HCCI Timing Control Using Iterative Feedback Tuning

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HCCI Timing Control Using Iterative Feedback Tuning

COLETTE CASTELL HERN´ ANDEZ

Masters’ Degree Project

Stockholm, Sweden 2006

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Abstract

The Homogeneous Charge Compression Ignition (HCCI) is an engine which combines some of the characteristics of the Diesel and Otto engines. As a result an engine with a high efficiency and low emissions is constructed. Unfortunately, there is not a direct way to control its start of combustion (SOC). One way to phase the SOC is using valve timings. There are two main methods, the Overlap, which consists in trapping more or less residual gas, and the IVC method, which acts affecting the effective compression ratio.

Iterative Feedback Tuning (IFT) is a control method that appeared in 1994, which has presented good performances in the tuning of PID and more complex controllers. The tuning is done by using data of closed loop experiments with the controller that is being tuned in the loop. Therefore, knowledge of the system and disturbances is not required.

That is one of the principal advantages of this method.

At the department of Machine Design at the Royal Institute of Technology (KTH) there is a single cylinder HCCI engine. It is based on a SCANIA truck engine and it includes an Active Valve Train System. In this equipment a control system based on non-linear compensation is used. Furthermore, a model of the real engine is available.

In this project a procedure which allows the application of IFT in the HCCI has been developed. The method was tested, first, on a model and, secondly, in the test bed of the HCCI engine explained above. Controllers were tuned for three different operating points of the engine. The overlap method was used in two of them and the IVC method in the third one.

However, more experience is required to determine how much improvement can be gained with the method. It was also noted that speed transients were very difficult to control due to long time delays.

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ACRONYMS

HCCI: Homogeneous Charge Compression Ignition SOC: Start of the Combustion

KTH: Royal Institute of Technology IFT: Iterative Feedback Tuning IVC: Inlet Valve Closure

AVT-System: Active Valve Train System EVO: Exhaust Valve Opening

EVC: Exhaust Valve Closure IVO: Inlet Valve Opening

CA50: Crank angle degree for 50 percent burnt CR: Compression ratio

CAD: Crank angle degree

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1. Introduction

There are two kinds of internal combustion engines: the petrol and the Diesel. The combustion processes of them are very different. In the Diesel engine the combustion is initiated because of some special conditions of pressure and temperature. However, in the petrol engine the combustion is caused by a spark that ignites a mixture that has been premixed before.

Due to these different kinds of combustion, the two engines have different characteristics.

The Diesel engine has a high efficiency, but it is very contaminating. Contrarily, the petrol engine is not very efficient but it has low emissions.

Nowadays, there is an increasing environmental concern which leads to the use of an engine with low emissions. However, high efficiency is as well required. Consequently, the idea of an engine which combines some of the characteristics of a Diesel engine with some of the Otto ones appeared.

The Homogeneous Charge Compression Ignition (HCCI) has high efficiency and low emissions. That is achieved because of a very good combustion process. As in an Otto engine, the mixture is premixed, and as in a Diesel, the combustion is initiated by pressure and temperature conditions.

Unfortunately, there is not a direct way to control the start of combustion (SOC). This problem is emphasized in transient conditions. It is important to notice that a too early combustion produces high pressures not desirable for the engine and a too late combustion may cause a misfire. Therefore, a control of the SOC is necessary.[1]

One way to phase the SOC is using valve timings. That means that changes in the time when the valves are open or closed produce a different SOC. There are two main methods, the Overlap, which consists in trapping more or less residual gas, and the IVC method, which acts affecting the effective compression ratio. In the Overlap method the difference between the time the exhaust valve is closed and the inlet valve is opened varies. In the IVC method the time when the inlet valve is closed is varied.

Hence, the control of the SOC may be done as follows. The SOC is measured in some way and it is compared to a desired value. Next, the valve timing is changed in such a way that the SOC will be modified to a value closer to the desired one. However, this control presents some performance problems, especially in the transients. At the present the utilized control is too slow to be used for real applications.

Iterative Feedback Tuning (IFT) is a control method that appeared in 1994, which has presented good performance in the tuning of PID and more complex controllers. The tuning is done by using data of closed loop experiments with the controller that is being tuned in the loop. Therefore, knowledge of the system and disturbances is not requested.

That is one of the principal advantages of this method.[2]

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On the one hand, the control of the SOC of an HCCI is a problem that has not yet been solved with a good performance. On the other hand, lastly, the IFT has performed good results tuning controllers. As a consequence, the idea of the application of the IFT to control the HCCI comes up.

At the department of Machine Design at the Royal Institute of Technology (KTH) there is a single cylinder HCCI engine. It is based on a SCANIA truck engine and it includes an Active Valve Train System, AVT-System. In this equipment a control system based on non-linear compensation is used. Furthermore, a model of the real engine is available.

The aim of this project is to apply the IFT method, first, in the model and, secondly, in the test bed of the HCCI engine explained above in order to achieve a controller which gives a good performance in the control of the SOC by using valve timings. The two methods utilized are the Overlap and the IVC.

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2. Background

The work done in this thesis consists in the application of a control method, IFT, in an HCCI. Thus, knowledge about, on the one hand, the control method, and on the other hand, the operating of the engine is necessary. Therefore, a summary of them will be presented below.

2.1. Homogeneous Charge Compression Ignition

The purpose of this project is to control the SOC of an HCCI. Thus, knowledge about its combustion and the different methods employed to control it are required.

First of all, a brief introduction to the four stroke Internal Combustion engine is required.

Secondly, the combustions events and the valve timings of the different engines will be explained. In that moment, it will be possible to focus more in the methods used to control the SOC, and the actual control strategy.

2.1.1. Internal Combustion Engine

First of all, the operation of an Internal Combustion engine will be explained. Among this kind of engine, there are the two stroke and the four stroke engines. Since the HCCI that is studied in this project has four strokes, we will focus on this type of engine.

The procedure of an Internal Combustion engine consists of transforming the energy obtained in a chemical reaction into mechanical energy. The reaction takes place when a fuel reacts with air, following this equation

2 2

2

2 3.77 )

(O N CO b H O c O d N

a

CH_x + ⋅ + ∗ → + ⋅ + ⋅ + ⋅ (1)

whereCH denotes hidrocarbures present in the combustible, _x O and₂ N are the oxygen ₂ and nitrogen present in the air, CO₂,H₂O,O₂andN are the exhaust gas. ₂

This reaction is exothermic, so we can obtain energy. The reaction takes place inside a cylinder. This cylinder contains a piston connected to a mechanism of a crank and a crankshaft, as can be seen in the Figure 1, which transform the chemical energy into mechanical one.

Figure 1. Mechanism crank and crankshaft [8]

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In the four-stroke engine, there are the following phases: Intake, Compression, Expansion and Exhaust. They are shown in Figure 2.

1- Intake: The piston moves from the top of the cylinder to the bottom, while the mixture is entering inside. The intake valves are open.

2- Compression: The piston moves from the bottom of the cylinder to the top, while the mixture is compressed and the pressure and the temperature increase. At the end of this stroke the combustion takes place. Both valves are closed.

3- Expansion: The energy obtained in the combustion moves the piston from the top to the bottom of the cylinder. Both valves are closed.

4- Exhaust: The piston moves from the bottom of the cylinder until the top throwing the mixture out. The exhaust valves are open.

That cycle is repeated all the time the machine is working. In the four strokes the crankshaft is doing two turns per cycle. This movement is mechanical energy, so the objective of the engine is obtained.

Intake Compression Expansion Exhaust

Figure 2.Four strokes of an Internal Combustion engine. [3]

2.1.2. Different combustion processes

The combustion event will be different depending on the way how the mixture ignites and the different conditions of pressure, temperature and proportion air fuel.

Consequently, the engines will have different efficiency and amount of emissions.

2.1.2.1. Otto engine

In an Otto engine, as well called, petrol engine, the combustion is provided by a spark.

First of all, the air is premixed with the fuel in a separate chamber. Then, in the intake stroke the mixture is inhaled. In the following stroke it is compressed and at the end of the compression a spark is lit and it ignites this mixture. A flame starting in the spark spreads spherically through the chamber. There is the risk that suddenly the charge ignites itself, called knocking. It is very important to avoid this, because it causes

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damages to the engine. In order to control that, the compression ratio has to be low. The compression ratio (C ) is the relation between the total volume of the cylinder and the _R volume of the combustion chamber.

c T

R V

C = V (2)

In the combustion much combustible remains unburnt in the chamber. Furthermore, the compression ratio must be reduced in order to avoid knocking problems.These two facts are translated into a low efficiency.

Nitrogen oxides (NO ) are generated because the nitrogen present in the air reacts with _x the oxygen at high temperatures. In a petrol engine, the proportion air fuel is close to the stoichiometrical so a three-way catalyst can be applied, reducing the NO ._x

2.1.2.2. Diesel Engine

In a Diesel engine the combustion is initiated because of the temperature and pressure conditions. In the intake stroke the air is introduced in the cylinder. At the end of the compression, when the air reaches high temperature and pressure, the fuel is injected. In that moment, the combustion takes place.

This operation is unthrottled, which means that the quantity of air introduced is not controlled, just the amount of fuel is adjusted. The proportion of the quantity of air in relation with the fuel is higher than in the Otto. These factors and the possibility of having a bigger compression ratio, make the Diesel engine have a high efficiency.

Nevertheless, the emissions ofNO and particulates are higher. Since the mixture has not _x been premixed before, some fuel remains unburnt, and as a consequence more particulate matter are released. The high emissions ofNO is caused because the mixture is less rich _x than in the Otto, which means that the proportion air/fuel is bigger. Therefore a three-way catalyst cannot be applied.

2.1.2.3. HCCI Engine

In an HCCI engine the mixture of air and fuel is premixed before the combustion. In the intake stroke this mixture is inhaled, as is the case for an Otto engine. At the end of the compression stroke, the mixture reaches a high temperature, which causes the combustion, similarly as in the Diesel engine.

As can be seen in [1], the combustion starts in some areas where the heterogeneities in the pressure, temperature and proportion fuel air, give some favorable conditions. When the combustion begins it causes a rise of the pressure of the chamber, which causes the ignition of more kernels. The operation is unthrottled, as in a Diesel, but during the combustion any fuel more is injected, because it has already been injected mixed with the air. Thus, the speed of the combustion is governed by chemical kinetics.

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The combustion is fast and does not reach a high temperature. There is not any problem of knocking, so the compression ratio can be big. That means that the engine will have a high efficiency and low emissions.

The problem occurring with this approach is that there is not a direct way to control when the combustion takes place.

2.1.3. Valve timings

As seen above a cycle consists of two revolutions of the crankshaft, which corresponds with 720 crank angle degrees (CAD). The origin reference is fixed at the end of the compression stroke.

At the end of the compression stroke the combustion takes place. After that, the energy released by this reaction moves the piston to the bottom of the cylinder, during the expansion stroke.

At the exhaust stroke, the piston starts to move up, and the exhaust valve is opened (EVO) that occurs at 180 CAD. During this stroke the mixture is expelled, and at the end, the valve is closed (EVC), which is timed at 360 CAD. At the intake stroke, the inlet valve is opened (IVO) at 360 CAD, and then the mixture is inhaled. At the end of this stroke the valve is closed (IVC) at 540 CAD.

0 180 360 540 720

0 2 4 6 8 10 12

CAD

Valve lift (mm)

Valve timing

Figure 3. Valve timing of an Otto and Diesel engine.

This explanation is a simplification of the real valve timing utilized in a Diesel, Otto or HCCI engine. In reality in a Diesel or Otto engine, the EVO is timed before 180 CAD and the IVC after 540 CAD, the IVO takes place before 360 and the EVO takes place later, as seen in Figure 3. That is done in order to minimize the gas exchange loss. The difference between the EVC and the IVO is called Overlap:

IVO EVC Overlap= −

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2.1.4. Control of the Combustion

As has been explained above, the SOC is difficult to control and this problem will be emphasized during transient conditions. It is important to state that the moment when the combustion takes place will directly affect the efficiency and the emissions of the engine.

Moreover, if the combustion takes place too early, high peak pressure and high pressure rises will occur. On the other hand, if the combustion is too late the engine might misfire.[1] Therefore, control of the start of the combustion is necessary.

A measurement of the SOC is desirable, but this is complicated. So, another measure of the moment when the combustion takes place will be utilized. The time when the half of the combustible is burnt (CA50) is a measure of the combustion time much easier to appraise. From now on, the CA50 is the value we will use to quantify the start of the combustion.

In [4] is shown that different procedures can be used to affect the CA50. Exhaust energy can be used to heat the intake charge. Another method consists in timing the combustion by aid of fuels with radically different octane numbers. However, the method we are going to apply is based on controlling the CA50 by changing the valve timings. Two methods will be used: the Overlap and the IVC.

2.1.4.1. Overlap method

The valve timing of an HCCI follows a similar scheme as the Otto or Diesel for some conditions. However, at the conditions of inlet temperature, pressure and engine speed that our engine will work, the valve timing requires to be a little different.

In our case, the Overlap will not be positive. That is due to the fact that at the end of the compression the combustion has to take place without the help of a spark, so high temperatures are demanded. If we put a positive Overlap the required temperature would not be reached. One way to increase this temperature is by trapping residual gas in the cylinder.

If there is a negative Overlap, some exhaust gas could not be given off, and it will remain in the cylinder. This residual gas has a high temperature, allowing the combustion to take place.

0 180 360 540 720

0 2 4 6 8 10 12

CAD

Valve lift (mm)

Valve timing HCCI

Figure 4. Valve timing of HCCI

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The Overlap method consists in changing the value of this negative Overlap, which means trapping more or less residual gas. The more gas there is in the cylinder, the higher temperature will be reached, and as a consequence, the earlier the combustion will be timed. So we will modify this Overlap in order to have the desired CA50.

2.1.4.2. IVC method

The IVC method consists in closing the inlet valve sooner or later in order to affect the effective compression ratio.

The position of the piston depends on the crank angle. At 540 CAD, the piston is situated at the bottom of the cylinder. After that, the piston starts to moves to the top of the cylinder, so the volume included by the piston will be smaller. The effective total volume is the volume determined by the piston. This volume is smaller than before, thus theC is_R lower, as can be seen in equation (2).

The lower theC is, the less temperature will be raised, and therefore, the later the _R combustion will be timed.

2.1.5. Actual Control Strategy

The actual control of the CA50 in the engine located at KTH is done as follows [5]. First, the CA50 is calculated from the measured cylinder pressure as described in [6]. Secondly, a desired value has been chosen as the most convenient for the optimization of the efficiency and the minimization of the emissions. This value is from 3 to 7.

In [6] the Overlap method is utilized when the load is low, while the IVC method is applied when the load is high. The load is a measure obtained by calculating the mean pressure inside the cylinder. It depends, amongst others, on the inlet pressure and the amount of fuel injected.

When the load is too low, the mixture will not reach enough temperature to ignite. As has been explained before, a way of augmenting this temperature is by trapping more residual gases. By contrast, if there is too high load, the temperature will be too big, and thus the combustion will take place too early. It might produce damage in the engine. To avoid that, a decrease of the temperature is needed. One way to do that is by lowering the compression ratio.

To sum up, at the range of high loads the IVC method will be applied, decreasing the C_R when the combustion is too early, and increasing C when the combustion is too late. At _R the range of low loads the Overlap method will be used, raising the negative-Overlap when the combustion is too early, and decreasing it when it is too late.

However, as seen in [6], the controller is not fast enough when changes in the engine speed occur. Hence, the idea of a controller based on non-linear compensation has

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appeared. In [5] the control of the CA50 takes into account some physical parameters as will be explained next.

The ignition delay,τ , can be calculated through an Arrhenious correlation:

T B

n e

p

A∗ ∗

= ⁻

τ ⁽³⁾

where A, n and B are positive coefficients, p is the pressure and T is the temperature. The data of the pressure and temperature are measured at -10 CAD.

The procedure utilized consists in constructing some maps which relate the engine speed, and valve timing with the ignition delay. First, some simulations with constant inlet pressure and temperature, but changing speed and valve timings are made. The in- cylinder pressure and temperature are stored. Therefore, two 3D-maps are obtained, both with valve timing and speed as independent variables. The first map has the in-cylinder pressure as a dependent variable, while the second one has the temperature.

Now, (3) is used in order to calculate the ignition delay. So, with the data of these two maps, another map can be obtained. This new map consists of a 3D map which relates the speed, valve timing and ignition delay.

While the engine is working, the CA50 and the engine speed are measured. In [5] it is explained how the control of SOC is done by utilizing these data, the map described above and a PID controller.

These maps are solely valid for a fixed inlet pressure and temperature. When the engine is working at different working points a correction of the parameters before entering into the maps can be done.

2.1.6. Specifications

The requirements for the correct operating of the engine are the following ones. A CA50 between 3 and 7 CAD are required in order to have the best efficiency and lowest emissions possible. Furthermore, it is requested to never leave the interval between 0 and 10 CAD. If the combustion takes place earlier than 0 CAD the pressure might reach too high temperatures that might damage the engine. By contrast, if the CA50 is timed after 10 CAD the engine could misfire.

In addition, it is not convenient to change the valve timing very much at the steady state.

The maximum crank angle that is allowed to be toggled is 2 CAD.

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2.2. Iterative Feedback Tuning

As has been discussed above, the control of the CA50 of the HCCI is required. Hence, a control method should be applied. An introduction about what the control is will be done.

Later, we will focus on the Iterative Feedback Tuning method.

2.2.1. Introduction to the control

In [9] it is seen that the control is based on the comparison of the actual performance on the work against a desired performance. We will represent the systems by block diagrams. The input signals enter into the block, then they are transformed depending on the system, and the output signals exit.

1 Out1

In1 Out1

System 1

In1

Figure 5. Block diagram.

The block is defined by some mathematical equations, which are a model of the system.

Now, some important concepts will be explained.

1. - The desired responsey^d is the output that is required.

2. - The response y is the real output that is obtained.

3.-The error e is the difference between the desired response and the response.

y y e= ^d −

4.-The reference signal r is the input.

5.- The disturbance v is un uncontrollable signal.

6.-The closed-loop consists in doing a feedback of the output. In the figure below a negative feedback is represented.

1 Out1

In1 Out1

System

Disturbance 1

In1

Figure 6. Closed loop system with negative feedback.

The main idea of the control is represented in the Figure 6. If the desired response is used as input, theorically, it will be obtained as output as well. However, in the real process a controller is required. In the next figure the scheme of a one-degree of freedom and a two-degrees of freedom controller are shown.

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ONE-DEGREE OF FREEDOM TWO DEGREES OF FREEDOM

1 response In1 Out1

Cr G0 1

reference

1 response In1 Out1

Cy G0 Cr

1 reference

Figure 7. Closed loop with a controller of one-degree of freedom and of two-degrees of freedom

The calculation of this controller is difficult and is one of the aims of the control. In this thesis, concretely, our aim will be find the appropriate controller for our system.

In order to carry out this control usually a model of the system is constructed, and many mathematic techniques have been developed. In [10] the theory and design techniques of control are divided into two categories: Classical and Modern control methods. The first ones are based on Laplace or Fourier transforms, while the seconds use ordinary differential equations. These methods are based on models, but in our case they are not going to be used, because we will do the control based on experimental data.

However, some other terms are required for the understanding of this thesis. The final response obtained is wanted to be as similar as the reference. Some concepts will be used in order to estimate the quality of this response. The concepts that will be used are the rise time, the settling time and the overshoot.

7.-The set value is the value wanted to be reached.

8.-The rise time is the time passed until the response achieves the first time the set value.

9.-The settling time is the time passed until the response arrives to the set value.

10.-The overshoot is the difference between the peak value and the set value.

2.2.2. The procedure of the IFT

As discussed in [2], many control methods are based on the minimization of a criterion function. Knowledge about the plant and disturbances, and freedom in the complexity of the controller are usually required to do this optimization

However, the complexity of the controller is usually restricted. In addition, the system and the disturbances are often unknown. Sometimes there is a model of the system, but this model is always an approximation of the reality. Thus, if we do the optimization based on this model, optimal performance may not be obtained. Therefore, a method which could tune a controller of fixed complexity without knowing a model of the system would be convenient.

Some iterative identification and control design methods using low order models existed before IFT [2]. These schemes do an identification of the system, and they optimize the

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controller based on the model. In these methods, some experiments with a closed loop with the controller are used. However, it has not been possible to prove convergence to the optimal controller, and it has been seen that sometimes these methods diverge.

Then, in 1994 the IFT scheme has been proposed [2]. IFT tunes an initial controller by using experimental data, so a model of the system is not needed. Furthermore, it can tune controllers of prescribed complexity. Contrarily to the iterative identification methods, the convergence has been proved.

Since every control objective consists in minimizing the error between a desired response and the real response, it seems intuitive to try to minimize a norm of this error.

The steps followed to create IFT are the following ones [2]. First, a function of the norm of the error is defined. Secondly, an equation which minimizes this error for some parameters of the controller is obtained. The last step consists of computing this expression using experimental data of the closed loop system, as will be seen next.

In Figure 8 we can see a scheme of the closed loop utilized. It uses a controller with two- degrees of freedom. The controllersC and _r C_yare linear time-invariant transfer functions parametrized by a parameter vectorρ∈Rⁿ^.

u

y.mat

y

v r1.mat

r

In1 Out1

G0

Cy Cr

Figure 8. IFT scheme with a two-degrees of freedom controller.

The output of the system is:

G v r C

G C

G y C

y y

r ⋅

+ + + ⋅

=

0 0

0

) ( 1

1 )

( 1

) ) (

( ρ ρ

ρ ρ ⁽⁴⁾

where G₀ is a linear time-invariant operator and v is a disturbance.

The error is the difference between the output and the desired response:

yd

y y( )= ( )−

~ ρ ρ ⁽⁵⁾

The following cost function of the error is chosen:

⎥⎦⎤

⎢⎣⎡ +

=

∑

₌^N

∑

₌

t

N

t u

yy L u

L N E

J

1 1

2

2 ( ( ))

))

~( 2

) 1

(ρ ρ λ ρ ⁽⁶⁾

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where ^E

[ ]

represents the expectation with respect to the weakly stationary disturbance v , and L ,_y L_uare some filters.

The minimum of a function is located where its derivate is equal to zero, so we aim to solve the following equation.

0 )

( =

∂

∂ ρ ρ

J (7)

The next formula represents an algorithm which is a solution of the equation above )

1 (

1 i i i i

i

R J ρ

γ ρ ρ

ρ ∂

− ∂

= ⁻

+ (8)

whereR is a positive definite matrix, and _i γ_i is a positive real scalar which determines the step size.

In order to solve (8), the gradient of the cost function should be calculated. It is given by

⎥⎦

⎢ ⎤

⎣

⎡

∂ + ∂

∂

= ∂

∂

∑

^N₌

∑

₌

t

N

t

t t

u u y y

N E J

1 1

) ( ) ( )

(

~ )

~ ( ) 1

( ρ

ρ ρ λ

ρ ρ ρ

ρ ρ ⁽⁹⁾

It has been shown in [2] that we can estimate the terms in (9) just using experimental data. These quantities can be calculated by three batch experiments.

In the first and third experiment we take the data of the closed loop seen in Figure 8. In the second experiment, called as well gradient experiment, we put as a reference the difference between the output and the reference of the first experiment.

1 1

2 r y

r = − (10)

A one-degree controller can be used as well. In this case, the third experiment will not be required. In (6) a weighting function can be added too.

To perform the method, the choice of a criterion and a step size have to be done in order to calculate R and_i γ_i. In addition, some other parameters as the desired response, the reference and weighting function have to be chosen.

2.2.3. The reasons for the application in the HCCI

As has been discussed before, we aim to control the CA50 of the HCCI. Now, we can specify that concretely, our objective is finding the best controller for this system.

Lastly, IFT has shown good results in the tuning of PIDs and more complex controllers.

In addition, it has presented a good performance for non-linear systems, which could be our case. Furthermore, at the Department of Machine Design at KTH, there is a single cylinder HCCI engine, which can be used to obtain the experimental data. Therefore, the IFT is chosen to find a controller for the HCCI.

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3. Application of IFT in the control of HCCI

The IFT has been utilized in many different processes, but never in the HCCI. Hence, a way of how to apply the method in this engine has to be developed.

The first step is transforming the engine characteristics into control parameters. The HCCI engine is the system, the CA50 is the response, a CA50 between 3 and 7 CAD is the desired response and the valve timing is the input.

We saw in Section 2.2.2 that IFT can tune controllers of one or two degrees of freedom.

In this case, a one degree of freedom controller is used. So, just the first and second experiments are required.

We know that IFT uses experimental data. However, the real experiments are expensive and they take much time to be performed. So, first, IFT will be applied in a model in order to gain experience with the method. Different approaches are used until the best one is defined. When the method gives a good performance, we will do the real experiments.

Furthermore, in IFT a criterion, a step size and some more design parameters have to be chosen. The reference and the desired response have to be analyzed too.

So, the work procedure will be as follows. First of all, the model will be studied and compared with the test bed. Secondly, the IFT scheme and the conditions of the engine in order to put both altogether will be elaborated. Later, the design choices and the steps of the procedure will be prepared. Finally, how to store and utilize the data of the test bed is explained.

3.1. Model of the HCCI

A model consists of some mathematical equations that represent a real system. A Simulink model of the HCCI is available. So, we can do different experiments very easily. First of all, some simulations will be performed in order to have an idea of the values we are working. Secondly, the model will be compared with the test bed.

3.1.1. Manual application of Overlap and IVC methods

Values of CA50 between 3 and 7 CAD are desired. Therefore, our objective is to change the valve timing producing that the CA50 will be between these values.

Six working points with different conditions of pressure, temperature, engine speed and amount of fuel are chosen. These working points represent normal conditions of the engine. At the three first working points the engine has a low load, so the Overlap method

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will be applied. By contrast, the other three provide a high load, so the IVC method will be used.

First, the Overlap method will be applied. The model has been constructed in such a way that if the user changes the EVC the IVO is changed too. The IVO is modified such that the Overlap is centred on 365 CAD. The Figure 9 represents the model.

1 Out1 T ermi nator6

T ermi nator5 T ermi nator4 T ermi nator3

T ermi nator2 T ermi nator1

-C-

T emperature

1000

Speed 1

Pressure average 1.6

Pressure IVO

571

IVC 6.75

Fuel

Ts

IV0

IVC

EVC

Tin

Pav g

f bin

ESpeed

Lambda

mf b

P10

T10

P010

T010

CA50

Cyl LambdaEst_8 0

Constant3 1

In1

Figure 9. Overlap in the model of the HCCI.

In every working point, the EVC will be changed in order to achieve the desired CA50 value, as we can see in Table 1, 2 and 3. Finally, knowledge about how much the EVC has to vary will be acquired.

Working point 1:

Table 1. Conditions of working point 1 and CA50 obtained for different EVC.

conditions Ts=6.75 ms IVC=571 CAD

Pin=1.6 bar Tin=60 C° E.Speed=1000 rpm

EVC CA50 desired 310 19.5 No 300 14.8 No 290 10.2 No 280 6.5 Yes 270 4.3 Yes 265 3,5 Yes 260 2.9 No

Range 280-265

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Now, the results will be analyzed. In the experiments above, we have actuated as if we were controllers, because we have changed the EVC in order to have the desired CA50.

At the first working point, the controller would change the EVC into a value between 280 and 265 CAD, and at the second working point into a value between 280 and 270 CAD.

The IVO should be changed in such a way that the Overlap is centred on 365 CAD.

At the third point, some problems have appeared. That is due to the fact that the load is quite high, so we are close to change to the IVC method. At 365 CAD the Overlap is saturated, which means that the CA50 cannot be timed later. Thus, if a CA50 of 5 CAD is requested, the IVC method should be applied. That is easy to see. When the EVC is timed at 365 CAD the combustion takes place before 5 CAD, thus the temperature should be reduced. In the Overlap method, the drop of the temperature is done by trapping less gas.

At 365 CAD of EVC, the IVC is timed at 365 as well, so no gas is trapped. It is impossible to reduce the temperature using this method. However, if the IVC method is used, the compression ratio is decreased, and as a consequence the temperature drops.

In our engine, the AVT-system allows 255 predefined valve profiles. So, the saturating point will not be exactly at 0 CAD of Overlap. It will be at a value of -10 CAD, which corresponds to an EVC of 360 CAD.

conditions Ts=8.5ms IVC=580 CAD Pin=1.8 bar Tin=60 C°

E.Speed=1200 rpm

EVC CA50 desired

300 12.2 No

290 9.1 No

280 5.9 Yes

270 3.9 Yes

260 2.5 No

250 1.7 No

240 1.2 No

Range 280-270

conditions Ts=8.25ms IVC=583 CAD Pin=1.8 bar Tin=60 C°

E.Speed=1250 rpm

EVC CA50 desired

310 13.7 No 320 11.5 No

330 9.7 No

340 8.2 No

350 7.1 No

355 6.7 Yes

360 6.5 Yes

365 6.5 Yes

Range 355-365

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Furthermore, we can add that the Overlap method has another saturating point at -168 CAD. Then the EVC is timed at 281 CAD and the IVO is timed at 449 CAD, which is too late. In this case the inlet valve is open too little time, and as a consequence too little fuel can be injected, which is not efficient for real applications. Depending on the working point the behavior of the engine is a little different. The working point is determined by the conditions of pressure, temperature, amount of fuel, engine speed and as well the valve timing. Then, a value of EVC is requested in order to determinate the working point. An average value of the EVC utilized in Tables 1, 2 and 3 is chosen. This value is 320 CAD.

When the control will be done, a constant of 320 CAD will be added in the input, as can be seen in next Figure 10.

1 Out1 r.mat

r Terminator6

Terminator5 Terminator4 Terminator3

Terminator2 Terminator1

Sum1

Sum Ground

Ts

IV0

IVC

EVC

Tin

Pav g

f bin

ESpeed

Lambda

mf b

P10

T10

P010

T010

CA50

CylLambdaEst_8 320

Constant8

1

Constant7 -C-

Constant6 1.8

Constant5

1000

Constant4 0

Constant3 571

Constant2 6.75

Constant1

Co

Figure 10. IFT scheme.

For the next working points the same procedure is followed, but now changing the IVC.

It is shown in Tables 4, 5 and 6.

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1 Out1 T erm inator6

T ermi nator5 T ermi nator4 T erm inator3

T ermi nator2 T ermi nator1

-C-

T emperature

1000

Speed 360

Pressure1

1

Pressure average 2.4

Pressure IVO 11

Fuel

Ts

IV0

IVC

EVC

Tin

Pav g

f bin

ESpeed

Lambda

mf b

P10

T10

P010

T010

CA50

Cyl LambdaEst_8 0

Constant3 1

In1

Figure 11. IVC in the model of the HCCI.

Table 4. Conditions of working point 4 and CA50 obtained for different IVC.

conditions Ts=11 ms

Overlap=-10 CAD Pin=2.4 bar Tin=60 C°

E.Speed=1000 rpm

IVC CA50 desired

580 2.7 No

590 2.9 No

600 3.2 Yes

610 3.6 Yes

620 4.1 Yes

630 4.8 Yes

640 5.9 Yes

650 7.4 No

Range 600-630

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At the working points 5 and 6 we are situated when the IVC method saturates. If a CA50 of 3 CAD is requested, then the Overlap method should be applied. When the IVC is timed at 540 CAD the effective compression ratio cannot be increased, because the piston is at the bottom of the cylinder. Hence, the temperature cannot be decreased in any way, so the combustion cannot be timed before. Concretely, in our engine we will fix the saturating point a little later, at 560 CAD.

Another saturating point is timed at 655 CAD.Then the IVC is timed so late that the fuel injected is very little.

A crank angle of 590 is chosen as a working point. So, in the control this value is going to be corrected.

In conclusion, it is necessary to pay attention when the crank angle is near the saturating points. In the Overlap method that occurs at -10 CAD, while in the IVC this is at 560 conditions

Ts=11 ms

E.Speed=1200 rpm

IVC CA50 desired

540 3.3 Yes

550 3.3 Yes

560 3.4 Yes

570 3.4 Yes

580 3.5 Yes

590 3.6 Yes

600 4 Yes

610 4.4 Yes

620 5 Yes

630 5.8 Yes

640 7 Yes

650 8.6 No

Range 540-640

conditions Ts=11 ms

E.Speed=1300 rpm

IVC CA50 desired

540 5 Yes

550 5 Yes

560 4.7 Yes

570 4.6 Yes

580 4.6 Yes

590 4.8 Yes

600 5.1 Yes

610 5.5 Yes

620 6.2 Yes

630 7.1 No

Range 540-630

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CAD. In these conditions, it will be necessary to swap between the methods. Also, it is important to set working points. In our case, an EVC of 320 CAD and an IVC of 590 CAD are chosen.

Furthermore, we can add that both methods have other saturating points when the valve timing is in such a way that the fuel injected is too little. That occurs at -168 CAD of EVC for the Overlap method and at 655 CAD of IVC for the IVC method

3.1.2. Comparison with test bed

A model is a representation of a system, but it is just an approximation of the reality. In order to analyze how the model works, a comparison with the test bed is done.

The experiment should be done with a controller in a closed loop in order to not achieve undesired values of CA50 which could damage the engine. A PI controller with

=0

Kp and 3Ki =0. is used.

A reference step from 3 to 7 is used as input as seen in Figure 12. The data are measured every cycle, so the sampling time is one cycle which corresponds to a number of seconds, depending on the speed, by the following relation

) / (

) ( 4

s rad Speed

time₌ π rad ₍₁₁₎

According to (11), if the engine speed is 1000 rpm one cycle lasts 0.12 seconds. The engine will be run during 1000 cycles, which is 2 minutes.

0 100 200 300 400 500 600 700 800 900 1000

2 3 4 5 6 7 8

cy cles

CA50

Referenc e

Figure 12

Initially, the conditions of the working point 1 were thought to be good ones for doing this experiment. However, when the reference reaches the value of 7 CAD, an EVC of 285 CAD is necessary, which is too near to the saturating point, as we can see in the experiments done in Section 3.1.1.

In order to solve this problem, we increased the amount of fuel somewhat. The new working point is given in Table 7.

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Working point A:

Table 7. Working point A

The scheme utilized is shown in Figure 10. The experimental results from the simulation and the test bed are shown in Figure 13.

0 100 200 300 400 500 600 700 800 900 1000

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

0 100 200 300 400 500 600 700 800 900 1000

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

MODEL TEST BED

Figure 13. CA50 response in the model without noise and in the test bed.

It is obvious that the experiments differ significantly. That is due to the fact that the conditions of the engine are not exactly the same during all the time the engine is running. The pressure, temperature, amount of fuel is subject to cycle-by-cycle variations and as a consequence the CA50 as well. To model this we have to add some disturbances to our model. These disturbances are random, so they will be approximated to a white noise in the model.

conditions Ts=7 ms IVC=571 CAD Pin=1.6 bar Tin=60 C°

E.Speed=1000 rpm

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y.mat

y r.mat

r Terminator6

Terminator5 Terminator4 Terminator3

Terminator2 Terminator1

Sum1

Sum Ground

Disturbance Ts

IV0

IVC

EVC

Tin

Pav g

f bin

ESpeed

Lambda

mf b

P10

T10

P010

T010

CA50

CylLambdaEst_8 320

Constant8

1

Constant7 -C-

Constant6 1.8

Constant5

1000

Constant4 0

Constant3 571

Constant2 7

Constant1

Co

Figure 14. Final IFT scheme.

A reasonable approximation of the test bed variations seems to be a white noise of variance 0.25, and a standard deviation of 0.5, which is shown next.

0 100 200 300 400 500 600 700 800 900 1000

-3 -2 -1 0 1 2 3

Disturbance

cycles

CAD

Figure 15. Disturbances.

The CA50 response is shown in Figure 16, the signal plotted with stars is the one of the model, while the normal line is the one of the test bed.

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0 100 200 300 400 500 600 700 800 900 1000 0

1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

0 20 40 60 80 100 120 140 160 180 200

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

380 385 390 395 400 405 410 415 420 425 430

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

Figure 16. CA50 response in the model with noise and in the test bed.

As seen from the figures, both signals are quite similar. However, in the first 200 cycles the graph of the model is very different from the one of the test bed. Later, it will be explained how disregard these first cycles in the optimization.

To sum up, in the comparison of the model it has been seen that it was necessary to add some disturbance to the model. Then, after some experiments it has been chosen as disturbance a white noise of variance 0.25. Also, it was noticed that the model does not approximate the engine well the first 200 cycles. It will be necessary to take this into account during the optimization.

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3.2. Design of IFT

An IFT toolbox in Matlab is available. This toolbox calculates signals in (6) and (9) and operates the update (8). The user just has to choose the criterion, the step size and some other parameters that will be explained in the Section 3.3. The scheme used in the toolbox, and the engine conditions required will be analyzed in this section.

3.2.1. Scheme

First, the block diagram has to be constructed. A closed loop with the controller is used.

3.2.1.1. Controller

In [2] it is explained that in order to suppress low frequency disturbances and to ensure correct static gain a fixed integrator should be included in the controller. So, the full controller consists of an integrator plus another controller. This last controller is the one that we optimize, and the integrator remains fix.

1 Out1 1

1-z -1 Integrator Part of control l er Control l er wi ch

wi l l be opti mi zed 1

In1

Figure 17. Scheme of the controller.

It is important to not forget that the controller that is being tuned is just this first part, without the integrator. So, if we want to analyze the controller we are using, we cannot study the tuned controller alone, it is necessary to add the integrator part. In the Figure 18 the scheme needed for the IFT toolbox is shown.

y.mat

y r.mat

r

n.mat

n

Sum5 Sum1

Sum

1 1-z -1 Integrator Part of controller

In1 Out1

Engine 320

Constant9 Co

Figure 18. IFT scheme with the integrator part separated from the controller.

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If the part of the controller that is being tuned is wanted to be known some iterations are required. The transformation required for a PID which is wanted to take out the integrator part is explained next. The transfer function of a PID is:

s s K

K K

PID= _p + ⁱ + _d ⋅ (12)

whereK_p,K_i and K_dare the proportional, the integral and the derivative gains, respectively.

However, we are not working in continuous time. So, an equation for the discrete PID is required. Many approximations exist, but the one chosen for this case will be the Tustin’s approximation, which is given by the following equation.

1 1 2

+

⋅ −

= z

z

s h (13)

where h is the sample time.

The substitution (13) in (12) gives the discrete PID controller 1

1 2 1

1

2 +

⋅ −

⋅

− +

⋅ +

= z

z K h z

z K h K

PID _p _i _d (14)

Now, the integrator part will be removed. That can be done just dividing the PID by the integrator as is shown in (15).

Integrator Controller PID

PID Controller

Integrator∗ = ⇒ = (15)

Furthermore, we will use a controller with the following structure:

2

1 −

− + ⋅

⋅ +

=a b z c z

Co (16)

Comparing with (15), we obtain:

d

d p

i

d i p

K c

K K K

b

K K K a

=

⋅

−

=

+ +

= 2 2

2

(17)

So, with (17) it is possible to change from a PID controller to the part of the controller we want to tune. That is the controller data that the IFT toolbox needs. In the other way around, if we want to know the whole controller from the tuned one another equation is required. Operating (17) the gains of the PID can be expressed in function of parameters a, b and c, as is shown in (18)

d i p

i d

K K a K

c b a K

c K

−

= + +

=

2

(18)

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In conclusion, in the IFT scheme the integrator part of the controller is considered apart from the tuned controller. Therefore, some operations have to be done to build the whole controller from the tuned one and viceversa.

3.2.1.2. Reference of the second experiment

Some care has to be exercised when perform the second experiment, because a change in the operating point could happen when interpreting (10). When we do the normal

experiment at the working point A, using a PI controller of Kp =0and 1Ki =0. , and the reference step between 3 and 7 we have the following response:

0 100 200 300 400 500 600 700 800 900 1000

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

Figure 19. CA50 response in the normal experiment.

If we see the theory in the special experiment we put as a reference the last reference minus the last output, as seen in (10). That is the difference between the two signals shown in Figure 19. The figure 20 represents this new signal.

0 100 200 300 400 500 600 700 800 900 1000

-5 -4 -3 -2 -1 0 1 2 3 4 5

ReferenceGradientExperiment

cycles

CAD

Figure 20. Error signal.

Now, this signal is introduced as a reference obtaining the signal of Figure 21

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0 100 200 300 400 500 600 700 800 900 1000 0

1 2 3 4 5 6 7 8 9 10

cycles

CAD

StepResponse

Figure 21. CA50 of the gradient experiment.

The CA50 reaches values greater than 10 CAD, a value that is requested to never be achieved. Thus, such a low reference cannot be introduced. The problem comes up because of the interpretation of (10). If we pay attention to the Figure 19, these two signals are centred on 5 CAD. At the contrary, the error is centred on 0 CAD as we can see in Figure 20. What is happening here is that the working point has been changed, which is something that is not desired. The error is required to be centred on 5 CAD as it is the CA50.

So if the origin of the crank angle would be placed at 5 CAD, we would have the following signals.

0 100 200 300 400 500 600 700 800 900 1000

-5 -4 -3 -2 -1 0 1 2 3 4 5

cycles

CAD

StepResponse

Figure 22. CA50 response centred on 0.

If we compute now (10) the resulting signal will be the same as in Figure 20, but at this time the origin is 5 CAD. So if we change again the reference to 0 CAD, we will have the signal in Figure 23.

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0 100 200 300 400 500 600 700 800 900 1000 0

1 2 3 4 5 6 7 8 9 10

cycles

CAD

ReferenceGradientExperiment

Figure 23. Reference signal of the gradient experiment.

This signal is the one which should be introduced as a reference. When we use the IFT toolbox with the scheme of the Figure 18, the signal introduced in the gradient experiment will be the one of Figure 20. Therefore, the scheme has to be changed to the one shown in Figure 24, and furthermore with a step reference signal centred on 0 CAD.

y.mat

y r.mat

r

n.mat

n

Sum5

Sum3

Sum2 Sum1

Sum

1 1-z -1 Integrator Part of controller

In1 Out1

Engine 320

Constant9 5

Constant8

5

Constant10 Co

Figure 24. IFT scheme needed for IFT-toolbox.

We now explain how this modified scheme works. In the normal experiment a reference centred on 0 is introduced. But, as can be seen at the left of the Figure 24 a constant 5 is added. Thus, really, the model is receiving the same signal as before (Figure 12). As we introduce the same input as before, the output will be the same, centred on 5 (Figure 19).

However, then a constant 5 is subtracted, as seen at the right of the Figure 24, so the output stored is centred on 0 (Figure 22). Consequently, in the model the same reference as before is introduced, and the same response is obtained. However, in the IFT toolbox the data stored are different. It saves as ‘r’ the reference minus 5 and as ‘y’ the output minus 5.

Now when the subtraction r-y is done for the gradient experiment, this signal will be centred on zero, as occurred before. Nevertheless, now when this signal is used as

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reference, the constant 5, at the left of Figure 24, is added, so the problem we had before is solved. Now when we do the gradient experiment we obtain the Figure 25.

0 100 200 300 400 500 600 700 800 900 1000

0 1 2 3 4 5 6 7 8 9 10

cycles

CAD

CA50 Gradient experiment

Figure 25. CA50 of the gradient experiment.

It is important to clarify that the CA50 of the experiments is centred on 5; by contrast, the data saved in the IFT toolbox are centred on zero. Therefore, all the data we have are centred on zero. Then, from now on, all the graphs that are going to be shown will be centred on zero, although in the reality they have an offset of 5. That means that we are changing our origin to 5 CAD. Thus, the Figure 25 will be represented by the following one.

0 100 200 300 400 500 600 700 800 900 1000

-5 -4 -3 -2 -1 0 1 2 3 4 5

cycles

CAD

StepResponse

Figure 26. CA50 of the gradient experiment stored in the IFT-toolbox.

To sum up, in the IFT toolbox, the reference signal introduced and the output signal stored will be centred on 0, at the opposite, in the system the input and output signals are centred on 5. This change is done in order to not change of working point when the gradient experiment is done. In addition, it is important to notice that the graphs shown from now on will be the one stored by the IFT toolbox, and as a consequence centred around 0, even if the real output is centred around 5.

HCCI Timing Control Using Iterative Feedback Tuning