technical documentation v1.0 - isy.liu.se · technical documentation [email protected] 2 project...

LiTH

Reglering av Avgaser, Tomgång och Trottel 2008-05-15

Reglerteknisk Projektkurs RATT LIPs Technical documentation [email protected] 1

Technical documentation Niclas Lerede

Version 1.0

Status

Inspected 2008-05-14 PA, NL, TL

Approved

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PROJECT IDENTITY 2008, RATT

Linköpings tekniska högskola, ISY- Fordonssystem

Name Responsibility Telephone E-mail

Daniel Ahlberg subsystem 1 070-2727992 [email protected]

Patrik Axelsson 073-3840900 [email protected]

Andreas Hall Delivery 070-5953327 [email protected]

Niclas Lerede Documents 070-2988254 [email protected]

Tobias Lindell 070-9306929 [email protected]

Andreas Myklebust quality/tests 070-2926793 [email protected]

Fredrik Petersson project leader (PL) 070-2579379 [email protected]

Andreas Thomasson subsystem 2 070-3399804 [email protected]

Peter Wallebäck subsystem 3 073-6720139 [email protected]

Home page: http://www.isy.liu.se/edu/projekt/tsrt71/2008/ratt

Customer: General Motors Powertrain Sweden AB

Contact at the customer: Richard Backman

Responsible for the course: Daniel Axehill

Buyer: Lars Eriksson

Instructor: Oskar Leufvén

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CONTENTS

1. INTRODUCTION ....................................................................................................................................... 5

1.1. PARTS ................................................................................................................................................... 5 1.2. PURPOSE AND AIMS ............................................................................................................................... 5 1.3. FUTURE USE .......................................................................................................................................... 5 1.4. BACKGROUND INFORMATION ............................................................................................................... 5

2. OVERVIEW ................................................................................................................................................ 6

2.1. THROTTLE SERVO CONTROLLER............................................................................................................ 6 2.1.1. Model ............................................................................................................................................. 7 2.1.2. Identification of parameters, model ............................................................................................. 11 2.1.3. The air momentum model ............................................................................................................ 14 2.1.4. Validation of the throttle servo- and air momentum models ........................................................ 15 2.1.5. The controller .............................................................................................................................. 17 2.1.6. Controller 1: Throttle servo controller ........................................................................................ 18 2.1.7. Parameter list: Throttle servo controller ..................................................................................... 20 2.1.8. Tuning of parameters: ................................................................................................................. 21 2.1.9. Validation Throttle Servo Controller ........................................................................................... 22 2.1.10. Controller 2: Throttle Air Controller .......................................................................................... 23 2.1.11. Parameter list, controller 2 ......................................................................................................... 24

2.2. FUEL CONTROL ................................................................................................................................... 25 2.2.1. Models ......................................................................................................................................... 25 2.2.2. Model Parameter Estimation ....................................................................................................... 28 2.2.3. Controller .................................................................................................................................... 30

2.3. DRIVER MODEL, VEHICLE MODEL AND ENGINE MODEL FOR STUDIES OF IDLE CONTROLLER ................ 35 2.3.1. Driver model ................................................................................................................................ 35 2.3.2. Vehicle model............................................................................................................................... 39 2.3.3. Model for studies of idle controller ............................................................................................. 46

2.4. IDLE CONTROLLER .............................................................................................................................. 50 2.4.1. Testing of idle controller and selector with model ...................................................................... 55

2.5. MODEL OF TURBOCHARGER ................................................................................................................ 55 2.5.1. Model ........................................................................................................................................... 56

2.6. MODULARITY AND ABILITY TO UPGRADE THE SYSTEM ....................................................................... 57

REFERENCES .................................................................................................................................................... 58

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Document history

Version Date Changes Done by Inspected by

1.0 2008-05-15 NL PA, NL, TL

0.2 2008-05-13 Changes made in accordance with the buyer’s comments and

further linguistic improvements

NL, PA,

TL, AT

PA, NL, TL

0.1 2008-05-09 First version all NL, PW

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1. Introduction

1.1. Parts

Richard Backman is our contact at the customer General Motors Powertrain Sweden. Lars

Eriksson at ISY – Vehicular systems is responsible for the order and Oskar Leufvén is

supervising the work. RATT is a group of students at LiTH and is the producer.

1.2. Purpose and aims

The purpose is to develop models and model based controllers for future use in turbo engines.

Engines in test cells as well as advanced prototype vehicles are used during the development

work. Safety aspects are of high importance since real engines and vehicles are used.

The aim is to improve the present models and controllers so they can be used in future

production vehicles. The functionality and performance of the controllers will be

demonstrated in several stages: simulation, tests in motor cell and finally tests in a prototype

vehicle.

1.3. Future use

The results will be used by GMPT-S in their continuous development of engine control

systems.

1.4. Background information

The engine is a 2 litre direct injected petrol engine with a twin scroll turbo, intercooler and

variable camshafts. The power in production versions is approximately 260 hp, but the

potential is essentially higher.

All vehicle producers are concerned with models and control systems for engines. The goal is

to create a system that within given economical and production technical frames are as good

as possible for the end user and the environment. Models and control algorithms must not

only manage reference conditions but also various kinds of noises and disturbances.

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2. Overview The system consists of a couple of subsystems

Figure 2-1: System overview

Figure 2-2: Controllers

Figure 2-3: Different models

2.1. Throttle servo controller

The throttle uses a DC servo to control the position of the throttle valve. To construct a

controller which controls the air mass flow with enough precision, a model of the throttle

servo is needed.

In the throttle servo there are nonlinearities which partly come from friction and partly from

the limp-home state. The limp-home state is the angle of the throttle valve that will guarantee

that the car will receive enough gas to be able to limp-home in the case of an electronic

breakdown.

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2.1.1. Model

Overview

What is referred to as “Throttle” in Figure 2-4 is the same as in the mean value engine model

that was delivered by ISY – Vehicular systems. The model “Throttle servo” is a subsystem

which among other things handle the limp-home functionality (see the throttle servo). Smaller

subsystems exist for the calculation of angle to area as well as air mass flow to torque on the

throttle valve caused by the air mass flow.

Figure 2-4: Simulink implementation of the throttle model. The model consists of four major

parts. The air momentum model, the throttle servo model which includes the limp-home

model, the effective area estimation and the original MVEM throttle model.

Inputs:

• Voltage (u) [V]

• Pressure in the intercooler (p up) [Pa]

• Temperature in the intercooler (T up) [K]

• Temperature in the intake manifold (T down) [K] • Pressure in the intake manifold (p down) [Pa]

Outputs:

• Air mass flow (m flow) [kg/s]

• Temperature of the air mass flow (T flow) [K]

Throttle servo model

The throttle is modelled with a limp-home model. It consists of two linear parts where the

back spring torque is linear with the throttle valve angle. At the limp-home angle (around

30% open) there is a dead zone, where a voltage change gives a very small (or non-existent)

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change of the throttle valve angle. There is also considerable friction in the throttle, which is

modelled as nonlinearity (see the model of the friction below).

Figure 2-5: Simulink implementation of the throttle servo model. The voltage gain is the back

voltage gain created when a momentum is generated by the DC servo.

Signals:

• mm – torque from the servo [N]

• ms – torque correction from the model of the limp-home model [N] • mL – throttle valve torque caused by the air mass flow [N]

• ωm – angular velocity of the servo [1/s]

• uemf – return voltage caused by the servo torque build up [V]

Parameters:

• Kv – Voltage amplification caused by the engine torque build up • Ka – DC engine amplification

• Ta – Time constant of the servo

• Kl – 1/ Kl = gear ratio

Input:

• u – voltage to the servo [V]

Output:

• θ – throttle plate angle (% open; range [0-1])

To allow parameter setting, Ka is moved to the friction and limp-home model, Kl is moved to

the limp-home model, the friction model and the friction gain. uemf is replaced by memf in

order to reduce simulation time. memf is having the same effect as a low pass filter reducing

high frequent disturbances, which is not normally occurring in a throttle, see Figure 2-6.

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Figure 2-6: Simulink implementation of a simplified throttle servo model. The voltage gain

has the same effect as a low pass filter and decreases the simulation time.

The throttle servo is described by the following equations [2].

uKm

dt

dmT am

m

a =+ (1)

vmemf Km *ω= (2)

emfLsmapp mmmmm −−−= (3)

m

dt

dω

θ=

(4)

)(θss fm = where fs(θ) is given by the limp-home model (5)

≥+−

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Figure 2-7: Model of the friction in the throttle servo. Maximum friction is determined by Mf.

Signals:

• mf – friction torque [N]

Parameters:

• Mf – Coulomb friction • Kf – Depends on Mf, see below for the definition • Kj – KaKl/moment of inertia

Input:

• mapp – Applied torque [N]

Output:

• ωm – Angular velocity of the servo [rad/s]

The friction is described by the equations (8) and (9).

otherwise

Mm

Mmif

Kdt

dm

ffm

ffm

mf

f

−≤≤

≥≥

= I

I

0

0,0

ω

ω

ω

(8)

)( fappj

m mmKdt

d−=

ω

(9)

ps

f

f

MK

θ= , where θps is the pre-slide coefficient.

(10)

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2.1.2. Identification of parameters, model

The time delay Ta is identified as the delay of a step in power to when the throttle valve reacts. Generally it is

much smaller than the sample time and is identified as 0.014s.

Ramp response analysis

To identify the parameters of the limp-home mode, θLH1, θLH2, mLH1 and mLH2, a slow ramp

response analysis is necessary. The DC engine input voltage u is ramped in both directions in

order to see the effects of the friction. From the results a mean value can be plotted and then

the parameters can be identified according to Figure 2-8.

Figure 2-8: Illustration of the limp-home mode. In the limp-home interval (between θLH1 and

θLH2) the return spring force is much stronger than outside the interval.

From this graph kLH1 and kLH2 can be determined as the slope of each line.

From a slow ramp θps, or the pre-slide coefficient, can be determined by plotting the angle

versus time. Then θps is the angle where the throttle valve, from being stationary, starts to

move. Mf is the torque where the breakpoint occurs.

[N]

[θ] θLH2 θLH1

mLH2

mLH1

kLH2

kLH1

θLH 0

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Figure 2-9: Limp home identification process. The data is divided and a model is

approximated.

The limp-home model is identified by the automated Hall-Ahlberg algorithm, described

below.

1. Load ramped data where θ has increased from closed to open. 2. Find the limp-home angle θLH. 3. Adapt a line to data above and below θLH by using e.g. lms. 4. Load ramped data where θ has decreased from open to close. 5. Repeat steps two and three. 6. Identify KLH1 and KLH2 by taking the mean value of both lines. 7. Identify mLH1 and mLH2 as the mean value of the offsets of both lines. 8. Identify Mf as half the difference of the offsets of the lines.

Linearization of a nonlinear model To be able to identify the parameters of the model, the model first needs to be simplified [2].

[10] A linear model is achieved by replacing the friction model and limp-home model with

the constants σ and Ks(θ), see Figure 2-10. But Ks(θ) is only valid when 1LHθθ ≤ or 2LHθθ ≥ .

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Figure 2-10: Simulink implementation of the linear throttle servo model

The closed system is given by:

≥

≤=

22

11)(

LHLH

LHLH

sk

kK

θθ

θθθ

(11)

sv

j

C

KsKsK

sG

+++

=

)(1

1)(

2 σ

(12)

To simplify the model further, the following assumptions have been made:

• The friction is much smaller than the damping of the DC servo (σ

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The parameters in Gp are identified with a step response of a second order system. This is

done by using an lms algorithm. It is more important to make sure that the curve is fitted

accurate close to the stationary value due to the dampening effect caused by the friction. This

dampening effect increases the rise time.

Figure 2-11: Fit of a 2nd

order system’s step response to measured data. It is important that

the curve has a good fit close to the stationary value.

2.1.3. The air momentum model

mL

1

ProductLookup Table

theta

2

m_dot _air

1

Figure 2-12: Simulink implementation of the air momentum model

The air momentum model is basically a function of θ and airm& . Unfortunately there wasn’t

enough time to determine the nonlinearity, other then an approximation from measurements.

If there is time in the future a more thorough analysis should be done on this part.

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2.1.4. Validation of the throttle servo- and air momentum models

The voltage data and the air mass flow data from the measurements were used as input to the

throttle servo model. The simulation outputs were compared to the measured outputs in order

to validate the model. The results can be seen in Figure 2-14. The model was tested in the

range [700-3000] rpm, for different load. Due to limited time for testing, a complete analysis

for the whole range of the engine has not been done. The air momentum model needs further

testing to verify its validity.

The limp-home angle is around 30%.

Table 1: A summary of all tests

Measurement type With air Fit Range (% open) Fit with 80% fric

Ramp No 94.6% [0-100] 89.6%

Ramp No 95.2% [0-100] 93.0%

Step No 66.3% [30-100] 85.4%

Step No 34.4% [0-30] 41.0%

Step No 55.9% [30-60] 78.5%

Step No 47.7% [0-30] 48.9%

Step No 78.0% [0-100] 98.5%

Ramp No 76.6% [0-50] 80.4%

Step No 73.0% [30-100] 78.0%

Step No 92.2% [0-30] 94.2%

Step Yes 81.4% [10-50] 74.5%

Step Yes 84.2% [0-100] 63.4%

Ramp Yes 98.2% [0-30] 85.6%

Ramp Yes 97.4% [0-30] 66.8%

Ramp Yes 78.4% [30-70] 51.2%

Ramp Yes 87.5% [30-90] 91.1%

Step Yes 97.5% [0-30] 47.4%

Step Yes 77.5% [30-70] 57.9%

Table 1: A summary of all tests describes the different tests done on the real engine. The

column “With air” specifies if the test was performed with or without air running through the

throttle. The fit is defined as when data is within a threshold of 3% of measured data, and then

it’s considered to be fitted, otherwise not. As you can see the fit is better if the friction is

lowered to about 80% of the original friction if there is no air running through the throttle.

However if there is air, the fit gets worse. One hypothesis is that when we have no air, there is

no pressure on the throttle plate, which makes it easier to turn. The exceptions are when the

throttle plate is turning slowly, as in the ramps, and then the friction still will affect the

throttle plate.

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Figure 2-13: Validation of the model for different air mass flows and θ with small load

Figure 2-14: Validation of the model for different air mass flows and θ with high load

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2.1.5. The controller

The controller converts requested air mass flow into a requested angle of the throttle valve to

be able to control the voltage to the throttle model. The controller must handle the

nonlinearity that is modelled in the throttle model and make sure that the overshoot from the

controller is not too large. The implementation of the controller must also make sure that the

end states are not reached with too large velocity to make sure that the throttle valve is not

harmed. With that taken into account the throttle still needs to have good enough

performance.

Inputs:

• Requested air mass flow [kg/s] • Air pressure before and after the throttle [Pa] • Air temperature before and after the throttle [K] • Throttle angle [rad] • Measured air mass flow [kg/s]

Output:

• Guiding voltage [V]

Figure 2-15: Throttle controller model

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Controller structure

The throttle controller can be split into two main parts. The first part inputs the requested

angle as well as the actual angle and from that calculates a guiding voltage to the throttle

servo as output. The second part inputs pressure and temperature before and after the throttle

valve as well as the requested and measured air mass flow and from that calculates a

requested throttle valve angle as output. To make sure that the end states are not reached with

too high velocity the second controller will not be allowed to request angles that are

physically impossible to achieve. Controller 1 must also make sure that there is no overshoot

in throttle angle when a step in reference signal is made.

1

Aeffu

Aef f

theta

Throttle platem_dot_air_refp_upT_upm_dot_airp_down

theta_ref

Throttle controller 2

theta_ref

thetau

Throttle control ler 1

5

p_down

4

m_dot_air

3

T_up1

2

p_up

1

m_dot_air_req

Figure 2-16: The controller structure is divided into the air throttle controller and the throttle

servo controller

2.1.6. Controller 1: Throttle servo controller

The structure of this controller can be seen below. It consists of a nonlinear compensation to

remove as much as possible of the nonlinear behaviour and on top of that a modified PID-

controller described below.

Figure 2-17: Simulink implementation of Controller 1, seen in Figure 2-16

A slightly simplified throttle model is used for the synthesis of this controller. To start with

the dynamics in equation (1) is considerable faster than the rest of the dynamics and it can be

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approximated by the static relation )( vmm Kum ω−= . Combine this with the equations (3) and

(9) to get:

ummmK

tKfLSmv

m

j

+−−−−=∂

∂ω

ω1

(17)

Where )(θSS mm = , ),( atLL mmm &θ= are static nonlinearities, and fm is given by equation

(8). The nonlinear controller is supposed to compensate for as much as possible of the

nonlinearities. Ideally we want to choose u as:

)( rmmmu fLS +++= (18)

The limp-home compensation is taken from the throttle model with the desired throttle angle

as input argument i.e. )( refSS mm θ= . The friction compensation is simplified to basically

adding slightly more then the maximum friction, Mf, if the throttle angle is below the

reference value and subtracting slightly more then the maximum friction if the throttle angle

is above the reference value. To avoid the friction compensation oscillating from max to min

value when the throttle angle is close to the reference value a small dead zone, given by the

parameter frdz, and a smooth transition, given by the parameter frdz_slope, is implemented.

Because of the difficulty in modelling the effect of the air-flow correctly mL is not

compensated for and is left to the PID-Controller to handle. Finally the output is saturated so

the maximum voltage to the throttle is not exceeded. The structure of the nonlinear

compensation can be seen below.

Figure 2-18: The nonlinear compensation block. It contains a compensation for limp-home

and friction torque.

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If the models for the nonlinearities are good and the effect of the air mass flow is small the

open system is approximated by the linear differential equation:

rK

tKmv

m

j

+−=∂

∂ω

ω1

(19)

For controlling this approximately linear system the modified PID-controller is used. The

anti-windup block disables the integration if the controller output is greater then a value,

given by the parameter I_umax, or if the reference differs from the measured throttle angle

more than what is given by the parameter I_ctrl. The integrator block also resets when a step

in reference greater than I_reset_ref_step is made. This is to avoid overshoot in the throttle

position when a step in reference is made as a result of a possibly large I-part before the step

is made. When a step in reference is made the main controller output is generated from the

limp-home and friction compensation and the P-part of the controller, only when the throttle

angle is within a certain interval of the reference the I-part steps in to eliminate stationary

error.

Figure 2-19: Simulink implementation of the PID-controller

2.1.7. Parameter list: Throttle servo controller

The following parameters are used for controller 1:

• Kp1, Kd1, Ki1 – PID-parameters.

• D_max – saturation of D-part

• I_max – saturation of I-part

• I_ctrl – The size of the interval around the throttle reference value for which the I-part is active

• I_umax – I_part will not integrate when the controller output is greater than this value

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• I_reset_ref_step – A step in reference greater then this will reset the I_part of the PID-controller

• Frcomp_gain – Gain value for the friction compensation based on the maximum friction Mf given by the throttle model.

• frdz – The size of the dead zone around the given reference angle for which the friction compensation is zero.

• frdz_slope – The size of the interval where the friction compensation goes from maximum to zero.

• Safe – Distance from the end states of the throttle where the reference value saturates and the MinMax limit in the throttle controller reacts to prevent damaging the throttle

plate.

• Parameters in the limp_home compensation are taken directly from the limp_home model of the throttle.

2.1.8. Tuning of parameters:

The friction compensation should work as a very strong P-controller which saturates slightly

above maximum friction. The frcomp_gain is therefore chosen slightly above one to make

sure that the throttle plate starts moving immediately if a small change in throttle reference is

made. The dead zone and the size of the region where the friction compensation goes from

maximum to zero was gradually made smaller to get the best performance without causing

oscillations in the throttle valve.

Parameter values: frcomp_gain = 1.2, frdz = 0.001, frdz_slope = 0.004

PID-Parameters The PID parameters are tuned manually with the throttle model to work well in simulation.

Kd1 is chosen so that the derivative part of the controller doesn’t reach values which are

greater then about 25 per cent of maximum controller output. Preferably Kd1 is set to about

1/100 and increased if needed as a result of overshoot in the throttle angle. Kp1 and Ki1 are

made as large as possible without giving a significant overshoot in the throttle angle. Original

settings where Kp1=0.5 and Ki1=10. The throttle behaviour where simulated and the

parameters gradually increased to give satisfying controller performance.

Parameter values: Kp1 = 1, Kd1 = 1/60, Ki1 = 20

The I_ctrl parameter should be chosen so that it doesn’t start to wind up unnecessarily but

larger than the stationary error with the I-part set to zero. I_umax is chosen as slightly greater

than the stationary controller output for maximum throttle. A greater output will for sure

make the throttle move in the right direction anyway and increasing the I-part will only lead

to greater overshoot. The I_reset_ref_step parameter, which causes the integration part to

reset when steps in reference are made, was implemented due to problems with

overshoot/undershoot in step responses with an already large I-part.

I_ctrl = 0.1, I_umax = 0.45, I_reset_ref_step=0.05

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The MinMax limit is implemented for safety reasons and should not be reached in normal

operation. The safe limit sets the controller output to zero when the throttle plate reaches

within the safe limit from the endpoints to avoid the throttle plate taking damage. The D_max

and I_max parameters which limits the output of the D-part and I-part was set to a slightly

higher value than what was reached during simulation.

Safe limit = 0.005, D_max = 0.5, I_max = 0.2

2.1.9. Validation Throttle Servo Controller

To evaluate the performance of the throttle servo controller a comparison between the old

controller and the one described above has been made. Several steps in reference angle were

made during a one hundred second long run and the results can be seen below.

Figure 2-20: Comparison between reference tracking for the old controller and the new

controller

It can bee seen that the new controller eliminates the steady state error quicker than the old

controller and has less overshoot in the step responses. Overshoot still exists in the new

controller but mainly when doing steps through the limp home angle of the throttle (which is

between 28 and 29 per cent opening angle).

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2.1.10. Controller 2: Throttle Air Controller

To achieve a fast response to changes in air mass flow a PI-controller with a feed forward is

used. The structure of the controller can be seen below.

Figure 2-21: Controller from requested air mass flow to requested throttle valve angle

The transformation block from mdot,at,u to θref makes use of the equations (22)-(24) to calculate

the desired throttle angle.

)()(

us

ds

eff

us

us

atp

pA

RT

pm ψθ=&

(20)

+−

+−

+>

−

−

=−

+

−

−+

else

ppp

p

rrr

r

1

1

1

2

112

1

2

1

2

1

2

1

2

1

2

)(γ

γ

γ

γ

γ

γ

γ

γ

γγγ

γ

γγ

γ

ψ

(21)

( ) )exp( 2210 θθθ cccAeff ++= (22)

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2.1.11. Parameter list, controller 2

The following parameters are used for controller 2:

• Kp2, Ki2 – PI-controller parameters • C0, C1, C2 – Parameters in Aeff estimation.

The parameters in Aeff are estimated with the least square method from a map of the engine.

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2.2. Fuel control

The purpose of the fuel system is to match the amount of fuel with the amount of air in the

cylinder and thereby keeping lambda at a desired level. The actuator is injection time and the

measurement is lambda, airflow, engine speed and fuel pressure.

lambda_ref

set points

m_air_dot_cy l

Lambda_req

Lambda

m_dot_f uel_req

lambda controller

p_f uel

p_cy l

n_engine

m_dot_f uel

t_inj

inverted injector model

p_f uel

p_cy l

n_engine

t_inj

m_dot_f uel

injector model

p_cy l

p_f uelrail

m_dot_air_cy l

n_engine

Virtual sensors

m_dot_f uel lambda

MVEM

Figure 2-22: Overview of fuel system. Controllers are blue and models yellow.

2.2.1. Models

Injector model

Inputs:

• Injection time injt [ms]

• Fuel rail pressure fuelrailp [Bar]

Outputs:

• Injected fuel mass flow fim& [mg/c]

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Figure 2-23: Injector model inputs and output

As the injector is nonlinear for small injection times the injection is handled as two separate

cases.

when critinj tt ≥ (23)

where P is a custom made polynomial of injt

when critinj tt <

(24)

Parameters:

• injc = injector constant

• fρ = density of the fuel

• 0t = time constant for the response time of the injector

• pcyl = the pressure inside the cylinder at injection time (constant in the model)

Because the injector is nonlinear at small injection times the nonlinear part of the model has

been defined as a polynomial, however the pressure still affects the injection time the same

way. This polynomial has been custom made for the specific injector, and has been fitted to

the nonlinear curve of injected fuel mass flow against injection time by MATLAB's polyfit

function. The degree of the polynomial is increased until a good fit is acquired. A

corresponding critical time, when the model seizes to be linear and becomes nonlinear, has

also been identified by looking at plots of injected fuel mass flow over injection time, see

Figure 2-24.

Injector model

injt

fuelrailp

fim&

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Figure 2-24: Injected fuel mass flow from simulated linear model, simulated nonlinear model,

Ezionic’s estimation and measurements from air flow and lambda

m_dot _fuel

1

timedelay

t0

t_inj _min

0

p_cyl

p_cyl

fueldensity

rho_f

Switch

Subtract

Product 2

Product 1

Polynomial

P(u)

O(P) = 7

MinMax

max

Math

Function

sqrt

Injectorconstant

C

Gain

2

Divide 1

Add

t_inj

2

p_fuel

1

Figure 2-25: Simulink implementation of the injector model

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Lambda Time Delay Model

Inputs:

• Engine speed N [rpm] • λ

Outputs:

• Measured λ

The measured lambda is a time delay of the real lambda. The time delay mainly originates

from the time the exhaust gas is trapped in the cylinder. Therefore the time delay is modelled

as proportional against the inversed engine speed.

(25)

(26)

2.2.2. Model Parameter Estimation

Injector model The parameters of the injector are determined through least square approximation of

stationary measurements of pfuelrail, acm&̂ and λ for different N, tinj, and pfuelrail.

(27)

(28)

Equation (27) is used to estimate the fuel mass flow and equation (23) can be rewritten to

(28) which MATLAB uses for a least square approximation of the parameters. This method

estimates the parameters very good as can be seen in Figure 2-26.

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Figure 2-26: Simulated fuel mass flow compared with Ezionic´s fuel mass flow and measured

fuel mass flow via air mass flow and lambda

Lambda time delay model Step response of lambda measured for a change in injection time, with all other variables

constant, has been used to give the time delay of the lambda at a given engine speed. The

experiment was repeated for different engine speeds and the result was used to get the lambda

delay as a function of engine speed by applying a linear least square approximation. The

result can be seen in Figure 2-27.

Figure 2-27: Simulated lambda versus measured

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2.2.3. Controller

Lambda controller

Inputs:

• Estimated air mass flow to cylinder acm&̂ [mg/combustion]

• Reference lambda value refλ

• Measured lambda value mesλ

• Engine speed N [rpm]

Outputs:

• Requested lambda reqλ , which is later transformed to reqfim ,& [mg/combustion]

m_dot _fuel

1

lambda regulator

lambda_ref

lambda

N

lambda_req

lambda -> m_dot _fuel

m_dot_air_cyl

Lambda_req

m_dot_fuel_req

Engine speed

4

lambda _mes

3

lambda _ref

2

m_dot _air _cyl

1

(29)

(30)

Parameters:

• TC = PI controller design variable, see below • K = PI controller gain • Ti = PI controller integral time constant • Ka = anti-wind up constant

• sFA )/( = stochiometric air to fuel mixture

Figure 2-28: Lambda controller

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Only the broadband lambda sensor is used for feedback through a PI controller to regulate the

required lambda. To improve reference tracking performance feed forward is used. To refresh

on feed forward theory see [7]. The transfer function, G, from λreq to λ is simply given by

(34), since the inverted injector model cancels out the injectors. If the time delay is accepted

in the reference model Gm it equals G. This leads to:

(31)

However, the variable time delay in Gm cannot be implemented with Rapid Pro. Therefore the

feed forward has been removed. Both simulation and tests in motor test bench indicates that

lambda is more stable without feed forward (Ff = 0, Gm = 1) compared to feed forward with

incorrect Gm.

The parameters in the PI(D) controller are chosen using IMC-theory, see [7]. The reason for

this is that IMC controller uses the model and the lambda model is considered good. Our

system, G, fits a three parameter model with unit gain, zero rise time and time delay, T,

according to (35).

(32)

(33)

(34)

This results in a PI controller depending on the engine speed through the time delay. TC is the

only design parameter in the controller. The wise way to choose TC is to let MATLAB try

several different values and choose the value that result in the lowest square error. Which

value of TC that will be favoured is dependent on the noise model.

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Anti-windup

1

lambda_req

500reset condition

lambda_real

w_elambda_mes

lambda_delay

1/2

const

Tc

Tc

SaturationProduct1

Product

w_e time_delay

N -> lambda delay

lambda delay

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Inverted injector model

Inputs:

• Requested fuel mass flow to cylinder reqfim ,& [mg/combustion]

• Fuel pressure in fuel rail fuelrailp [bar]

• Pressure in cylinder cylp (estimated constant) [bar]

Output:

• Injection time injt [s]

t_inj

1

p_cyl

p_cyl

inv _injektormodell

m_dot_fuel_req

p_fuel

p_cyl

t_inj

lambda _ref

2

m_dot _fuel _req

1

Equations:

0

,

)(2t

ppC

mt

cylfuelrailfuelinj

reqfi

inj +−

=ρ

& when critinj tt ≥

(35)

First the pressure is compensated for then injt is decided by an inverse map of

the polynomial in (24) when critinj tt <

(36)

Parameters:

• injc = injector constant

• fρ = fuel density

• 0t = response time constant of the injector

An inverted model of the fuel injectors has been implemented to convert a requested fuel

mass flow into an injection time. Small injection times will be handled separately by using an

inverted map of a polynomial from the normal injection model (see above). In production

engines there are no sensors for the cylinder pressure and because of that that pressure will

have to be estimated by a constant (it will be small compared to the fuel rail pressure).

Figure 2-31: Inverted injector model

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t_inj

1

t_inj _min

0

Tidsfördröjning

t0

Switch

Subtract

Product 2

MinMax

max

Math

Function

sqrt

Inverterad olinjäritet .

fuel_m_times_p t_inj

Gain 1

-K-

Gain

2

Divide

Densitet bränsle

rho_f

Add

p_cyl

3

p_fuel

2

m_dot _fuel _req

1

Figure 2-32: Simulink implementation of the inverted injector model

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2.3. Driver model, vehicle model and engine model for studies of idle controller

These models are implemented so that controllers and other models can be tested, both

separately and as a complete system.

2.3.1. Driver model

The purpose of the driver model is to be able to simulate different driving scenarios and then

analyse the system’s behaviour. The model is for example able to test “tip in tip out” and

maximal acceleration.

Inputs:

• Speed reference [m/s] • Actual speed [m/s]

Outputs:

• Gas [%] • Brake • Clutch • Gear

This model uses a predefined matrix to simulate the driver. Which type of controller the

driver model should use is specified by changing some constants, this is described further

down.

Driver model

Speed reference

Actual speed

Gas

Brake

Clutch

Gear

Figure 2-33: Driver model inputs and outputs

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Several MATLAB-scripts have been implemented that test different specific driving scenarios.

They are defined as a matrix, consisting information of time, speed reference, clutch position,

gear, gas pedal position and brake pedal position. The following scenarios are implemented:

• ETC drive cycle • ”tip in tip out” • maximal gas • idle running • load drive cycle

Common to all scenarios except standard drive cycle is that Acc. Pedal Switch and Brake

Pedal Switch (see Figure 2-34) are set to the position in which they forward data from MATLAB

Workspace. The driver model generates outputs for gear, gas pedal, brake pedal and clutch

pedal. All these can either be defined directly in a driving scenario file or be generated by the

controller (see Figure 2-34). If the gear signal from workspace is not used, the gear is chosen

from a lookup table with vehicle speed as input and gear as output. This functionality imitates

a simple automatic gear box. A problem is that the gear changes instantly without using the

clutch when the lookup table is used, but for simulation purposes only the response is

acceptable.

Speed demand

DriverOut

1

Transfer Fcn

1

0.01s+1

Shift Gear Control

sgc

Product

PI Driver

PI

inp

ut

PI

r ese

t

PI

ou

t

MinMax 1

min

MinMax

max

Lookup TableGear Control Switch

Gas/Brake

Mode Switch

0

From Workspace4

Speed

From Workspace3

BrakePedal

From Workspace2

AccPedal

From Workspace1Clutch

From Workspace

Gear

Brake Pedal Control

bpc

Brake Gain

-1 Acc. Pedal Switch 1

Acc. Pedal Switch

Acc. Pedal Control

apc

DriverIn

1

Gear

Clutch

AccPedal

BrakePedal

Figure 2-34: Simulink implementation of the driver model

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The PI-driver controller aims to minimize the error between actual speed and speed reference.

The parameters Kp and Ki have been determined empirically. An anti wind-up functionality is

implemented to make the controller not sensitive to integrate wind-up.

PI out

1

Saturation

Kp

.03

Ki

.01

Integrator

1

s

0

Anti -Windup Switch

PI reset

2

PI input

1

Figure 2-35: Simulink implementation of the PI-driver controlling throttle and brake, with

anti-windup functionality

ETC

This scenario tests the performance during a more normal drive. The first part of the cycle

contains three transients simulating driving in an urban environment. Next part simulates

driving in a rural environment and the last part simulates driving on a highway. The PI-driver

is used to control speed and brake demand.

Figure 2-36: Vehicle speed plotted when the European transient drive cycle is used

Tip in tip out/tip out tip in In this driving scenario the gas pedal position is set to maximum during a short period of time

and then released again. Then the opposite behaviour is tested, the gas is released from a

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steady state to zero during a short interval of time and then restored to its initial value. The

purpose of the test is to analyse the behaviour in fast changes of gas demand. The behaviour

of both “tip in tip out” and “tip out tip in” can be observed by doing several “tip in tip out”

after each other.

Figure 2-37: Vehicle speed plotted when the tip in tip out drive cycle is used

Maximal gas This driving scenario aims to analyse how the vehicle responds to a protracted powerful

acceleration with automatic gear shifting.

Figure 2-38: Vehicle speed plotted when the max drive cycle is used

Idle running

In this driving scenario, the idle controller performance is evaluated. Activation and

deactivation is of special interest since it should be done without discomfort for the driver.

The test contains a rise in engine speed above the limit where the idle controller actuates i.e.

the idle controller is not actuating. Then after a while the engine speed is decreased and the

idle controller starts actuating again and keeps the engine speed at the reference (900 rpm).

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Figure 2-39: Vehicle speed plotted when the idle running drive cycle is used

Load drive cycle

In this driving scenario the idle controller is constantly active and after a while a sudden load

is applied to test the reaction of the idle controller to a sudden change. The load applied is

simulated by shifting from neutral to 1st gear and releasing the clutch in one second when the

engine is running on idle.

Figure 2-40: Vehicle speed plotted when the load drive cycle is used

2.3.2. Vehicle model

The purpose of this model is to be able to test how the engine model works in a simulated

vehicle, in which driveline dynamics and air- and rolling resistance are regarded.

Inputs:

• Engine torque [Nm] • Clutch • Gear • Brake

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Outputs:

• Engine speed [rps] • Vehicle speed [m/s]

Figure 2-41: Vehicle model inputs and outputs

Modelling Mechanical equations for rotational system are used in order to model the driveline. The

equations take the engine torque and transform it to angular velocity of the engine and the

wheels. The impact of the rolling resistance and the air resistance are also used. A sketch of

the driveline with all variables is presented in Figure 2-42. Every part of the driveline is

described in more detail below. The propeller shaft is not used because it is a front wheel

drive vehicle.

mθ

wθ

tθcθ

fθ

pθ

wθpθ

wMdMfM

fMpMtMcM

ww Fr

mM

mfrM : tfrM :

ffrM : wfrM :

Figure 2-42: A sketch of the driveline model

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Engine

The torque depends on the engine friction and the load from the clutch. Newton’s second law

gives equation (37).

cmmmcmfrmmm MbMMMMJ −−=−−= θθ

&&&:

(37)

Clutch The clutch is modelled with a loose, a wind up and a damping factor. The torque is thereby

dependent on the difference between the angles and angle speeds before and after the clutch.

There are no torque losses and the model is shown below:

)()( cmccmctc ckMM θθθθ&& −+−== (38)

Transmission There is a change of angle speed and torque in the transmission depending on which gear that

is used. Friction losses are modelled as viscous damping and are dependent on the angular

speed. Remaining torque loss is the load from the propeller shaft. By using Newton’s second

law, the following equations can be derived:

ttc i θθ = (39)

pttttptfrtttt MbiMMMiMJ −−=−−= θθ

&&&:

(40)

Propeller shaft The propeller shaft is modelled as the clutch with a wind up- and damping factor. There are

no torque losses and the outgoing torque depends on the angles and angular speeds. The

propeller shaft is not used in our application since the prototype vehicle is front-wheel driven.

)()( ptpptpfp ckMM θθθθ&& −+−== (41)

Final gear The final gear is modelled as the transmission, but with a constant conversion ratio between

the incoming and outgoing torque and angular speed. The torque losses are modelled as a

viscous damping and by applying Newton’s second law, the following equations can be

derived.

ffp i θθ = (42)

dftffdffrffff MbiMMMiMJ −−=−−= θθ

&&&:

(43)

Drive shaft The drive shaft is modelled as the clutch and propeller shaft. There are no torque losses and

the outgoing torque depends on the angles and angular speeds.

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)()( wfdwfdwd ckMM θθθθ&& −+−== (44)

Wheel/Vehicle

Equation (45) gives the torque from the wheel. The torque losses depend on friction in the

suspension, modelled as a viscous damping factor and influence of the ambient environment.

The force that drives the vehicle forward is given by Newton’s second law and shown in

equation (46). α is defined as positive in an ascent. The forces that work counter to the propulsion are air- and roll resistance, described in equations (47) and (48). The vehicle speed

is derived from the angular speed of the wheel and shown in equation (49).

wwwwwwwwfrwww FrbMFrMMJ −−=−−= θθ

&&&:

(45)

braw FmgFFvmF ++++= )sin(α& (46)

2

2

1vAcF aawa ρ=

(47)

)( 221 vccmgF rrr += (48)

wrv θ&= (49)

Reference [8] is used to determine the parameters.

Implementation of driveline in Simulink

Figure 2-43: Simulink implementation of the driveline

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Figure 2-43 shows the implementation of the driveline. The inputs to the system are engine

torque, gear, brake pedal and the slope of the road. Engine speed and the velocity of the

vehicle are outputs. The blue blocks contain Newton’s second law, i.e. equation (37), (40) and

(45). See the implementation in Figure 2-44. The green blocks contain the equation for

torsion, i.e. equation (38) and (44). Figure 2-45 show the implementation of the green blocks.

The block that is called Vehicle contains the forces acting on the vehicle, i.e. equations (47)

and (48) and the implementation is demonstrated in Figure 2-46.

Theta1

Integrator 1

1

s

Integrator

1

s

Gain 1

- K-

Gain

- K -

Add

Torque

1

t h e t a _ d o t _ m t h e t a _ mt h e t a _ d d o t _ m

< M m >

< M c >

Figure 2-44: Simulink implementation of Newton’s second law

The blue blocks take the torque before and after the mass as input and give angular

acceleration, angular velocity and the angle of the mass as output.

Torque

1

Gain 1

- K-

Gain

- K-

Add 2

Add 1

Add

Theta

1

< t h e t a _ m >

< t h e t a _ c >

< t h e t a _ d o t _ m >

< t h e t a _ d o t _ c >

Figure 2-45: Simulink implementation of the torsion

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The green blocks take the angular velocity and the angle of the masses before and after the

torsion as input and give the torque from the torsion as output.

Fr

Fa

Fw

1

sin ( alpha )

sin

m * g

- K-

V ^2

u2

Gain 6

- K -

Gain 3

- K -

Gain 2

- K-

Gain 1

m

Fb _gain

- K-

Constant 2

cr 1

Add 3

Add 1

v_ dot

4

v

3

alpha

2

Fb

1

Figure 2-46: Simulink implementation of the forces acting on the vehicle

When simulating the driveline together with the ETC the engine speed goes to infinity. This

depends on the high stiffness in the differential equations used to model the driveline. Figure

2-47 shows that this occurs around 55 s. Figure 2-47 also shows that the engine speed

oscillates a lot. The vehicle speed is demonstrated in Figure 2-48 and shows that the vehicle

follows the requested speed well until the speed goes to infinity. This driveline

implementation is not used in the simulations because of this. A more simplified model is

used instead.

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Figure 2-47: Engine speed during a drive, using the driveline model described above

Figure 2-48: Vehicle speed during a drive, using the driveline model described above

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2.3.3. Model for studies of idle controller

This model has been used during the development of the idle controller. It calculates the

engine speed, using demanded air mass flow and ignition angle.

Inputs:

• Air mass flow [kg/s] • Ignition angle [rad]

Outputs:

• Engine speed [rps]

atm&

N

N

ip

ep

acm&

fcm&

ignθ

eM

Figure 2-49: Engine model overview

Intake manifold The air mass flow is calculated by the pressure build-up and volumetric efficiency. R is the

ideal gas constant, iT is the temperature in the intake manifold, iV is the volume in the intake

manifold, dV is the displaced volume and N is the engine speed. The volumetric efficiency is

defined by a three parameter model shown in equation (52).

( )acat

i

ii mmV

RT

dt

dp&& −=

(50)

ir

idvolac

RTn

NpVm η=&

(51)

Ncpcc ivol 210 ++=η (52)

The constants in (52) are determined using least square estimation, applied on measurements

in which the engine is run in several steady states. At least three different states are required

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and then volη can be approximated with a polynomial. By using equation (51), volη is derived

as follows:

NnVp

RTnm

cyldi

irat

vol

&=η

This equation is only valid in steady states when acat mm && = .

=

=

=

=

33,

3,

11,

1,

33,

11,

2

1

0

1

1

NnVp

RTnm

NnVp

RTnm

B

Np

Np

A

c

c

c

x

BAx

cyldi

irat

cyldi

irat

i

i

&M

&

MMM

x = A\B

Fuel injection

The fuel flow into the cylinder is calculated with the following equation, where ( )sF

A is the

stochiometric air-to-fuel ratio. λ is assumed to be 1.

( ) λs

ac

fc

FA

mm

&& =

(53)

Exhaust manifold pressure estimation The pressure in the exhaust manifold is used to calculate pump losses in the cylinder. It is

derived with the following equation:

0pmcp acexhe += & (54)

The constants exhc and 0p are determined using least square estimation, based on

measurements in which the engine runs in steady states. The fuel mass flow is neglected

since atfc mm &&

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( )00 pmcpmmcp acexhfcacexhe +≈++= &&&

[ ]

−

−

=

=

=

=

acn

en

ac

e

exh

m

pp

m

pp

B

A

cx

BAx

&

M

&

M

0

1

01

1

1

x = A\B

Cylinder

The torque is derived by subtracting the pump- and friction losses from the net work. LHVq is

the heating value, chig ,η are combustion chamber losses due to heat losses and cycle to cycle

variations, ignθ is the ignition angle, optign,θ

is the optimal ignition angle, cr

is the

compression ratio and γ is the ratio of specific heats. optign,θ is mapped by doing stationary

measurements on the engine.

r

fpig

mn

WWWM

⋅

−−=

π2

(55)

igLHVfcig qmW η

~= (56)

( ) chigignc

c

igr

,1,1min

11~ ηηλη

γ

−=

−

(57)

( )( )2, ,,1 λωθθη feoptignignignign mC −−=

(58)

N

nmm rfcfc &=

(59)

( )ietotdp ppVW −= , (60) ( )2210, NcNccVW ffftotdf ++= (61)

The friction loss fW is defined by the three parameter model shown in equation (61). The

constants are determined using least square estimation, applied on measurements in which the

engine runs in steady states. At least five measurements are necessary and during the

calculations ( )cλ,1min is assumed to be 1.

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( ) ( )

( )( )( ) ( )

( )ietotdmr

fffdoptignignignchig

c

LHV

s

rac

ffftotdietotdigmr

ppVMn

NcNccVcr

qN

FA

nm

NcNccVppVWMn

−+=

=++−−−

−

⇔++−−−=

−

,

2

210

2

,,1

1,

2

210,,

2

11

1

2

π

θθηλ

π

γ

&

( ) ( )( )

( ) ( )( )

( )

( )

−+

−+

=

−−−−−

−−−−−

=

−=

=

=

−

ninetotdnmr

ietotdmr

ntotdntotdtotdnoptignnignLHV

ns

rnac

LHV

ns

rnac

totdtotdtotdoptignignLHV

s

rac

LHV

s

rac

c

f

f

f

ignchig

chig

ppVMn

ppVMn

B

NVNVVCqN

FA

nmCq

NF

A

nm

NVNVVCqN

FA

nmCq

NF

A

nm

A

rC

c

c

c

c

x

BAx

,,,,

11,1,

2

,,,

2

,,,

,,

2

1,1,,

2

1,,1,

1

1,

1

1

2

1

0

,

,

2

2

11

π

π

θθλλ

θθλλ

η

η

γ

M

&&MMMMM

&&

x = A\B

Vehicle model

The engine speed is derived from the following simple model:

τ

πτθ

πd

J

MdN

m

m

m ∫∫ == 21

2

1 && (62)

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2.4. Idle controller

The controller’s task is to keep the engine speed as close to a reference speed as possible

during idle drive. To prevent that the engine stops if there is a sudden change of load, a torque

reserve is created by letting the engine ignite at a non optimal ignition angle. This is

compensated by an increase of the air mass flow. This reserve can then be used instantaneous

by adjusting the ignition angle towards the optimal one. The controller consists of three

sections, shown below. In the selector (see Figure 2-50) the requested ignition angles and the

air mass flows from the idle controller are compared with those requested from the others

controllers to achieve bump less transfer.

Out idle controller

1

selector

N_engine_speed [rps]

mdot_idle_req [rad]

theta_ign_req [rad]

mdot_air_demand [kg/s]

theta_throttle [rad]

theta_ign [rad]

mdot_ac [kg/s]

idle_flag [-]

Idle Controller

Engine speed [rps]

Air mass flow in [kg/s]

Air mass flow out [kg/s]

Theta ignition [rad]

In idle controller

1

idle_flag

theta_ign

mdot_ac

Figure 2-50: Idle controller with selector

Inputs:

• Engine speed ]/[ sradN

• Engine speed reference ]/[ sradN ref

Outputs:

• Air mass flow ]/[ skgma&

• Ignition angle ][radadjθ

Map for adjusted ignition angle A map that delivers the optimal ignition angle based on the current air mass flow per

combustion and engine speed is used by the idle controller. That angle is then adjusted by

decreasing it closer to top dead centre and both angles are then sent as outputs to other blocks.

Controller for requested ignition angle This controller should eliminate the error between the current measured engine speed from a

sensor and the desired engine idle speed. This error is used as the input for a PI-controller. If

there is an error, the controller adjusts the ignition angle to eliminate this error. A max-

function makes it impossible for the ignition angle output to be smaller than the current

optimal ignition angle. An anti-windup switch is implemented to eliminate the I-part from

growing when the output is saturated. Both the requested and the desired angles are sent as

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outputs to the ignition control. The desired angle is the one that the PI-controller wants; this

one will be used in the air mass flow controller described below.

The constants Kii and Kpi should be trimmed using an engine model. They will be set in the

initiation file.

Theta ign controller [rad ]

2

Theta ign [rad ]

1max

Theta SaturationKpi

Kpi

Kii

Kii

Integrator

1

s

Constant

0

Anti -windup Switch

Engine speed [rps]

4

Theta optimal [rad ]

3

Theta adjusted [rad ]

2

Engine speed reference [rps]

1

Figure 2-51: Simulink implementation of the controller for requested ignition angle, with

anti-windup functionality

Inverted engine model and air mass flow controller This part takes as inputs the optimal ignition angle and the adjusted angle that we want to

ignite with. The inverted engine model delivers an air mass flow that corresponds to a value

close to the steady state idle run and also depending on the current engine speed. This air

mass flow request is then combined with a request from a controller. The inverted engine

model is described below. The engine model used in MATLAB is then simplified to decrease

computer performance demands.

The controller uses the error between the desired adjusted ignition angle and the current

ignition angle that the ignition controller uses. If this error is non-zero a PID-controller

eliminates this error. An anti-windup switch is implemented to eliminate the I-part from

growing when the output is saturated. The constants Kpa, Kpi and Kpd are set in the initiation

file.

Using equation (57), where ),1min( cλ is made equal to one, the following is achieved.

ignchig

c

igr

ηηηγ ,1

11~

−=

−

(63)

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Equations (63), (53), (56), (59) combined with 1=λ returns the following equation for the work created from fuel burning in the cylinder.

( ) igLHVr

S

ac

ig qN

n

FA

mW η~

&=

(64)

The air mass flow is then calculated using equations (64), (55), (60), (61) and (62) and the

following equation is achieved.

( ) ( ) ( )( )( )

( )( )

−−

−

+++−+=

−

2

,,1

2

210,,

2

11

1

2

optignignignchig

c

LHVr

Sffftotdietotdmr

ac

Cr

qn

NF

ANcNccVppVNJnm

θθη

π

γ

&

&

(65)

When there is a sudden change of load, the actual air mass flow and engine speed are lowered.

If equation (65) is used, an even lower air mass flow will be requested. To prevent this, a

constant replaces the terms that are dependent on engine speed or air mass flow. The constant

is derived by observing the values during steady state idle run, and the following final

equation is achieved.

( )( )( )

( )( )

rpmN

NmC

Cr

qn

NF

ACNJnm

ref

W

optignignignchig

c

LHVr

refS

Wmr

ac

900

591,

11

1

2

2

,,1

2

=

≈

−−

−

+=

−θθη

π

γ

&

&

(66)

WC is now representing constant pumping and friction work for idle run.

When implementing equation (66) in Simulink one thing that causes a problem is the

derivation of engine speed ( N& ) which may result in very large values for short times. These

spikes are reduced by using a low-pass filter before the signal is derived. The implementation

of equation (66) can be found in Figure 2-52.

LiTH



Modelled air mass flow [kg/s]

1

theta opt

theta adjusted

out

Saturation Noise reduction filter 1

1

0.1s+1

Noise reduction filter

1

0.1s+1

Kda

Integrator

1

s

IdleSpeedWarm

-C-

Kia

Kpa

Gain

-K-

Divide

Derivative 1

du /dt

Derivative

du /dt

C_W

Constant 0

Anti -windup

Switch

Add

AFs

-K-

Theta adjusted [rad ]

4

Theta optimal [rad ]

3

Engine speed [rps]

2

Theta ign Controller [rad ]

1

Figure 2-52: Simulink implementation of the controller for requested air mass flow with anti-

windup functionality

Controller mode selector

The controller mode selector handles the bump less transfer functionality when switching

actuator between idle controller and other controllers actuating on throttle and ignition. It’s

implemented in Simulink using an embedded MATLAB function block where the function is

used to handle the switching between which signals should be actuated and which signals that

should not. The function block works with the following cases:

• The engine speed is falling and reaches 1100 rpm. If the requested air mass flow from the idle controller is greater than the requested air mass flow from some other throttle

controller, the requested air mass flow and ignition angle from the idle controller are

sent to actuate on the engine. Otherwise the request from the other controller continues

to actuate.

• The engine speed is above 1200 rpm. Some other controller actuates on the engine.

• The engine speed is between 1100 and 1200 rpm. The controller that was actuating the last sample will be actuating until the engine speed reaches beyond the engine speed

borders for this case.

LiTH



Bump less transfer functionality

This function block makes sure that the switching is done smoothly when switching from one

ignition angle to another i.e. the controller mode switch is changing which controller that

should actuate. It is only when a switch happens that the filtered ignition angle is sent to

actuate, otherwise it is the exact non-filtered ignition request from the controller mode

selector. As long as the difference between the requested angle and the actuated angle, after a

switch in request, is greater than a small constant the actuated value is slowly adjusted

towards the requested. When the difference is small enough the actuated angle is changed

from the filtered one to the requested one from the controller mode selector.

controller mode selector

bumpless transfer functionality

idle _flag [-]

3

mdot _ac [kg/s]

2

theta _ign [rad ]

1

thetaIdle

thetaDemandFilt

thetaDemand

idleFlag

idleFlagOld

thetaThrottle

idleFlagOldBeforeLastChangeMem

thetaIgnOut

idleFlagOldBeforeLastChange

filterHandler

mdot_idle

mdot_throttle

IdleUpperLimit

N_engine

theta_idle

theta_throttle

idle_old

theta_dem

mdot_ac

idle_flag

fcn

Transfer Fcn

1

.01s+1

Memory 2

Memory

IdleUpperLimit

-C-

theta _throttle [rad ]

5

mdot _air_demand [kg/s]

4

theta _ign _req [rad ]

3

mdot _idle _req [rad ]

2

N_engine _speed [rps]

1

idle_flag

mdot_ac

theta_dem

Figure 2-53: Embedded MATLAB functions used in selector

Theta ignition [rad ]

2

Air mass flow out [kg/s]

1

Map and ignition adjustment

Engine speed [rps]

Model air mass flow [kg/s]

Theta adjusted [rad]

Theta optimal [rad]

Inverted engine model and air controller

Theta ign Controller [rad]

Engine speed [rps]

Theta optimal [rad]


Modelled air mass flow [kg/s]

Ignition Controller

Engine speed reference [rps]


Theta optimal [rad]

Engine speed [rps]

Theta ign [rad]

Theta ign controller [rad]

Idle engine speed reference [rps]

-C-

Air mass flow in [kg/s]

2

Engine speed [rps]

1

Figure 2-54: Idle controller overview, consisting of three parts; ignition angle map with

adjustment, ignition angle controller and air mass flow controller

LiTH



2.4.1. Testing of idle controller and selector with model

Tests of the idle controller and selector are done by simulating them together with models of

mean value engine, clutch and gearbox, vehicle and a driver that requests a specified air mass

flow based on one of the driving scenarios. All these models are described in section 2.2.

The inputs that should be connected to the controller from sensors are as follows: engine

speed [rps], current air mass flow in intake manifold [kg/s], pressure in intake manifold [Pa],

temperature in exhaust manifold [K]. The controller delivers the following outputs: ignition

angle [rad] and air mass flow [kg/s] that will actuate on the engine.

rps->rpm

60

exhaust temp 500

Vehicle

Wh

eel S

pe

ed

[ra

d/s

]

Bra

ke P

ed

al

Ve

hic

l e I

nert

ia

Ve

hic

le T

or q

ue

[Nm

]

Ve

hic

le S

pe

ed[k

m/h

]

Idle Controller 1

In idle controllerOut idle controller

I_e

Jm

[N_engine _sens]

[VehicleSpeed ]

IdleControllerFlag

[VehicleSpeed ]

[N_engine _sens]

[N_engine _sens]

[VehicleSpeed ]

IdleControllerFlag

Engine model for testing of idle controller

Ignition angle [rad]

Air mass flow [kg/s]

Engine Speed [rps]

p_i [Pa]

mdot_ac [kg /s]

Engine Torque [Nm]

Driver Model

DriverIn DriverOut

Displayo

1.00

44 .58

798 .24

Convert Pedal Pos

to mDotAirDemand 1

AccPedal

N

currentAirFlow

mDotAirDemand

thetaDemand

Clutch and gearbox

Engine Inertia [kg m 2̂]

Engine Torque [Nm]

Vehicle Torque [Nm]

Vehicle Inertia [kg m 2̂]

Gear

Clutch Pedal

Engine Speed [rps]

Wheel Speed [rad/s]

N_engine_sens

mdot_at_sens

p_i_sens

T_e_sens

thetaDemand

vehicle speed

mDotAirDemand

Figure 2-55: System for simulation of different drive cycles, drivelines, and evaluation of the

idle controller’s performance

2.5. Model of turbocharger

This model has been developed as a separate module, then integrated and tested in the

complete engine model.

LiTH



2.5.1. Model

The compressor increases the pressure in the intake manifold and is powered mechanically

from the turbine. The turbine is powered from the exhaust gas flow.

Inputs:

• Pressure before compressor ][, Pap usc

• Temperature before compressor ][, KT usc

• Air mass flow after compressor ]/[, skgm usc&

• Temperature before turbine ][, KT ust

• Pressure before turbine ][, Pap ust

• Air mass flow after turbine ]/[, skgm ust&

Outputs:

• Air mass flow through compressor ]/[, skgm dsc&

• Temperature after compressor ][, KT dsc

• Pressure after compressor ][, Pap dsc

• Temperature after turbine ][, KT dst

• Pressure after turbine ][, Pap dst

LiTH



Compressor

Turbine

Power transfer

uscp ,

uscT ,

dscm ,&

dscT ,

dscp ,

dstT ,

dstp ,

ustT ,

ustp ,

dstm ,&

tM

cM

tcω

tcω

Figure 2-56: Sketch over the turbo

Compressor The compressor model derives the change in pressure and temperature. An already completed

model of a compressor, taken from [4] is used in this application.

Turbine The turbine is modelled with a part that determines which torque is generated and a part that

derives the change in pressure and temperature. An already completed model of a turbine,

taken from [4] is used in this application.

Power transfer Based on the torque given by the compressor and turbine, the angular speed is derived. An

already completed model of a power transfer, taken from [4] is used in this application.

2.6. Modularity and ability to upgrade the system

The system is modular and it is possible to upgrade every separate module without changing

the other depending ones.

LiTH



References

[1] Projektmodellen LIPS version 1.3 (2007), Tomas Svensson, Christian Krysander

[2] An electronic throttle control strategy including compensation of friction and limp-home effects (2004), Joško Deuer et al.

[3] Vehicular Systems, (2007), Lars Eriksson, Lars Nielsen

[4] Air Charge Estimation in Turbocharged SI Engines (2005), Per Andersson

[5] Automotive control systems (2005), Uwe Kiencke, Lars Nielsen

[6] www.engineeringtoolbox.com/pump-energy-equation-d_631.html 2007-02-25

[7] Industriell reglerteknik Kurskompendium, (2008), Reglerteknik, Institutionen för systemteknik, Linköpings Universitet

[8] Laborationskompendium Fordonssystem TSFS05, (2007), Linköpings tekniska högskola, ISY, Fordonssystem

[9] User manual, version 1.0 (2008), Niclas Lerede

[10] Automatic Tuning of Electronic Throttle Control Strategy (2003), Joško Deuer et al.

[11] Constrained optimal control of an electronic throttle (2005), Mario Vašak et al.

[12] Hybrid Theory-Based Time-Optimal Control of an Electronic Throttle (2007) , Mario Vašak et al.