the battery and the open angle of the wastegate at the same time.

The outline of this thesis is as following:

1. Modeling the battery using Simulink.

2. Develop the conventional turbocharged engine model and validate each componentof the engine.

3. Form the hybrid turbocharger model by replacing the turbo shaft with the battery.

4. Run simulations to demonstrate the performance of the hybrid turbocharger in

engine downsizing and eliminating turbo lag.

5. Apply model predictive control to the system to minimize the fuel consumption.

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CHAPTER 2BATTERY MODELING

2.1 Battery Description

There are a lot of proposed battery models that have been made previously, as

described in , , . However, they do not provide a good parameter estimation

result for this thesis either in the battery discharging mode or charging mode.

The battery used in this thesis to charge the compressor is a sealed 50-module

nickel metal hydride (NiMH) battery pack providing 60.5 volts and 6.5 Ah capacity. In

this chapter, only one module of the battery pack is modeled and validated. The specific

value of the battery module is as following (

is battery constant voltage(V), is

battery capacity(Ah), is internal resistance( [1]

Table 2-1. Battery Parameter

Parameter Value (Unit)

E

1.2101 (V)Q 6.5 (Ah)

R 0.002 (

2.2 Battery Modeling

The battery model is achieved by making the Simulink model according to the

mathematical equations of the battery charging and discharging mode. The model is

validated using the manufacturers data. The following assumptions have been made [1]:

The internal resistance is assumed constant during the charge and dischargecycles and does not vary with the amplitude of the current.

The models parameters are deduced from the discharge characteristics andassumed to be the same for charging.

The capacity of the battery does not change with the amplitude of the current (no

Peukert effect). The temperature does not affect the models behavior. The self-discharge of the battery is not represented. The battery has no memory effect.

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2.2.1 Mathematical Equations of Battery Discharging and Charging

2.2.1.1 State of Charge

The state of charge (SOC) is a very important parameter of the battery. It

represents how much longer the battery can discharge. The mathematical equation

for SOC is given as:

(21)

where

=the initial state of charge of the battery

i = the current in the battery

Q = battery capacity

2.2.1.2 Discharging Mode

The proposed discharge model can be represented accurately by the voltage

dynamics when the current varies and takes into account the open circuit voltage as a

function of SOC. The battery voltage obtained is given by:

(22)

where

=battery voltage(V)

=battery constant voltage(V)

K=polarisation constant(V/(Ah))

Q=battery capacity(Ah)

it=idt=actual battery charge(Ah)A=exponential zone amplitude(V)

B=exponential zone time constant inverse(Ah)

R=internal resistance( )

i=battery current(A)

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=filtered current(A)

The exponential zone of equation (2-1) can be obtained by the following equation:

| | (23)where

exp(t)=exponential zone voltage(V)

i(t)=battery current(A)

u(t)=charge or discharge mode

2.2.1.3 Charging Mode

For a NiMH battery, after the battery has reached the full charge voltage, the voltage

decreases slowly, depending on the current amplitude. This behavior is represented

by modifying the charge polarisation resistance. When the battery is fully charged,

the voltage starts to drop. This phenomenon can be represented by decreasing the

polarisation resistance when the battery is overcharged by using the absolute value of

the charge (it):

| | (24)

Thus, the mathematical equation for the charging mode is:

| |

(25)

Now, the Simulink battery model is ready to be made according to the mathematical

equations for battery discharging and charging mode.

2.3 Simulink Battery Modeling and Validation

2.3.1 Simulink Model

The basic modeling of the battery in Simulink is based on equation (2-1) and (2-4).

However, the detailed modeling is more complicated.

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Parameter estimation is performed in Simulink to obtain all the unknown parameters

given the input and output of the battery according to the manufacturers data. The next

step is to validate the battery model.

2.3.2 Model Validation

Figure 2-1 and 2-2 shows the results of validation of the battery model in discharging

and charging modes respectively. It could be obviously found that the model is validated

very well according to the validation results.

Figure 2-1. battery model validation in discharge mode

2.4 Chapter Conclusion

The battery is a very important component of the hybrid turbocharger system. In

this chapter, a NiMH battery pack is formed based on mathematical equations, modeled

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Figure 2-2. battery model validation in charge mode

and validated in Simulink. According to the model validation, it can be found that the

estimated parameters of the battery provide reasonable results. Now the battery model

is ready to be used in the engine model which will be made in the following chapters.

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CHAPTER 3TURBOCHARGED SI ENGINE MODELING

3.1 Model Overview

In this chapter, a mean value engine model (MVEM) with turbocharger installed is

presented.The model is completed by firstly creating subsystems of each component of

the engine and then connecting each subsystems to form the final engine model. The

mass flow through the engine is central in the modeling, and thus the modeling is based

on the air flow path. The air enters the engine through the air filter to be cleaned. Then

the clean air enters the compressor where the pressure and temperature increase. The

air needs to be cooled down before entering the engine cylinder to avoid knock, and this

process is done via a heat exchanger called the intercooler. The amount of air into the

engine cylinder is controller by the throttle in order to control the engine output power.

Then the air is mixed with fuel in the intake manifold. The mixture enters the cylinder,

where combustion takes place. The pressure and temperature increases significantly

after combustion. The hot gas, which gets out of the engine via the exhaust manifold,

is the power to drive the turbine. The turbine then drives the compressor to spin at very

high speed through the turbo shaft. A wastegate is used to regulate the air flow into theturbine. Finally the wasted gas leaves the engine through the exhaust system. All the

components will be modeled in the following sections and finally the whole engine model

will be validated according to experimental data.

One simplification has been made here. The air filter does not have significant

influence on neither the pressure nor the temperature of the air. Since this model is only

for simulation, the air filter will not be modeled in the following sections.

3.1.1 Model Input

The input into the model is shown in Table 3-1:

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Table 3-1. Model Input

Name Description Unit

N Engine speed rpm Throttle angle deg

Wastegate opening -

Ambient pressure Pa

Ambient temperature K

Table 3-2. Model States

State Description Unit

pressure after compressor Pa

temperature after compressor K

pressure after intercooler Pa

temperature after intercooler K

intake manifold pressure Pa

intake manifold temperature K

exhaust manifold pressure Pa

exhaust manifold temperature K

pressure after turbine Pa

temperature after turbine K

turbocharger speed rad/s

3.1.2 Model States

After subtracting the air filter from the engine model, the system contains 11 states,

including the pressure and temperature after each component and the turbocharger

speed. All the states are listed in Table 3-2:

3.1.3 Model Constants

Table 3-3 shows all the constants of the engine model that will mentioned in the

following chapters :

In the following chapters, each component of the hybrid turbocharged engine will be

modeled in the order of the air flow path.

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Table 3-3. Model Constants

Name Description Value(unit)

Gas constant 287( / ) Heat capacity ratio 1.4

Heat capacity at constant pressure 1003.4( / )

Heating value of fuel 44 (J/kg)

Ambient pressure 101.7( )

Ambient temperature 296(K)

Compressor volume 0.005(m

Intercooler volume 0.005(m

Intake manifold volume 0.002(m

Exhaust manifold volume 0.002(m

Exhaust system volume 0.01(m

Turbo shaft inertia 0.15( / )

3.2 Compressor Modeling

3.2.1 Pressure Model

The dynamic equation for the compressor can be derived from the first law of

thermodynamics, and is given as:

(31)

where

=compressor volume,

=mass flow rate through the intercooler, /

=mass flow rate through the compressor, /

3.2.2 Temperature Model

If the expansion of gases through the compressor was isentropic, i.e.

=1,the

temperature after the compressor could be modeled as:

/ (32)

Despite its simplicity, due to the high efficiency of the compressor which makes

the isentropic approximation more appropriate, this model works well according to the

experimental data, which can be shown from Figure 3-1:

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Figure 3-1. Validation of the compressor temperature model

3.2.3 Mass Flow Model

The compressor mass flow depends mainly on the compressor speed and the

pressure ratio. Some basic requirements are that the mass flow must be zero when the

turbo shaft speed is zero, and when there is no pressure difference before and after the

compressor. One possible model is presented as:

(33)

where

to

are unknown parameters to be determined.

However, this model is difficult to tune since it produces imaginary numbers for

some circumstances. Therefore, another mathematical equation is used to model the

compressor mass flow:

(34)

where

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In this model,

to

are determined by using the function in Matlab.

The validation shows a good result of the parameter estimation for the compressor mass

flow model, shown in Figure 3-2:

Figure 3-2. Validation of the compressor mass flow model. The group of pointsrepresent turbo shaft speeds 80000 RPM,10000 RPM, 12000 RPM and

14000 RPM respectively from left to right.

3.2.4 Efficiency Model

The efficiency is defined by the ratio of the isentropic and the actual specific input

work. The mathematical equation for the efficiency model is given as:

(35)

The efficiency model is difficult to be estimated, however, equation (3-5) stills yields a

reasonable result of the compressor efficiency.

3.3 Intercooler Modeling

Due to the first law of thermodynamics

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Thus when the pressure of air increases when being compressed by the compressor,

the air temperature also rises. The high temperature of the intake air into the engine will

cause knock in the cylinder. Therefore, the air needs to be cooled and this is the main

reason why the intercooler is modeled.

3.3.1 Pressure Model

The intercooler can be treated as a static flow restriction.The dynamic equation for

the intercooler can be derived from the first law of thermodynamics, and is given as:

(36)

where

=intercooler volume

=mass flow rate through the intercooler, /

=mass flow rate through the throttle, /


The relationship between the pressure drop in the intercooler and the mass flow

rate has been found to fit the following equation:

(37)

Then the mass flow through the intercooler can be modeled as:

(38)

where k is the unknown parameter to be estimated in Matlab using function.

The validation shows that this model fits well with the experimental data.


The ability of the intercooler to lower the temperature of the compressed air

depends on the intercooler efficiency. For perfect gas the heat capacity is a function of

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the temperature only, and thus the intercooler efficiency can be expressed as:

(39)

Thus the intercooler temperature is ready to be expressed as:

(310)

where

in this thesis is equal to the atmospheric pressure

.

3.3.4 Model Validation

Figure 4-1 shows the result of the parameter estimation of the intercooler temperature

model. It could be seen that the temperature model fits the experimental data well.

Figure 3-3. Validation of the intercooler temperature model

3.4 Throttle Modeling


In gasoline engines, a throttle is used to control the air mass flow into the cylinders.

Thus it is important to model the throttle mass flow rate precisely. The mass flow

through the throttle can be modeled like the flow of an ideal gas through a venturi. A

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standard model for this type of flow is

(311)

where

A=throttle opening area

C=discharge coefficient

C depends on the shape of the flow area.

is a function of the pressure ratio

given as:

if

>

otherwise

(312)

where

is the pressure ratio

Since both the opening area A and the discharge coefficient C depend on the

throttle plate opening angle, it is reasonable to lump A and C together to form another

equation

to expressing the opening of the throttle. There are many validated

model for

according to previous researches. The model used in this thesis is

given as

(313)

where

,

,

and

are unknown parameters that will be determined by using the

function in Matlab. Figure 3-4 shows the validation of the parameters of the

function

:

Now the mathematical equation of throttle mass flow rate model can be expressed

as a function of,

,

and

, which is given as:

(314)

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Figure 3-4. Validation plot for Q-function

The throttle mass flow is a central quantity in the engine. It has a significant

influence on the combustion process, and therefore determines the output power of

the engine. Thus the accuracy of the mass flow model is important. Figure 3-5 shows

the validation of the throttle mass flow model.

Figure 3-5. Validation of throttle mass flow model. This shows that the the model fits the

experimental data well

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3.4.2 Throttle Pressure Model

Similarly to the pressure model of the intercooler and the compressor, the throttle

pressure model can be derived from the first law of thermodynamics and is given as:

(315)

where

=intake manifold volume

=the mass flow rate into the cylinder


The temperature change in the throttle is neglected, which means the temperature

after the throttle is the same as the one after the intercooler.

(316)

3.5 Intake Manifold Modeling

The intake manifold is where the air and fuel are mixed and is the path where the

mixture enters the cylinders. The pressure and temperature are just considered to be

the ones that are after the throttle. So in this section, only the mass flow into the cylinder

is modeled. One of the parameters that governs the mass flow into the cylinder is the

volumetric efficiency

. Many mathematical equations have been used by previous

researchers for modeling

. In this thesis,

is modeled as a function of the intake

manifold pressure

and the engine speed N, which is given as :

(317)

Figure 3-6 shows the validation of the volumetric efficiency.

Now the mass flow into the cylinder is ready to be modeled as:

(318)

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Figure 3-6. Validation of volumetric efficiency modell

where N is the engine speed in [RPM] and

is the displacement volume of the engine

in [m

3.6 Combustion Modeling

During the combustion precess, the mixture of air and fuel is burnt to generate

torque and power. The amount of air into the cylinder affects the extension of the

combustion, so that it will influence the output power of the engine. In order to inject a

correct amount of fuel into the engine, it is important to know the theoretical proportion

of air and fuel, which is called the stoichiometric air to fuel ratio

(319)

In this thesis, this ratio is set to be 14.7. An important parameter is the ratio

between the true air to fuel ratio (A/F) and

/

/

/

(320)

When there is excess air in the combustion( > ), the mixture is referred to as lean

and when there is excess fuel in the combustion( < ),the mixture is called rich. An

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engine that runs under lean conditions will emit large amount of

and if the mixture

is rich there will inevitably be unburned hydro carbons and CO in the exhaust gases.

Thus, it is essential to keep close to one in order to maintain good catalyst function,

which will yields the fuel mass flow rate as:

(321)

The torque generated by the engine depends on the work produced and consumed

in the engine, which is given as :

(322)

where

is the number of engine revolutions per cycle. In this thesis, the model is a

2-stroke engine, so

=2.

is the indicated gross work produced by the engine,

is

the pumping work consumed and

is the friction work consumed. The mathematical

expressions for these three terms are as follows:

(323)

where

is the combustion efficiency. There are also many validated mathematical

expressions for

. In this thesis, the equation is given as following:

(324)

where

is the intake manifold pressure in bar and C is an unknown parameter to be

estimated using the function in Matlab.

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The engine torque model is validated according to the experimental data, which is

shown in Figure 3-7.

Figure 3-7. Validation of engine torque model

Then the output engine power can be easily expressed as:

(325)

where M is the engine torque in , N is the engine speed in rpm.

3.7 Exhaust Manifold Modeling

The mixture burnt in the engine cylinder generates very high pressure and

temperature into the exhaust manifold, which is used by the turbine to drive the

compressor. Thus the pressure and temperature out of the exhaust manifold is modeled

here.

3.7.1 Mass Flow Modeling

Firstly, the mass flow through the exhaust manifold is modeled because it will be

used to model the pressure. The exhaust manifold mass flow is just the sum of the air

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Figure 3-8. Validation of exhaust manifold temperature model

makes a good fit with the experimental data provided by the manufacturer.

(329)

Equation (3-29) is linear in parameters

and

so that the parameters can be

adjusted to measured data by using standard least square methods. Actually, the

parameters are estimated by using the function in Matlab. Figure 3-9 shows a

good validation result.

3.8.2 Pressure Modeling

Similar to other components, the pressure modeling of the turbine can also be

derived from the first law of thermodynamics, which is given as:

(330)

where

is the exhaust system mass flow rate in (kg/s).

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Figure 3-9. Validation of turbine mass flow model

3.8.3 Temperature Modeling

As what was done to the compressor, it is possible to model the turbine temperature

in the same way given as:

/ (331)

However, this model does not hold as expected. One possible explanation is that

the great heat transfer form the turbine to the surroundings makes the model fail to

capture

. Thus, another model is introduced here, which shows a good fit with the

experimental data.

/

(332)

where

are parameters to be determined by using function in Matlab.Figure

3-10 shows the validation result of this turbine temperature model.

3.8.4 Efficiency Model

The turbine efficiency model can be calculated by the equation given as:

(333)

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Figure 3-10. Validation of turbine temperature model

The turbine efficiency is important since it determines the power delivered to the

compressor. It is not clear what the efficiency is when there is no mass flow through

the turbine. The relationship between the turbo shaft speed and the turbine efficiency

is complicated and very difficult to measure. As an approximation, a model which is

independent of turbine speed is used in this thesis given as:

(334)

where

are the unknown parameters to be estimated using the function in

Matlab. Figure 3-11 shows the validation of the turbine efficiency model.

3.9 Exhaust System Modeling

The pressure drop from the turbine through the exhaust system to the surrounding

air is significant, therefore it is necessary to model this pressure loss. The exhaust

system can be regarded as a tube with a sudden restriction. The mathematical equation

for the pressure drop in this tube is given as:

(335)

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Figure 3-11. Validation of turbine efficiency model

Figure 3-12. Validation of exhaust system mass flow model

In order to form the exhaust system mass flow rate to be used for calculating turbine

pressure, equation (3-35) is redefined as following:

(336)

This exhaust system mass flow model is validated in Figure 3-12

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3.10 Wastegate Modeling

The turbocharger will overspeed very easily at high loads, which causes excessive

boost pressure or even turbocharger bearing failure. If the turbo shaft speed is too high,

the compressor will consequently spin at a very high speed, resulting in high intake

manifold pressure, which will cause knock in the engine cylinder. To prevent the turbine

from over speeding, it is necessary to deviate some amount of exhaust gases away

from flowing into the turbine directly. This is achieved by using a valve called wastegate.

This will keep the driving torque and therefore the turbine speed at a lower level when

the wastergate is open. The wastgate can be modeled in a similar way as the throttle

modeling. Equation (3-12) and (3-13) will be used. The only difference is that the Q

function will be replaced with a function of the opening area of the wastegate. The

mathematical equation for wastegate modeling is given as:

(337)

where

=wastegate flow coefficient, 0.9

=the opening of the wastegate,

D=the diameter of the wastegate tube

=the pressure ratio

/

3.11 Turbocharger Dynamics

According to Newtons Second Law for rotating systems, the turbine and compressor

are connected by the mathematical equation given as:

(338)

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where

stands for the driving torque of the turbine and

is the braking torque

acting on the compressor.

denotes the inertia of the turbo shaft and

is the

rotational speed of the turbo shaft.

The theoretical maximum torque delivered by the turbine depends on the exhaust

manifold temperature

and the ratio

/

. If the process would be reversible, which

means there would not be any frictional losses in the turbine, the work would be called

isentropic. However, since the turbine gets red hot at high loads, this is not an isentropic

case. Thus the turbine efficiency

is introduced here to calculate the true portion of

power delivered by the turbine. The mathematical equation for the turbine power is given

as

/

(339)

The mathematical equation for compressor power can be modeled in a similar way.

Since the compressor consumes energy, the net amount of produced power is negative.

Moreover, the compressor is not ideal, so the efficiency

is also introduced here.

/ (340)

The torque and the power are connected through equation

, thus theequations for the turbine and compressor torques are given as:

/

/

(341)

Substituting equation (3-41) into equation (3-38) yields a differential equation

of| . The turbo shaft rotating speed can be calculated by solving this differentialequation for

.


This chapter covers the modeling and the validation of all the components in the

turbocharged SI engine. Validation results show that each component works well

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separately, which will provide a reasonable turbocharged engine system. The next step

is to combine the battery model with the engine model to form the hybrid turbocharger

and make comparisons with the conventional turbocharger and the natural aspirated

engine to demonstrate the advantages of the hybrid turbocharger. Figure 3-13 shows

the top level of the Simulink model of the turbocharged SI engine.

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Figure 3-13. Turbocharged SI engine model

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CHAPTER 4HYBRID TURBOCHARGER

4.1 Hybrid Turbocharger Simulink Model

4.1.1 DC Motor Modeling

The first task is to model the dc motor which is used to drive the compressor. The

requirements for the motor are:

Reach the full operating speed within a very short time.

The full operating speed should be over 10000 /The mathematical equation for the dc motor is given as:

(41)

where

J=moment of inertia of the rotor, 0.01 /

b=motor viscous friction constant, 0.01(Nms)

R=electric resistance, 1

L=electric inductance, 0.1H

=electromotive force constant,0.001 / /

=motor torque constant, 2 /4.1.2 Hybrid Turbocharger Modeling

The battery model and turbocharged SI engine model have already been completed

in previous chapters. Therefore, it is ready to make the engine with the hybrid turbocharger.

This is done by replacing the turbo shaft with the battery and power electronics. Power

electronics consist of the motor and the generator. The battery is used to start the

motor to drive the compressor. The generator, which is driven by the turbine, is used for

charging the battery when the state of charge (SOC) of the battery drops to a certain

level.

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Figure 4-1. Hybrid turbocharged SI engine model

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Figure 4-2. Hybrid Turbocharger working process showing the charging and dischagringmode

In this thesis, the motor used is modeled as a DC motor which can reach the full

operating speed (12000 rad/s) in about 0.8s. The generator in this thesis is just picked

from the SimPowerSystem DC Machine Library which is powered by the turbine torque.

The top level Simulink model of the hybrid turbocharger is shown in Figure 4-1. The

working process is to use the battery to drive the motor in order to drive the compressor.

When the SOC of the battery drops to 40%, the switch is turned on to start the generator

to charge the battery until the SOC reaches 80%. This repeats during the whole

working process, which is shown in Figure 4-2. The input to the system are atmospheric

pressure, temperature and the throttle angle. The important outputs are the engine

torque and power.

4.2 Advantages of Hybrid Turbocharger

4.2.1 Comparison with Conventional Turbocharger

The most significant advantage of the hybrid turbocharger against conventional

ones is that it eliminates the turbo lag. Turbo lag means the time it takes the engine to

generate required engine torque, or in other words, the vehicle reaches the required

speed after the driver depresses the gas pedal. The turbo lag is resulted from the

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Figure 4-3. Turbo lag elimination

inertia of the turbo shaft, which is the main reason that causes the turbo shaft to reach

the required speed in a few seconds. The hybrid turbocharger solves this problem

well because the compressor is driven by the motor directly, which is able to reach full

operating speed in less then 1s and independent of the turbine. Since there is no shaft

between the compressor and the turbine, turbo inertia is not a problem any more.

This comparison is completed by using a step throttle angle input to simulate the

case that the driver depresses the gas pedal to make the throttle angle increase from

to , and check the time it takes the two engine to reach the required speed, as

shown in Figure 4-3.

It is easy to found the difference between the time it takes the engines with the two

types of turbocharger installed to reach the required torque. The result demonstrates

well that the hybrid turbocharger eliminates the turbo lag significantly.

4.2.2 Comparison with Naturally Aspirated Engine

The second advantage of the hybrid turbocharger is compared to the naturally

aspirated engine, since they are able to eliminate the turbo lag. Then why should we

use the hybrid turbocharger but not just the naturally aspirated engine? The answer is

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Figure 4-4. Engine downsizing with hybrid turbocharger Installed. The two engines arein the same condition(same throttle angle and same load). The solid line

shows a 1L engine with hybrid turbocharger installed. The dashed lineshows a 2L naturally aspirated engine.

that the hybrid turbocharger plays an important role in engine downsizing, which means

the engine with the hybrid turbochager installed is able to generate equal or even more

power than the naturally aspirated engine of a larger size. This is shown by Figure 4-4.

It can be seen in Figure 4-4 that with the hybrid turbocharger installed, the 1L

engine has a even larger output power and higher engine speed than the 2L naturally

aspirated engine, which means the engine downsizes about 50%.


In this chapter, comparisons between the hybrid turbocharger with the conventional

turbocharger and the naturally aspirated engine have been made. It can be found that

the hybrid turbocharger has a great significance in eliminating the turbo lag and engine

downsizing. In the next chapter, the controller will be made to control the system.

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CHAPTER 5INTRODUCTION TO MODEL PREDICTIVE CONTROL

5.1 Why Use MPC

Even though PID-control is normally used in industry, the control method used in

this thesis is model predictive control(MPC), an advanced method of process control.

The reasons are as follows .

MPC allows the current timeslot to be optimized, while keeping future timeslots inaccount.

MPC has the ability to anticipate future events and can take control actionsaccordingly. PID and LQR controllers do not have this predictive ability.

MPC can handle safety constraints. More than one input and output (MIMO-systems) can be handled using MPC.

5.2 MPC Overview

Model Predictive Control is an advanced process control technique widely adopted

in industry as an effective method to deal with large multivariable constrained control

problems. MPC uses a model of the system to predict its future behavior, and then

optimizes a quadratic performance based on the prediction. The main idea is to choose

the control input by solving an on line optimal control problem repeatedly, aiming at

minimizing a performance criterion over a future horizon. This future horizon is called

the prediction horizon

, which means the number of samples one looks ahead.

Another important term is the control horizon

, meaning the number of samples that

the optimal input is calculated for.

and

are not necessarily the same. If the

is

shorter than

, the complexity of the problem is reduced. In this thesis,

is picked to

equal to

.

The procedure of the MPC is as following: Assume the system is running during the

period of time T. Discretize the time period T into N pieces of equal length, which is the

sampling time

/ . Then perform the discretization of the continuous system.

Assume starting at time k which is given as the initial condition, predict the states from

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k+1 to

. The optimal input u is calculated at time k by solving the optimal control

problem. Select the first element of u as

and substitute it into the dynamic equation

to calculate

, which is regarded as the initial condition of the next prediction horizon.

Since the input is optimized at each time step, finally the best U will be obtained.

5.3 MPC Derivation

Considering the dynamic equation:

(51)

The first step is to dicretize the continuous equation. This can be completed by

using the function in Matlab. The discretized equation is given as:

(52)

Substitute

in to the state space equation to obtain

. Repeat this process

times to obtain all the predicted states from

to

. This is given as follows:

...

(53)

Put all these equations into matrices to rewrite the state space equation as

...

...

... ...

...

...

(54)

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Define

...

...

(55)

and let

...

(56)

... ...

...

(57)

Now the state space equation is rewritten as

(58)

In a similar way, it is easy to form the expression for the output state space

equation. It can be done by calculating

to

and substituting into the state

space equation to form the output vector, which is given as:

..

.

..

.

..

.

...

...

..

.

(59)

Therefore equation (5-9) can be rewritten as

(510)

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Now it is ready to solve the optimal problem. The cost function is designed

depending on what to minimize. If it is required to minimize the error between the

actual output and the desired output , then the cost function looks like:

||

||

||

||

(511)

where

is the discretization of the desired trajectory in the continuous domain. If

we define

(512)

then the error matrix can be obtained as

...

(513)

Now equation (5-11) can be rewritten as:

(514)

where Q and P are weighting functions.

The optimal problem can be solved by taking the first derivative of J with respect to

U and making it equal to zero:

(515)

This yields to an equation containing U and

. Therefore, the optimized input U could

be expressed by the initial state

as

(516)

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Since

is the initial state which is given, the optimized input vector U at time k is

obtained by plugging in the value of

. Then take the first element of U, which is

out

of the vector:

(517)

Substitute the value of

back into equation (5-2) and together with the value of

, it is easy to calculate the value of

. Then use

as the new initial condition

to repeat the process above to obtain

. After repeating the process for N times

(N is defined previously), the best input U which is optimized at each time step will be

obtained.


In this chapter, the benefits, introduction, and derivation of MPC is discussed in

detail. Now it is ready to apply this control method to the hybrid turbocharger system to

achieve the desired goal.

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CHAPTER 6MODEL PREDICTIVE CONTROL OF HYBRID TURBOCHARGER

6.1 Model Reduction

In this chapter, the MPC will be applied to the hybrid turbocharger system. As

mentioned at the beginning of chapter 3, the turbocharged SI engine model contains

11 states, which is too many for MPC. Therefore, model simplification is necessary.

According to previous researches, some states do not have significant influence on the

system performance so it is reasonable to have them truncated. has proposed a

reduced engine model with 5 states. Therefore, the simplest proposed model for the

hybrid turbocharger consists of 6 states together with the states of the motor, which is

given as follows:

(61)

6.2 Model Linearizion

According to the reduced model, all the mass flow rate functions are nonlinear in the

states. Since the control method used in this thesis is just linear MPC, it is necessary

to linearize the model. Before the linearizion, some parameters need to be set toconstants.

(62)

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Linearizion is completed around the equilibrium point, which is obtained by

equalizing all the differential equations to zero.

(63)

Substitute all the constants into the equations and solve for the solution. The

equilibrium point is obtained as:

(64)

The linearized model is given as:

(65)

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In equation(6-5), the battery voltage V and the wastegate opening

are the inputs

to the system u. The throttle angle and all the constants in the equation are considered

to be the measured disturbance

. Then it is now possible to rewrite equation (6-5) in

state space form as

+

(66)

The output of the system is the fuel mass flow

which is given as equation

(3-18) and (3-21), and the engine torque

, which is given as equation (3-22) and

(3-23). These two equations are also nonlinear in states, so they need to be linearized

too.

A expression for the air mass flow into the cylinder linear in the state

is given as

(67)

where

and

are parameters to be estimated by using the equation in

Matlab. The validation of the linearized model is shown in Figure 6-1.

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Figure 6-1. Validation of linearized mass flow into the cylinder

Here assume that the engine speed is constant N=3000 rpm and the intake

manifold temperature is constant

=302K. Then the air mass flow into the cylinder can

be expressed linearly in the state

, so is the fuel mass flow rate

, given as

(68)

The other output of the system is the engine torque, given as

(69)

For the equation to be linear in states

and

, the same assumption has to

be made, that is, N=3000. Moreover, set the combustion efficiency

to be a constant

0.3469. Thus the engine torque is able to be expressed linearly in states

and

,

which is given as:

(610)

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Figure 3-2 shows the validation of the linear engine torque model.

Figure 6-2. Validation of linearized engine torque model

In equations (6-8) and (6-10),

to

are all constants that are easily calculated.

Combining equations (6-8) and (6-10), it is possible to form the output matrices of

the system, given as

(611)

Now according to equations (6-6) and (6-11), it is ready to form the state space

equation for the linearized system as

(612)

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where

(613)

Now everything is prepared, thus it is ready to apply MPC to the system according

to the procedure described in Chapter 5.

6.3 MPC Implementation In Matlab

The objective is to minimize the fuel consumption and the deviation from the

requested engine torque. In this thesis, the required engine torque

=200 . There

fore, the cost function can be expressed as:

(614)

where , and are weighting functions in the form of

. . .

(615)

where the subscript i stands for f, M and u respectively.

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According to the procedure described in chapter 5, the first step is the discretization

of the continuous system. This can be completed in Matlab by doing

(616)

where is the sampling time.

Here, the matrices A and C are the same as the ones of the original system. The

matrix is the combination of

and

, and the same goes with the D matrix, given as

(617)

where matrix

is just zero matrix. Now the discretization can be expressedas

(618)

where

=

=

=

=

=

Following the procedure described in chapter 5, the prediction state space equation

can be expressed as:

(619)

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where

,

and

are of the same form of the ones described equations (5-6), (5-7)

and (5-9) in Chapter 5. The measured disturbance term

and

are given as

... ...

...

(620)

... ...

...

(621)

Since there are two outputs of the system

and

which are both in the cost

function, there needs to be two matrices that will separate the two outputs, given as

. . .

. . .

(622)

Thus the cost function can be expressed now as

+(C

+u

(623)

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where R is the reference matrix:

...

(624)

Take the first derivative of J with respect to U and solve the differential equation:

(625)

Then U can be expressed in the initial state

. Since the system has two inputs, the

optimized should be the first column of the matrix U, given as:

(626)

Repeating the process described in chapter 5, it is easy to obtain the optimized input U

6.4 MPC With Constraints

In reality, there should be constraints on the input of the system, which means the

battery voltage input and wastegate opening should be both in a reasonable range. In

this thesis, the input constraints are

(627)

Now it is ready to add constraints to the system.

6.4.1 Overview of MPC with Constraints

With the same cost function, now the goal is to solve the optimal problem subject to

some constraints, described as

(628)

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where matrices H, F, L and b are formulated by

,

,

,

,

,

,

,

,

and

given before.The next step is to form the matrices H, F, L and b and apply the

constraints to the system.

6.4.2 Add Constraints to the System

It is necessary to rewrite the equation (6-27) to form the matrices L and b in the

following way:

(629)

Rewrite (6-29) into matrix format as

(630)

Define

(631)

Now it is ready to form the L and b matrices as

. . .

. . .

(632)

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The next step is to rewrite the cost function J to form the matrices H and F. Based

on the original cost function, it is easy to rewrite it in the following form

(633)

where

Now using the Hildreth Quadratic Programming procedure described in [19], it is

ready to run the simulation of the system with constraints.

6.5 Simulation

After implementing the MPC controller, it is ready to run the simulation. Set the

control horizon and predict horizon to be the same

and run the simulation

for 90s. Figure 6-3 and Figure 6-4 shows the simulation results.

Figure 6-3. Fuel consumption after optimization

The results show that the designed MPC controller achieves the goal of minimizing

fuel consumption and in the meantime preventing the engine torque from deviating too

much from the desired torque.

Figure 6-5 and 6-6 shows the optimized inputs of the system. It can be concluded

that in the case the throttle angle at and engine speed at 3000 rpm, it requires

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Figure 6-4. Tracking of the desired engine torque

54.76V battery voltage and 26% wastegate opening to obtain the minimum fuel

consumption and deviation from the desired engine torque.

Figure 6-5. The required battery voltage to minimize the fuel consumption and deviation

from desired engine torque


In this chapter, the hybrid turbocharger model designed in Chapter 4 is reduced

and linearized so that the linear MPC controller could be designed and applied to it. The

simulation results show that the designed controller works well on the linearized system

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Figure 6-6. The required wastegate opening to minimize the fuel consumption and

deviation from desired engine torque

by achieving the goal of minimizing the fuel consumption and and the deviation of the

real engine torque output.

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CHAPTER 7CONCLUSION AND FUTURE WORK

In this thesis, the SI engine with a hybrid turbocharger installed is designed by

building the battery model and each component of the turbocharged SI engine. The

comparison has been made between the hybrid turbocharger with the conventional

turbocharger and the naturally aspirated engine respectively, demonstrating the

two main advantages of the hybrid turbocharger in eliminating the turbo lag and

engine downsizing. Then the linear MPC controller is designed and applied to the

simplified hybrid turbocharger system after model linearization to realize the objective of

minimizing the fuel consumption and deviation from the required engine torque.

Future works that needs to be done focus on two aspects: the first one is to design

the nonlinear MPC controller which can be applied directly to the nonlinear hybrid

turbocharger model without model linearization. This will provide a more accurate result

and can be used in experiment with real hardware. The second one, as mentioned in the

first aspect, is to perform the real-time MPC by designing the nonlinear MPC controller

and applying it to the real engine model, which has a very practical and important

significance.

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REFERENCES

[1] Olivier Tremblayi, Louis-A.Dessaint, Experimental Validation of a Battery DynamicModel for EV Applications, World Electric Vehicle Journal Vol. 3 - ISSN 2032-6653 -

2009 AVERE

[2] Ryan C. Kroeze, Philip T. Krein Electrical Battery Model for Use in Dynamic ElectricVehicle Simulations, University of Illinois at Urbana-Champaign Department of

Electrical and Computer Engineering

[3] Min Chen,Student Member, IEEE,and Gabriel A. Rinc on-Mora,Senior Member,

IEEE Accurate Electrical Battery Model Capable of Predicting Runtime andIVPer-formance, IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2,JUNE 2006

[4] Olivier Tremblayi, Louis-A.Dessaint, Experimental Validation of a Battery DynamicModel for EV Applications, World Electric Vehicle Journal Vol. 3 - ISSN 2032-6653 -

2009 AVERE

[5] Lar Erikkson, Lars Neilson Modeling of a Turbocharged SI Engine, SAE TechnicalPaper 2002- 01-0374.

[6] Guzzella, L., U. Wenger and R. Martin (2000) IC engine Downsizing and Pressure-

Wave Supercharging for Fuel Economy, SAE Technical Paper 2000-01-1019.

[7] A.Karnik, J.Buckland, and J.Freudenberg Electronic throttle and wastegate controlfor turbocharged gasoline engines, American Control Conference,Portland,USA,

2005.

[8] Muller, Martin, Elbert Hendricks and Spencer C. Sorenson (1998). Mean ValueModelling of Turbocharged Spark Ignition Engines., AE SP-1330 Modeling of Sland Diesel Engines (SAE Technical Paper 980784), 125-145.

[9] Moraal, Paul and Ilya Kolmanovsky (1999). Turbocharger Modeling for Automotive

Control Applications, SAE Technical Paper 1999-01-0908 pp. 309-322.

[10] Lar Erikkson Mean value models for exhaust system temperatures, AnnualReviews in Control 26 (2002) 129-137

[11] Fredrick Pettersson Simulation of a Turbo Charged Spark Ignited Engine LiTH-

ISY-EX-3010, Department of Electrical Engineering of University of Linkoping,2000

[12] Johan Bergstrom, Jan Brugard Simulation of a Turbo Charged Spark IgnitedEngine LiTH-ISY-EX-2081, Department of Electrical Engineering of University ofLinkoping, 1999

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[13] Per Andersson, Lars Eriksson Air-charge estimation and prediction in spark ignitioninternal combustion engines., In Proceedings of the American Control Conference,

pages 217221, San Diego, California, June 1999

[14] Mrdjan Jankovic and Steve W. Magner Air Charge Estimation in Turbocharged

Spark Ignition Engines, Society of Automotive Engineers, 2004. SAE TechnicalPaper No. 2004-01-1366.

[15] Per Anderson Air Charge Estimation in Turbocharged Spark Ignition Engines,Linkoping Studies in Science and Technology Thesis No. 989 ISSN 0345-7524,

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[16] Mohammadreza Saeedi A Mean Value Internal Combustion Engine Model inMaplesim, Department of Mechanical Engineering of University of Waterloo,2010

[17] Rahul Sharma, Dragan Ne sic, Fellow, IEEE, and Chris Manzie, Member, IEEEModel Reduction of Turbocharged (TC) Spark Ignition (SI) Engines, IEEE

TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 19, NO. 2,MARCH 2011

[18] L. Eriksson, S. Frie, C. Onder, and L. Guzzella Control and optimization of tur-

bocharged spark ignited engines, presented at the 15th Triennial World Congr.,Barcelona, Spain, 2002

[19] Roberto Argolini, Viviana Bloisi On optimal control of the wastegate in a tur-

bocharged SI engine, Masters Degree Project Stockholm, Sweden June 2007

[20] Liuping Wang Model Predictive Control System Design and Implementation UsingMatlab

[21] Ida Kristoffersson Model Predictive Control of a Turbocharged Engine, Master ofScience Thesis Performed at S3 for General Motors Powertrain,2006

[22] D. Axehill and J. Sjoberg Adaptive Cruise Control for Heavy Vehicles, Master

Thesis, Linkoping Institute of Technology, Linkoping 2003.

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BIOGRAPHICAL SKETCH

Kang Rong received his Bachelor of Science degree in Automotive Engineering

in 2008 in Shandong University, Jinan, China. He is now pursuing his Masters

of Science degree in the Department of Mechanical and Aerospace Engineering

in University of Florida. His research interests are: Turobocharged SI engine

modeling, Hybrid turbocharger design and Application of nonlinear control and

Model Predictive Control.

rong_k

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