lamberson ms thesis

8/6/2019 Lamberson Ms Thesis

1/80

TORQUE MANAGEMENT OF GASOLINE ENGINES

By

Daniel Michael Lamberson

BS (Illinois Institute of Technology) 1998

BA (Wheaton College) 1999

A report submitted in partial satisfaction of theRequirements for the degree of

Masters of Science, Plan II

in

Mechanical Engineering

at the

University of California at Berkeley

Committee in Charge:Professor J. Karl Hedrick, Chair

Professor Andrew Packard

Fall 2003


2/80

i

Abstract

Torque Management of Gasoline Engines

by

Daniel M. Lamberson

Masters of Science in Mechanical Engineering

University of California at Berkeley

Professor J. Karl Hedrick, Chair

A torque management strategy for gasoline engines is developed. The torquemanagement concept is described in detail. A cylinder air flow observer isderived. Open loop estimation is shown as a starting point. Non-linear observertheory is used to derive an improved estimate for cylinder flow. An engine torquecontrol strategy is developed using the commanded throttle position of theelectronic throttle as the system input. Control of manifold pressure as a meansof torque control and direct control of driveline torque are investigated and theresults compared. Finally, a complete torque management strategy is derived.The derivation assumes a known estimate of engine torque, either by the use ofa torque sensor or some type of torque estimation algorithm. The torquemanagement strategy involves the coordinated control of the throttle, ignitiontiming, and the air to fuel ratio. Non-linear controllers are derived for ignitiontiming and air to fuel ratio setpoint. The controllers are designed to maintainengine speed through transient torque loadings. Simulation results are given foreach observer and controller. Attention is given to the application of MoBIES(Model Based Integration of Embedded Systems) tools and methodology in thedesign and implementation process of such a controller.


3/80

ii

Table of Contents

List of Figures iiiList of Variable v

1 Introduction ...................................................................................................12 Plant Model ...................................................................................................83 Previous Control Development....................................................................12

3.1 Electronic Throttle Control.................................................................... 123.2 Air to Fuel Ratio Control ....................................................................... 12

4 Cylinder Air Flow Estimation........................................................................144.1 Background.......................................................................................... 144.2 Open Loop Estimation using a Manifold Pressure Sensor ................... 164.3 Open Loop Estimation Using a Mass Air Flow Sensor......................... 184.4 Sliding Observer using Multiple Sensors.............................................. 24

5 Engine Torque Management.......................................................................27

5.1 Background.......................................................................................... 275.2 Sliding Mode Control Review ............................................................... 315.3 Engine Torque Control using Manifold Pressure Control .....................335.4 Engine Torque Control .........................................................................395.5 Torque Management Strategy.............................................................. 52

5.5.1 Derivation of the Control Laws...................................................... 565.5.2 Selection of Pressure Control or Torque Control Strategy............ 595.5.3 Results.......................................................................................... 60

6 Application to the MoBIES Project...............................................................677 Future Work................................................................................................. 678 Summary..................................................................................................... 699 Acknowledgements ..................................................................................... 7010 References.................................................................................................. 71


4/80

iii

List of Figures

Figure 1. Schematic of a gasoline engine............................................................ 2Figure 2. Pedal position to desired engine torque map for sporty vehicle feel.

(taken from [7]).............................................................................................. 5

Figure 3. Pedal position to desired engine torque map for economical vehiclefeel. (taken from [7]) ...................................................................................... 5Figure 4. Schematic of gasoline engine with modeled states............................ 11Figure 5. Schematic of feed-forward plus P-I control of fuel flow....................... 14Figure 6. Open loop estimate of cylinder flow using manifold pressure sensor -

perfect model............................................................................................... 17Figure 7. Open loop estimate of cylinder flow using manifold pressure sensor -

10% error in volumetric efficiency................................................................18Figure 8. Open loop estimate of cylinder flow using a throttle flow sensor -

perfect model............................................................................................... 20Figure 9. Open loop estimate of cylinder flow using a throttle flow sensor ..... 21

10% error in volumetric efficiency....................................................................... 21Figure 10. Open loop estimate of cylinder flow using a throttle flow sensor ... 2210% error in volumetric efficiency. (detail of Figure 9)........................................ 22Figure 11. Open loop estimate of cylinder flow using a throttle flow sensor ... 2310% error in volumetric efficiency and step input in throttle position. .................23Figure 12. Open loop estimate of cylinder flow using throttle flow sensor ....... 2410% error in throttle flow measurement.............................................................. 24Figure 13. Closed loop estimate of cylinder flow using throttle flow sensor and

manifold pressure sensor 10% error in throttle flow measurement........... 25Figure 14. Closed loop estimate of cylinder flow using throttle flow sensor and

manifold pressure sensor 10% error in volumetric efficiency. ..................26Figure 15. Schematic of the torque management control strategy. ...................27Figure 16. Engine torque change with air to fuel ratio. ...................................... 30Figure 17. Engine torque change with ignition timing. ....................................... 30Figure 18. Pressure control results throttle..................................................... 37Figure 19. Pressure control results pressure and torque................................ 38Figure 20. Pressure control results pressure and speed. ............................... 38Figure 21. Pressure control results control surfaces....................................... 39Figure 22. Torque control results throttle........................................................ 43Figure 23. Torque control results torque and pressure................................... 44Figure 24. Torque control results torque and speed....................................... 44Figure 25. Torque control results control surfaces.......................................... 45Figure 26. Torque constant (CT) parameter estimate using adaptive control law.

.................................................................................................................... 51Figure 27. Torque setpoint and engine speed used to test adaptive control law.

.................................................................................................................... 52Figure 28. Engine response to accessory load with no torque control ............53throttle and accessory. ....................................................................................... 53Figure 29. Engine response to accessory load with no torque control ............54torque and speed................................................................................................ 54


5/80

iv

Figure 30. Engine response to accessory load with pressure control only throttle and accessory. ................................................................................ 55

Figure 31. Engine response to accessory load with pressure control only pressure and speed.....................................................................................55

Figure 32. Torque management with discontinuous ignition timing control law

throttle and accessory. ................................................................................ 61Figure 33. Torque management with discontinuous ignition timing control law pressure and speed.....................................................................................61

Figure 34. Torque management with discontinuous ignition timing control law ignition timing. .............................................................................................62

Figure 35. Torque management with smooth ignition timing control law pressure and speed.....................................................................................63

Figure 36. Torque management with smooth ignition timing control law ........ 63ignition timing. ....................................................................................................63Figure 37. Torque management results using only ignition timing to control

engine speed pressure and speed. .......................................................... 64

Figure 38. Torque management results using only ignition timing to controlengine speed ignition timing and air to fuel ratio. ..................................... 65Figure 39. Torque management results using both ignition timing and air to fuel

ratio to control engine speed pressure and speed.................................... 66Figure 40. Torque management results using both ignition timing and air to fuel

ratio to control engine speed ignition timing and air to fuel ratio............... 66


6/80

v

List of Variables

Variable Name Description Units

Stoichiometric air to fuel ratio dimensionless

CT Torque constant N.m.rad/kg

vol Volumetric efficiency dimensionless

Ignition timingdegreesBTDC

Fraction of fuel delivered as vapor in thefuel wall wetting model

dimensionless

Ieng Engine rotational inertia kg.m2

Air to fuel ratio dimensionless

cylm Cylinder flow kg/s

fcm Commanded fuel flow kg/s

fom Actual fuel flow kg/s

maxm Maximum throttle flow kg/s

throttlem Throttle flow kg/s

n Number of engine cylinders dimensionless

Neng Engine speed rpm

eng Engine speed rad/s

Pa Atmospheric pressure Pa

Pm Manifold pressure Pa

Pm,exh Exhaust manifold pressure Pa

R Gas constant for air J/kg.K

T Intake manifold temperature Kelvin

fTime constant used in fuel wall wettingmodel

sec

maf_sensor

Time constant of the mass air flow sensor sec

th Time constant of the electronic throttle sec

th Throttle angle degrees

TQacc Accessory torque N.m

TQcomb Engine combustion torque N.m


7/80

vi

Variable Name Description Units

TQfric Engine friction torque N.m

TQimp Impeller torque N.m

TQpump Engine pumping torque N.mVdispl Engine displacement m

3

Vm Intake manifold volume m3

X Cylinder air charge kg/stroke


8/80

1

1 Introduction

In a conventional gasoline engine, shown in Figure 1, the driver controls the

pedal position. The pedal is mechanically linked to the engine throttle body. In

this way, the driver controls the throttle position and, in a way, the air flow to the

engine. In general, the amount of torque produced by an engine is directly

related to engine air flow. Thus, the engine performance and, to a great extent,

the vehicle performance is defined once the engine is selected. Advanced

engine technologies are currently being developed to improve engine fuel

economy and reduce engine emissions. Many of these technologies can be

separated into two categories. First, there are engine systems that divert engine

torque away from the driveline during portions of the drive cycle. These types of

engine systems include engine accessories (air conditioner, etc.) and hybrid

engine technologies. Second, there are engine systems that change engine

torque production, for the same air flow through the throttle, during portions of the

drive cycle. These types of engine systems include variable cam timing engines

and lean burn engine technologies. When a mechanical throttle is used, any

engine function that diverts engine torque away from the driveline or changes the

torque output of the engine during portions of the drive cycle adversely affectsvehicle performance. The current automotive market will not permit vehicle

performance degradation caused by the use of these advanced engine

technologies. In order to make these technologies an attractive option, vehicles

using these advanced engine technologies must perform as well or better than

those in the current market.


9/80

2

AccessoriesDriveline

Pedal Throttle

MechanicalLinkage Engine

Cylinders

Exhaust Manifold

OxygenSensor

Fuel Injectors

Intake Manifold

Idle Air

Bypass Valve

Figure 1. Schematic of a gasoline engine.

With the advent of electronic throttle systems, the pedal is not mechanically

connected to the throttle. Instead, the throttle plate is driven by an electric motor.In these systems, the pedal position is read as a voltage signal by the throttle

control system. Based on this pedal position signal, the controller determines the

actuating signal to send to the throttle motor. Since the engine control unit has

control of the throttle position, use of an electronic throttle allows for greater

flexibility on the control system. This flexibility can be used to improve engine


10/80

3

performance and help meet legislative emissions requirements. In addition, use

of an electronic throttle system may be used to improve the performance of the

aforementioned advanced engine technologies. Current effort is being made to

develop control strategies that make use of electronic throttle systems and these

advanced engine technologies. The goal of these control strategies is to improve

overall vehicle performance and to maintain vehicle performance as the engine

system changes its mode of operation.

It is possible to implement the electronic throttle control system so that it behaves

in a similar manner to the mechanical throttle system. To do this, the pedal

position signal is interpreted as a desired throttle opening. The controller drives

the throttle to the desired throttle opening in closed loop using the throttle

position sensor signal as feedback. The only difference between this

implementation and the mechanical throttle are the dynamics associated with the

electronic throttle system. In this implementation of an electronic throttle system,

the time lag of the throttle position can be used to give the controller an

advantage in predicting the future position of the throttle and the future mass air

flow. Magner et. al. [14] developed an improved cylinder air charge algorithm

using the delta air charge anticipation based on the difference between thecommanded and actual throttle position of an electronic throttle.

However, with an electronic throttle system, the control system can interpret the

pedal position signal in any number of ways and drive the throttle based on that

interpretation. To better take advantage of the control flexibility available with an

electronic throttle system, an engine torque management strategy can be used.

A torque management strategy has two goals. First, a torque management

strategy uses vehicle performance as a parameter in the control design process.

The desired vehicle performance is used to develop a map that converts pedal

position to a desired torque delivered to the driveline. The position of the

electronic throttle is then controlled to achieve this desired engine torque.

Second, a torque management strategy tries to eliminate transients caused by


11/80

4

the engine system changing its mode of operation. As the engine changes its

mode of operation, the torque delivered to the driveline changes. By using the

throttle to control the driveline torque, it is possible to design a control strategy

such that vehicle performance is maintained as the engine changes its mode of

operation.

In a torque management scheme, the pedal position signal is interpreted as a

commanded torque delivered to the driveline. Using this interpretation, the

vehicle response is no longer physically correlated to the pedal position. Instead,

the pedal position is passed into a map to determine the desired torque delivered

to the driveline. Possible pedal position to desired engine torque maps are

shown in Figures 2 and 3 for both a sporty vehicle feel and an economical

vehicle feel. These maps give desired engine torque as a function of pedal

position and engine speed. A sporty vehicle feel is achieved with a large

change in torque demand for a small change in pedal position at relatively low

pedal positions and low engine speeds. At high pedal positions and high engine

speeds, this sporty map is approximately the same as the economical map.

These maps are not unique and can be designed to fit the application.


12/80

5

Figure 2. Pedal position to desired engine torque map for sporty vehicle feel.(taken from [7])

Figure 3. Pedal position to desired engine torque map for economical vehiclefeel. (taken from [7])


13/80

6

Under normal driving operation, the torque management strategy uses the

throttle position to achieve the desired driveline torque while the fuel and ignition

timing are controlled to minimize fuel consumption, emissions, etc. The engine is

controlled in this manner for changes in pedal position, road grade, and other

conditions where the resulting vehicle response is anticipated by the driver.

However, during the onset of an accessory load or the changing of the cam

timing, the amount of engine torque transmitted to the driveline is immediately

changed in a way that is unexpected by the driver. These mode changes of the

engine can be sudden (accessory loads) or occur over a short period of time

(variable cam timing). Also, once in a given mode, the engine tends to stay in

that mode for an extended period of time. Since the throttle is being used to

control the driveline torque, the throttle will adjust to maintain the desired

driveline torque regardless of the engine operating mode. However, for sudden

changes in the driveline torque, the throttle and intake manifold dynamics may be

too slow to compensate for the torque transients without an adverse effect on

vehicle performance.

The magnitude and the time of application of these torque loads are known a

priori by the controller. Thus, if an actuator were fast enough to offset the torquechange, vehicle performance could be maintained until the throttle and manifold

dynamics have caught up. Under some restrictions, the ignition timing and the

air to fuel ratio can be adjusted to achieve the instantaneous change in engine

torque required to maintain the driveline torque while the throttle is adjusted.

These actuators, while fast, have limited control authority and are limited by other

considerations such as emissions and component life.

The transient torque rejection goal of the torque management strategy is similar

to the engine idle speed control problem. In controlling the engine idle speed,

the mechanical throttle is closed. The air flow to the engine is controlled by the

idle air bypass valve, shown in Figure 1. Due to the throttle valve dynamics and

the manifold filling dynamics, this actuator is unable to robustly control idle speed


14/80

7

in the presence of torque disturbances acting on the engine. The ignition timing

and, if necessary, the air to fuel ratio are used to control idle speed during these

disturbances. In order to give the ignition timing a torque reserve, the ignition

timing is retarded slightly from maximum brake torque. This gives both the

ignition timing and the air to fuel ratio sufficient control over the engine torque, in

both the positive and negative directions, that these actuators can maintain

engine idle speed during torque transients. In the torque management strategy,

the ignition timing and the air to fuel ratio are also used to reject torque

disturbances. However, in order to minimize fuel consumption, the ignition timing

is not retarded throughout the engine map. This further limits the control

authority of the ignition timing in the torque management strategy.

In the following, a full torque management strategy for gasoline engines is

derived. First a plant model is discussed as well as a short description of

previous work done in the areas of electronic throttle control and air to fuel ratio

control. Various methodologies are used to derive a cylinder air flow observer.

Non-linear control theory is then used to develop two engine torque controllers.

The first strategy controls intake manifold pressure as a means of torque control.

In the second strategy, driveline torque is controlled directly. Finally, a completetorque management strategy is developed to control the throttle position, ignition

timing, and the air to fuel ratio in a coordinated manner.


15/80

8

2 Plant Model

The engine model used for controller development is based on the model

developed by Cho et. al. [2]. This is a lumped parameter [1], mean value engine

model. The throttle flow is given by

( ) ( )amthmaxthrottle P,PPRITCmm = (2.1)

where maxm is the maximum flow through the throttle, TC(th) accounts for the

effect of throttle angle, and PRI(Pm, Pa) accounts for the effect of the pressure

ratio across the throttle. The functions TC(th

) and PRI(Pm

, Pa) act to reduce the

flow through the throttle with decreasing throttle angle (th) and increasing

manifold pressure (Pm). Using the ideal gas law, the intake manifold dynamics

are given by

( )

m

cylthrottle

m

manifold

mV

TRmm

V

TRmP

=

=

(2.2)

where cylm is the flow to the engine cylinders (out of the manifold), Vm is the

manifold volume, R is the gas constant for air, and T is the intake air

temperature. The derivative of temperature is neglected since the manifold

temperature is assumed constant. In general, the temperature derivative can be

neglected since it has only a minor effect on the manifold pressure dynamics

[11]. The engine flow is found from a speed density approximation

( )TR

P,PV

4

1m mengengmvoldisplcyl

= (2.3)


16/80


17/80

10

load torque from the driveline (i.e. the impeller torque if an automatic

transmission is used). The pumping torque is given by

( )mexhm,displ

pump PP4

V

TQ = (2.7)

where Pm,exh is the exhaust manifold pressure. The friction torque can be

approximated using

2eng1fric CCTQ += (2.8)

where C1 and C2 are engine specific constants.

Figure 4 shows a schematic of the engine with the modeled variables shown. As

shown, the air flows through the throttle and into the intake manifold. Flow from

the manifold mixes with fuel from the injectors before entering the engine

cylinders. Combustion of the air/fuel mixture produces an increase in cylinder

pressure and results in an applied torque about the engine crankshaft. Exhaust

gases pass out of the engine cylinders and into the exhaust manifold. In theexhaust manifold, an oxygen sensor is used to measure the amount of oxygen in

the exhaust stream.


18/80

11

OxygenSensor

FuelInjector

thm

mP

cylm

exh,mP

Combustion ofAir/Fuel Mixture

eng

Piston

Friction BetweenPiston and

Cylinder Wall

)TQ( fric

)TQ( comb

SparkPlug

th

Figure 4. Schematic of gasoline engine with modeled states.

This engine model does not include the effects of exhaust gas recirculation

(EGR). Exhaust gas recirculation is the process of passing hot exhaust gases

into the intake manifold. This process is becoming more widely used in gasoline

engines as a way to reduce emissions and fuel consumption. It is neglected here

to simplify the derivation of the torque management strategy. The model is

implemented in Matlab/Simulink and, for the following analysis, is parameterizedto represent a Ford Taurus engine.


19/80

12

3 Previous Control Development

3.1 Electronic Throttle Control

A detailed model of an electronic throttle system and an associated control law

was developed by Griffiths [5]. This model accounted for the non-linearities of

the electronic throttle system including the Coulomb friction of the valve.

For implementation, the non-linearities of the throttle body must be accounted

for. However, of more importance for this application is the non-linear effect of

throttle position on the throttle flow. So, the following derivations use an

electronic throttle model of the form

cmd

th

th

th

th

1

1 += (3.1)

This simplification will ease the control derivations while still allowing for an

overall torque management strategy to be developed and evaluated.

3.2 Air to Fuel Ratio Control

An air to fuel ratio controller was previously developed by Souder [17]. The

controller is designed to deliver fuel in order to achieve a stoichiometric air to fuel

ratio. The output of the oxygen sensor is used in feedback to control the amount

of fuel delivered. This model includes the non-linear effects of fuel wall wetting.

In gasoline engines, fuel is delivered to the air stream prior to entering thecylinders. However, not all of the fuel vaporizes as it mixes with the air. Instead,

some of the fuel forms a puddle on the manifold wall. Over time, fuel from the

puddle is vaporized and enters the cylinders. Inclusion of this effect in the control

model leads to improved air to fuel ratio control.


20/80


21/80

14

4 Cylinder Air Flow Estimation

4.1 Background

Most production air to fuel ratio controllers consist of a feed forward term and aproportional plus integral (P-I) closed loop portion as shown in Figure 5. The

feedback portion of the control scheme uses the output of the oxygen sensors in

the exhaust stream as an indication of the air to fuel ratio. The oxygen sensor is

a highly nonlinear sensor giving a non-saturated reading only in a narrow range

around the stoichiometric air to fuel ratio. In practice, this sensor can only be

used to determine if the mixture is rich or lean.

The P-I portion of the control cannot be relied on during transients and cold start.

This is due to two factors. First, fuel is injected in the intake ports, before the

intake valves are opened, while the oxygen sensor is placed in the exhaust

stream. This leads to a large time delay in the system that varies with engine

speed. Second, the oxygen sensor is only operational once it has reached its

operating temperature. Thus, the feed forward portion of the control is of

particular importance in maintaining precise air to fuel ratio control.

Oxygen SensorOutput

Mass Air Flow,Intake Temperature,

Engine Speed

Kp

Ki1

s

Feed-Forward

+

+

+

+Desired Fuel

Flow

Figure 5. Schematic of feed-forward plus P-I control of fuel flow.


22/80

15

A non-linear, sliding mode control for air to fuel ratio was developed by Souder

[17]. The sliding mode control was derived using a sliding surface defined by

focyl mmS = (4.1)

where fom is the mass of fuel entering the cylinder. The final control law was

given as

ym

1m

mm cyl

f

fc

f

cylfc += (4.2)

where fcm is the commanded fuel, and y is the output of the oxygen sensor

defined as

( ) ymmsgnSsgn focyl == (4.3)

The output of the control is a desired mass flow rate. This requires equation 4.2

to be integrated. After this integration, the term cylm appears in the control law.

Thus, the same feed forward term required in the P-I controller is also needed in

this sliding control.

The feed forward portion of an air to fuel ratio controller requires an accurate

estimate of cylinder air flow ( cylm ). Since a cylinder flow sensor is currently not a

cost effective option, this estimate is made using either a mass air flow sensorplaced at the throttle body or an intake manifold pressure sensor.

In fuel control systems, the use of a throttle flow sensor, instead of a manifold

pressure sensor, is made for a variety of reasons as listed below


23/80

16

No need for ambient pressure measurement

Unreliable accuracy of the throttle position sensor

High mass flow leads to a high pressure drop across the air filter

Controller able to distinguish between air and EGR

Improved accuracy of the cylinder flow estimate

Most importantly, the accuracy of the estimate of the cylinder air charge is

improved when a throttle flow sensor is used. The throttle flow depends on the

pressure upstream and downstream of the throttle. The air pressure upstream of

the throttle (downstream of the air filter) and the barometric pressure are usually

not continuously sensed variables. In the case of barometric pressure, it is

usually sensed at engine startup and assumed to remain constant over the drive

cycle. Even if this were a valid assumption, relating the atmospheric pressure to

the pre-throttle/post-filter pressure is non-trivial. Use of a mass air flow sensor

eliminates this issue. However, the mass air flow sensor is more expensive and

has a lower bandwidth than a manifold pressure sensor.

The following sections will look at some possible cylinder flow estimators using

these sensors. In current production engines, only one of these sensors wouldbe used at a time. However, a scenario is investigated using both sensors

simultaneously. Use of redundant sensors can be used to improve the quality of

the flow estimate and allow for improved diagnostic functionality [8]. In section

4.4, non-linear observer theory is used to create a closed loop cylinder flow

observer. An extended Kalman filter [4] could also be used for this purpose.

4.2 Open Loop Estimation using a Manifold Pressure Sensor

A direct estimate of cylinder air flow can be made using a manifold pressure

sensor. In this case, the speed density approximation, given in equation 2.3, can

be used to calculate cylinder flow.


24/80

17

Figure 6 shows the cylinder flow estimate using the speed density approximation

when the cylinder pumping model is perfect. In this example, the engine speed

is held constant. As expected, the estimate tracks the actual cylinder flow

perfectly.

Figure 6. Open loop estimate of cylinder flow using manifold pressure sensor -perfect model.

Due to engine to engine variations and engine deterioration over time, the

volumetric efficiency of the engine may be different than that of the engine used

to develop the volumetric efficiency map. Figure 7 shows the cylinder flow

estimate using the speed density approximation when the plant has a volumetric

efficiency 10% greater than the model. This model uncertainty leads to a

significant (10%) error in the cylinder flow estimate.


25/80

18

Figure 7. Open loop estimate of cylinder flow using manifold pressure sensor -10% error in volumetric efficiency.

4.3 Open Loop Estimation Using a Mass Air Flow Sensor

In steady state, the throttle flow is equal to the cylinder flow. However, due to the

manifold filling dynamics, a direct estimate of cylinder air flow cannot be made

using a mass air flow sensor when the engine is operating under transient

conditions. Instead, the estimate is based on a model of the flow sensor

dynamics and the manifold dynamics. This air flow estimate derivation is based

on work done by Grizzle et. al. [6].

First, by differentiating the ideal gas law, the rate of change of the manifold air

pressure is given by

( )( )mengcylthrottlem

manifold

m

m P,mmV

TRm

V

TRP

=

= (4.4)


26/80

19

where )P,(m mengcyl is an experimentally determined cylinder flow as a function

of engine speed and manifold pressure. Development of the cylinder flow

function [ )P,(m mengcyl ] is similar to that of the volumetric efficiency map of

equation 2.3. The air charge in the cylinder (per stroke) is given by

( )mengcyleng

P,mNn

120

= (4.5)

where n is the number of engine cylinders, Neng is the engine speed in rpm, and

the factor of 120 accounts for the necessary unit conversions. The dynamics of

the mass air flow sensor also should be taken into account and are given by

throttle

maf_sensor

measuredthrottle, m1s

1m

+= (4.6)

where maf_sensor is the time constant for the flow sensor and s is the Laplace

operator. In order to eliminate the derivative of measuredthrottle,m in the pressure

equation (4.4), a new variable, x, can be defined as

measuredthrottle,maf_sensor

m

m mV

TRPx

= (4.7)

Substituting equations 4.6 and 4.7 into equation 4.4 gives

+

=

measuredthrottle,maf_sensorm

engcylmeasuredthrottle,m

mV

TRx,mm

V

TRx (4.8)

Equation 4.8 is numerically integrated, using the forward Euler method of

integration, leading to


27/80

20

+

+=

(k)mV

T(k)R1)x(k(k),m

(k)m

V

T(k)Rt1)x(kx(k)

measuredthrottle,maf_sensorm

engcyl

measuredthrottle,

m

(4.9)

Thus, the mass of air in the cylinders is given by

+

= (k)m

V

T(k)Rx(k)(k),m

(k)Nn

120(k) measuredthrottle,maf_sensor

m

engcyl

eng

(4.10)

Figure 8, shown below, shows the estimated cylinder flow assuming a perfect

model is available. In this case, the engine speed is held constant and the

sensor is assumed infinitely fast. As shown, the cylinder flow estimate is

identical to the actual cylinder flow.

Figure 8. Open loop estimate of cylinder flow using a throttle flow sensor -perfect model.


28/80

21

Figures 9 and 10 show the cylinder flow estimate given a sinusoidal input in

throttle position. In this case, the volumetric efficiency of the engine is 10% lower

than the engine pumping model in the estimator. As shown, the manifold

pressure estimate is significantly incorrect (10%). However, the cylinder flow

estimate is close to the actual cylinder flow (less than 1% error). This is a much

better result than the open loop observer using the manifold pressure sensor

developed in section 4.2.

Figure 9. Open loop estimate of cylinder flow using a throttle flow sensor 10% error in volumetric efficiency.


29/80

22

Figure 10. Open loop estimate of cylinder flow using a throttle flow sensor 10% error in volumetric efficiency. (detail of Figure 9)

One interesting point about this estimator is the fact that the steady state

estimate does not depend on an accurate model of the engine volumetric

efficiency. Using the pressure dynamics given in equation 2.2 and assuming the

system is in steady state, it is shown that

( )

m

mengengmvoldispthrottle

m

cylthrottle

m

V

TRTR

P,PV

4

1m

V

TRmm0P

=

==

(4.11)

Solving equation 4.11 for the manifold pressure (Pm) gives

( )engmvolengthrottle

disp

m,P

TRm

V

4P

= (4.12)


30/80

23

As shown, the manifold pressure is inversely proportional to the volumetric

efficiency. Thus a decrease in the volumetric efficiency leads to an equal

percentage increase in manifold pressure. Thus, an inaccurate model of the

volumetric efficiency will lead to an equally incorrect pressure estimate (but in the

opposite direction). Since the cylinder flow is proportional to the product of

volumetric efficiency and manifold pressure (equation 4.12), the cylinder flow

estimate would be correct.

Figure 11 shows the cylinder flow estimate during a step input in throttle. As

shown, an error exists in the flow estimation during the transient. However, as

the system reaches steady state, the difference between the actual flow and the

flow estimate tends toward zero.

Figure 11. Open loop estimate of cylinder flow using a throttle flow sensor 10% error in volumetric efficiency and step input in throttle position.


31/80

24

4.4 Sliding Observer using Multiple Sensors

If a manifold pressure sensor were used in conjunction with the throttle flow

sensor, a sliding observer could be used to improve the estimate of cylinder flow

derived in section 4.3. A sliding observer [15] would lead to a pressure estimate

of

( )mm1

m

cylthrottle

mPPk

V

TRmmP +

=

(4.13)

Use of these multiple measurements (throttle flow and manifold pressure) can be

used to improve the estimate in the presence of model uncertainty. For instance,

if the estimator of section 4.3 is used and an error exists in the throttle flow

measurement, an incorrect cylinder flow estimate would be calculated. These

results are shown in Figure 12.

Figure 12. Open loop estimate of cylinder flow using throttle flow sensor 10% error in throttle flow measurement.


32/80

25

Using a manifold pressure sensor and the sliding observer defined by equation

4.13, an improved estimate can be made. These results are shown in Figure 13.

Figure 13. Closed loop estimate of cylinder flow using throttle flow sensor andmanifold pressure sensor 10% error in throttle flow measurement.

A more common error in the cylinder flow model would be in the volumetric

efficiency, vol. The results of the closed loop estimate with a 10% error in

volumetric efficiency are shown in Figure 14. This estimator improves the

estimate of the manifold pressure, but the estimate of cylinder flow is significantly

degraded.


33/80

26

Figure 14. Closed loop estimate of cylinder flow using throttle flow sensor andmanifold pressure sensor 10% error in volumetric efficiency.

As discussed in section 4.3, in the presence of a volumetric efficiency error, use

of the mass air flow sensor estimator leads to a zero steady state error in the

cylinder flow estimate although a significant error exists in the pressure estimate.

If a pressure sensor is used to try to improve the estimate, this would lead to an

improved pressure estimate but an incorrect estimate of cylinder flow. Thus, the

most likely type of model error must be determined before the application of this

type of observer.

The true benefit of closed loop observers is the estimation of unmeasured

system states. This closed loop observer is only used to improve on an estimate.

Implementation of this multiple measurement estimator would be most effective ifthe pressure sensor could be used for more than just improving the cylinder flow

estimate (i.e. diagnostic functionality, etc.).


34/80

27

5 Engine Torque Management

5.1 Background

Torque management is a strategy that uses the individual throttle, fuel, and

ignition timing controllers and adds an additional layer of control which

determines the desired setpoints for each of these low level controllers. The

torque management control strategy consists of two modes, the first is used for

normal operation and the second used for short duration transient torque

rejection. Figure 15 shows a schematic of the torque management strategy.

Normal Operation

Throttle changed toachieve torque

demand Ignition timing set to

'optimal'

Desired AFR set to'optimal'

Transient Torque Rejection

Throttle changed to'eventually' achieve torquedemand

Ignition timing changed toInstantaneously meettorque demand

Desired AFR changed toinstantaneouly meet torquedemand (if necessary)

Throttle Control(Closed Loop)

Ignition Control(Open Loop)

Fuel Control(Closed Loop)

PedalPosition

Other KnownTorque

Demands

Short Term TorqueAddition/Subtraction

Required

Throttle PositionSetpoint

Ignition TimingCommand

Ignition TimingSetpoint

Throttle PositionCommand

Fuel FlowCommand

Air to Fuel RatioSetpoint

Desired Cylinder ChargeAttained

Figure 15. Schematic of the torque management control strategy.


35/80

28

The inputs to the high level controller are the pedal position and all known torque

demands acting on the engine. These other torque demands are known at some

higher level of the engine control strategy and are passed to the torque

management strategy. In the torque management strategy, the pedal position is

interpreted as a desired torque at the driveline. To this effect, the pedal position

signal is passed through a torque map to determine the desired driveline torque.

This map is not unique and can be made to fit the application or desired

drivability feel (e.g. a sport car feel versus an economy car feel). The desired

driveline torque is summed with all the other known torque demands acting on

the engine. This desired engine torque is compared to the actual engine

torque. The actual engine torque is found using a torque sensor, some open

loop approximation of engine torque, or using some more advanced torque

estimation algorithm. The difference between the actual and the desired engine

torque is used to drive the position of the electronic throttle.

In Normal Operation, when the load demands are to be handled only by the

throttle, the throttle position is adjusted to achieve the desired driveline torque.

The strategy functions in this mode for conditions where the resulting vehicle

response is anticipated by the driver (changes in throttle position, road grade,etc.). In this mode, the fuel and ignition timing are controlled to try to minimize

emissions and brake specific fuel consumption. This requires strict control of the

air to fuel ratio around stoichiometric and has motivated the previous derivations

for cylinder flow estimation.

Due to the throttle dynamics and the pressure dynamics of the intake manifold, a

near instantaneous change in engine torque is not achievable using only the

throttle. For small, instantaneous torque variations in engine loading or torque

production, the ignition angle and/or air to fuel ratio can be modified to change

the engine torque to compensate for the torque transient. The magnitude and

the time of application of these torque loads are known a priori by the torque

management strategy. Once the strategy is signaled that a change in load


36/80

29

torque is coming, the strategy moves to Transient Torque Rejection mode. In

this mode, the throttle is controlled to achieve the control objective (constant

driveline torque). The ignition timing and, if necessary, the air to fuel ratio are

controlled to maintain engine speed through the transient.

Under normal operation, the spark timing of the engine is retarded slightly from

the angle for maximum torque in an effort to reduce engine emissions. Also, the

air to fuel ratio is kept at stoichiometric to achieve good emissions. However, for

short periods of time, the ignition timing can be advanced/retarded and the air to

fuel ratio be increased/decreased to achieve a lower/ higher engine torque for the

same amount of air flow. These two systems have much faster dynamics than

the throttle valve and intake manifold. However, there are additional

considerations when using the ignition timing and the air to fuel ratio to adjust

engine torque. First, the upper and lower limits for ignition timing are governed

by pre-ignition of the air/fuel mixture and other component requirements. The

upper and lower limits for the air to fuel ratio are governed by emission

requirements and component requirements. Figures 16 and 17 show examples

of how engine torque varies with air to fuel ratio and ignition timing. As shown in

Figure 16, engine torque increases as the air/fuel mixture is rich and decreaseswhen the mixture is lean. As shown in Figure 17, the engine torque decreases

as the ignition timing is retarded (positive degrees) from the point of maximum

brake torque (MBT). Advancing the timing from MBT is not done due to the

possibility of pre-ignition of the air/fuel mixture. In the following analysis, an

ignition timing of five degrees from the point of maximum brake torque is selected

as the nominal operating point.


37/80

30

Figure 16. Engine torque change with air to fuel ratio.

Figure 17. Engine torque change with ignition timing.


38/80


39/80

32

where is strictly positive. The control law is designed so that, using the worst

case model uncertainty,

sgn(S)S = (5.4)

Once the control law has been derived, is can be shown that

SSS (5.5)

meaning that the derivative of the Lyapunov function candidate is negative

definite. Thus, the surface is stable and the Lyapunov function candidate is atrue Lyapunov function.

As stated this is a robust control strategy. The control gain, , is used to account

for all known model uncertainty. Provided the parameter uncertainty in the model

can be bounded, is selected to be large enough to ensure stability of the

surface. Once the system has reached the surface, the sliding condition is

achieved. This means that the system remains on the surface and travels toward

the equilibrium point in a manner defined by S. Using this method, the surface is

defined such that

The control goal is achieved (or will be achieved asymptotically) at S=0

The control input appears in the definition of S

In cases where the control input does not appear in the definition of S , methods

such as multiple surface control or dynamic surface control are available. These

control methodologies are most commonly used when a parameter uncertainty

appears in a system state that has no control input. This type of system is

termed a mismatched system.


40/80

33

As stated, the robustness term, , is used to account for model uncertainty. A

methodology known as adaptive control can be used to reduce the uncertainty in

the model. In addition to meeting the control objective, an adaptive controller

attempts to estimate an unknown, constant parameter in the system. This is

done by creating a parameter update law in such a way that the estimate

converges to the true value of the parameter. By adapting on an unknown

parameter, the model uncertainty is reduced and a smaller can be used in the

control law.

To achieve perfect tracking, sliding mode control requires infinite sampling

frequency and high control activity. This is due to the use of the discontinuous

sgn() function in the control law. For implementation, smooth control laws can be

developed. Use of these smooth control laws eliminates the possibility of perfect

tracking but reduce the control activity.

In section 5.3 a sliding control is developed to control the manifold pressure as a

means of torque control. This control uses dynamic surface control, a variant of

sliding control. In section 5.4 an adaptive, dynamic surface control is developed

to control driveline torque directly.

5.3 Engine Torque Control using Manifold Pressure Control

When controlling engine torque, the control goal is to drive the engine torque to

the desired engine torque (TQengineTQdesired). As shown in equation 2.4, engine

combustion torque is a function of cylinder air flow. From equation 2.3, cylinder

air flow is a function of the manifold pressure. Thus, assuming constant air to

fuel ratio and ignition timing, the control goal can be redefined as PmPm,des. In

the following, a sliding mode control is developed to control manifold pressure.

First, a positive definite Lyapunov function candidate is chosen as


41/80

34

2

1S2

1V = (5.6)

where the control surface is defined as

des1 PPS = (5.7)

Taking the derivative of the control surface gives

( ) ( )

( ) desm,mengengmvoldisp

amthmax

m

descylthrottle

m

desm,m1

P

TR

P,PV

4

1

P,PPRITCm

V

TR

P)mm(V

TR

PPS

=

=

=

(5.8)

The control surface is attractive if

111 SSS (5.9)

Using the worst case model uncertainty, the control law is derived so that

)sgn(SS 11 = (5.10)

From equation 5.8, the actual throttle angle appears in the derivative of the

sliding surface. However, since this engine is equipped with an electronic

throttle, the input to the system is a throttle command. Thus, a synthetic input

(d) is defined and the control law is derived using this synthetic input. The

control law is given by


42/80

35

( )( )( )

( )( )

+

+

+

=

1TR

P,PV

4

1

P,PPRIm

1

PSsgnTR

V

P,PPRIm

1

cosm

engengmvoldisp

ammax

desm,11m

ammax1d

(5.11)

Now a second control law must be derived to drive the throttle angle to the

desired throttle angle. Using a similar Lyapunov function candidate as that given

in equation 5.6, a second control surface is used to achieve the control goal,

thd. This second sliding surface is defined as

dth2 S = (5.12)

Derivation of a control law using this sliding surface requires the time derivative

of d to be known. In almost all cases, the rate of change of this synthetic input is

unknown. In order to eliminate this requirement, the control surface can be

redefined as

zS th2 = (5.13)

where z is the output of a first order filter defined by

d2 zz =+ (5.14)

Taking the derivative of the second surface yields

( ) ( )z

1

1zS

d

2

thcmd

th

th2

=

= (5.15)


43/80

36

Since d is passed through a first order filter, knowledge of the derivative of d in

the control law is no longer a requirement. As shown, the input to the system,

cmd, appears in the derivative of this second surface. Again using the worst

case model uncertainty, the control law is given by

( ) ( ) thd2

22thcmd z

1Ssgn +

+= (5.16)

The final control law is defined as

( ) ( )

( )

( )( )( )

( )( )

+

+

+

=

=

+

+=

1TR

P,PV

4

1

P,PPRIm

1

PSsgnTR

V

P,PPRIm

1

cos

z

1z

z

1Ssgn

mengengmvoldisp

ammax

desm,11m

ammax1d

d

2

thd

2

22thcmd

(5.17)

In this derivation, the derivative of the desired manifold pressure ( desm,P ) is

assumed known. In implementation, the derivative of the desired manifold

pressure ( desm,P ) would have to be calculated using the rate of change of the

pedal position.

Figures 18 to 21 show the results of the pressure control strategy for a sinusoidal

input in the pressure setpoint. Figure 18 shows the throttle position and throttle

flow required to achieve the control objective. As stated, the throttle actuator is

used to achieve the desired manifold pressure. Figure 19 shown the actual and

desired manifold pressure as well as the combustion torque. Figure 20 shows

the transient portion of the pressure control as the controller begins to track the

pressure setpoint. Engine speed is also shown in Figure 20. In this test, the

engine speed is not held constant, but is assumed known. Figure 21 shows the


44/80

37

two control surfaces defined in the control law. As shown, the system converges

to the two control surfaces. Once the system reaches the control surfaces, the

system stays on each surface as desired.

Figure 18. Pressure control results throttle.


45/80

38

Figure 19. Pressure control results pressure and torque.

Figure 20. Pressure control results pressure and speed.


46/80

39

Figure 21. Pressure control results control surfaces.

5.4 Engine Torque Control

In section 5.3, a manifold pressure control is derived as a means of controlling

engine torque. The control goal, however, is to control the engine torque. With

the use of a torque sensor or an engine torque estimation algorithm, a feedback

control on driveline torque can be made. Control of engine torque is required if

the control is to be robust with respect to the effects of engine aging. Although

this type of torque control may not be required for automotive applications, it is

included here for completeness.

Again, starting with the Lyapunov function candidate

2

1S2

1V = (5.18)

where the control surface is defined as


47/80


48/80

41

( ) ( )

( ) ( )

4

V

P

P

TR

V

4

1

SPIAFIC)h(

C

m

PP

TR

V

4

1

SPIAFICg()

displ

m

volmengengvol

displ

eng

T

1

eng

cyl

eng

volmengmvol

displ

eng

T

+

+

=

+

=

(5.22)

where g() and h() are functions of the system parameters and states, including

the torque constant, CT. Using these functions, equation 5.21 simplifies to

desmeng1 Ph()g()S += (5.23)

As in section 5.3, the commanded throttle position does not appear in the

derivative of the control surface. Instead, a synthetic input (d) is used to derive

the control law. Using this synthetic input, the control law is defined as

( )

( )( )

+

+

+

=

1TR

P,P

4

V

P,PPRIm

1

)h(

)g()sgn(S

TR

V

P,PPRIm

1

cos

mengengmvol

disp

ammax

engdes1m

ammax1d

(5.24)

A second control law is then defined to drive th to d. As in section 5.3, dynamic

surface control is used to derive this second control law. To this end, a second

control surface is defined as

zS th2 = (5.25)


49/80

42

where

d2 zz =+ (5.26)

Taking the derivative of the second surface yields

( ) ( )z

1

1

zS

d

2

thcmd

th

th2

=

=

(5.27)

As shown, the input to the system appears in the derivative of this second

surface. The control law is then derived as

( ) ( ) thd2

22thcmd z

1Ssgn +

+= (5.28)

The final control law is given by

( ) ( )

( )

( )

( )( )

+

+

+

=

=

+

+=

1TR

P,P

4

V

P,PPRIm

1

)h(

)g()sgn(S

TR

V

P,PPRIm

1

cos

z

1z

z

1

Ssgn

mengengmvol

disp

ammax

engdes1m

ammax1d

d

2

thd2

22thcmd

(5.29)

Figures 22 to 25 show the results of the torque control strategy for a sinusoidal

input in the driveline torque setpoint. Figure 22 shows the throttle position and

flow for this test. Figure 23 shows the actual and desired torque as well as the

manifold pressure. Figure 24 shows the transient portion of the torque control as


50/80

43

the controller begins to track the torque setpoint. Also shown, is the engine

speed. In this test, the engine speed was not held constant, but was assumed

known. Figure 25 shows the control surfaces for the system.

Figure 22. Torque control results throttle.


51/80

44

Figure 23. Torque control results torque and pressure.

Figure 24. Torque control results torque and speed.


52/80

45

Figure 25. Torque control results control surfaces.

This derivation has assumed the model for engine torque, throttle flow, and

engine flow are exactly correct. However, over time, the engine parameters may

change. For instance, over time, the engine will not produce as much torque as

when it was new. Therefore, the torque constant (CT) may change over time. In

some cases, it may be appropriate to account for this variation using the

robustness parameter, , in the sliding control. However, this would lead to

increased control effort. Instead, an adaptive controller can be used to account

for an unknown, slowly varying parameter such as this. In addition to meeting

the control objective, an adaptive controller attempts to estimate an unknown,

constant or slowly varying parameter in the system. This is done by creating a

parameter update law in such a way that the estimate of the parameter

converges to the true value of the parameter. Use of an adaptive controller

reduces the uncertainty in the model. This allows for a lower gain, , to be used

in the controller.


53/80

46

For the adaptive control strategy, the synthetic input (d) of equation 5.24 is

defined using the estimate of CT (call this TC ). Solving for d using the estimate

TC gives

( )

( )

( )( )

+

+

+

=

1TR

P,P

4

V

P,PPRIm

1

)Ch(

)Cg(Ssgn

TR

V

P,PPRIm

1

cos

mengengmvol

displ

ammax

T

engTdes1m

ammax1d

(5.30)

Substituting this control law into the derivative of the sliding surface leads to

des

T

engTdesadapt

T

engTadapt

)Ch(

)Cg()sgn(S)h(C

)g(CS

+

+=

(5.31)

Defining CT to be

TTT CCC= (5.32)

and substituting into equation 5.31 yields

( ) ( )

( ) ( )

( ) ( )

( )( )

+

+

+

+=

engTdesadapt

engmvolT

vol

T

eng

eng

cyl

mvol

displ

eng

T

adaptadapt

Cg)sgn(S

TRPSPIAFIC

mPSPIAFI

C

mP

TR

1

4

V

SPIAFIC

)sgn(SS

(5.33)


54/80

47

The goal is to define a parameter update law for TC . Thus, the system must be

converted into a two state system consisting of the states Sadapt and TC .

Using a Lyapunov argument, a Lyapunov function candidate can be defined as

2

CS

2

1V

2

T2

adaptadapt += (5.34)

where defines the rate of parameter convergence and TC is the difference

between CT and TC . This Lyapunov function candidate is a positive definite

function in the two states S and TC . The derivative of the Lyapunov function

candidate is given by

TTadaptadaptadapt CCSSV += (5.35)

Since CT is assumed to be slowly varying, it can be treated as a constant. Thus,

adaptV reduces to

+= TTadaptadaptadapt CCSSV

(5.36)

By substituting the definition of adaptS , given in equation 5.33, into adaptV

, it is

shown that


55/80

48

( ) ( )

( ) ( )

( ) ( )

( )( )

+

+

+

+

+

=

engTdesadapt

engmvolT

mvol

T

eng

eng

cyl

mvol

displ

eng

T

adapt

adapt

TTadapt

Cg)sgn(S

TRPSPIAFIC

PSPIAFI

C

mP

TR

1

4

V

SPIAFI

C

)sgn(S

S

CCV

(5.37)

The system is stable if adaptV is negative definite. Towards this end,

TC

is

defined to be

( ) ( )

( ) ( )( ) ( )

( )( )

+

+

+

=

engTdesadapt

engmvolT

mvol

eng

eng

cyl

mvol

displ

eng

adaptT

Cg)sgn(S

TRPSPIAFICPSPIAFI

mP

TR

1

4

V

SPIAFI

S1C

(5.38)

where TC

has been defined to cancel out the CT terms in the derivative of the

Lyapunov function (equation 5.37). With this parameter update law, adaptV

reduces to

)sgn(SSV adaptadaptadapt = (5.39)

which is a negative semi-definite function of the system states.


56/80

49

Since Tdes is not constant, Barbalats Lemma [16] must be used to determine the

stability of the time varying system. Barbalats Lemma has three conditions,

which, if satisfied, guarantee a negative semi-definite Lyapunov function

candidate has only a one solution. The conditions are

1. V is lower bounded Vadapt is positive definite. Thus, it is lower bounded.

2. V is negative semi-definite As stated in equation 5.39

3. V is uniformly continuous OR V is bounded The second derivative of

the Lyapunov function is bounded provided des is bounded.

Since the three conditions of Barbalats Lemma are satisfied, the equilibrium

point of the Lyapunov function candidate is globally, asymptotically, stable.

The modified control law is given by


57/80

50

( ) ( )

( )

( )

( )

( )( )

( ) ( )

( ) ( )

( ) ( )

( )( )

+

+

+

=

+

+

+

=

=

+

+=

engTdesadapt

engmvolT

mvol

eng

eng

cylmvol

displ

eng

adaptT

mengengmvol

displ

ammax

T

engTdes1m

ammax1d

d2

thd

2

22thcmd

Cg)sgn(S

TRPSPIAFIC

PSPIAFI

mP

TR1

4V

SPIAFI

S

1C

1TR

P,P

4

V

P,PPRIm

1

)Ch(

)Cg(Ssgn

TR

V

P,PPRIm

1

cos

z

1z

z

1Ssgn

(5.40)

The parameter update law requires Tdes to vary ( 0S ) in order for the parameter

estimate to converge. This is due to the persistency of excitation requirement of

adaptive control systems [16].

Figure 26 shows the convergence of the parameter estimate for a low and high

initial estimate. Parameter convergence has been demonstrated. However, a

rigorous proof of convergence is not given here.

Figure 27 shows the desired driveline torque used in the convergence test. Thedesired torque is a single sinusoid with additive white noise. In implementation,

the normal drive cycle of a vehicle should provide enough excitation to the

system to ensure convergence.


58/80

51

It should be noted that holding engine speed constant in effect changes the order

of the system. Since the parameter CT only acts to change the engine speed,

adaptive control on this parameter requires that engine speed not be constant.

Figure 26. Torque constant (CT) parameter estimate using adaptive control law.


59/80

52

Figure 27. Torque setpoint and engine speed used to test adaptive control law.

5.5 Torque Management Strategy

At this point, two control laws have been developed which control the engine

torque to a desired level using only the engine throttle. However, due to the

throttle and manifold dynamics, the engine throttle cannot compensate for

instantaneous changes in the driveline torque. These changes can occur due to

changes in the accessory loads acting on the engine or due to changes in the

actual engine torque production of the engine (such as when the cam timing

changes). In addition, this type of strategy also has applications in lean burn

engines and hybrid engine technologies. An example of the engine performance

during the onset of an accessory load is shown in Figures 28 and 29. With the

throttle position held constant, the addition of an accessory load causes thesystem to reach a new steady state. This change in engine speed and driveline

torque directly effects the vehicle performance in a way that is unexpected by the

driver. As shown in Figures 28 and 29, the throttle position is held constant (as

with a mechanical throttle) and an accessory load is removed from the engine.

This decrease in engine load causes the engine to accelerate to a new steady


60/80

53

state engine speed. Due to the change in operating condition, the combustion

torque is decreased. For this analysis, the change in engine loading or engine

torque production will be achieved through the accessory load. However, the

following derivation would be similar for any known change in engine loading or

engine torque production.

Figure 28. Engine response to accessory load with no torque control throttle and accessory.


61/80

54

Figure 29. Engine response to accessory load with no torque control torque and speed.

If an electronic throttle is used in conjunction with a pressure control strategy or a

torque control strategy (as described in sections 5.3 and 5.4), the engine

achieves the same steady state engine speed after a short transient. This is

shown in Figures 30 and 31. At the time the accessory is removed from the

engine, the pressure setpoint changes. Over a short period of time, the throttle

adjusts to achieve the new pressure setpoint. However, at the time the

accessory is removed, the engine initially accelerates. As the manifold pressure

approaches the new setpoint, the engine decelerates and achieves the speed

prior to the accessory load change. The rate at which the system converges to

the new pressure setpoint is defined by the robustness term, , in the sliding

control. This is a design parameter. However, increasing also increases thecontrol effort.


62/80

55

Figure 30. Engine response to accessory load with pressure control only throttle and accessory.

Figure 31. Engine response to accessory load with pressure control only pressure and speed.


63/80

56

The goal of the torque management strategy is to maintain the torque to the

driveline through these short transients. This would have the effect of keeping

the engine speed constant.

Jankovic et. al [10] designed a feed forward control strategy for the electronic

throttle on an engine with variable cam timing. This control was designed to

cancel out the dynamics in cylinder flow during changes in cam timing. The

strategy used by Heintz et. al. [7] uses ignition timing and air to fuel ratio to

eliminate these types of torque transients. This strategy is more general and

applicable to a variety of applications requiring torque management. This

general framework has been used to develop the strategy discussed in the

following sections.

5.5.1 Derivation of the Control Laws

As shown in equation 2.4, the engine torque is a function of cylinder air flow, air

to fuel ratio, and ignition timing. In the previously derived torque controllers of

sections 5.3 and 5.4, it has been assumed that the low level air to fuel ratio

control and ignition timing control are working properly and in such a way that

their effects on engine torque can be assumed constant. In the torque

management strategy, the ignition timing and, if necessary, the air to fuel ratio

will be changed to maintain the torque to the driveline until the air flow can be

adjusted to produce the desired torque. The amount of torque change produced

by each of these actuators is limited by pre-ignition of the fuel, engine emissions,

and other component considerations. Also, the time spent away from the optimal

ignition timing and the optimal air to fuel ratio is limited due to engine emissionsand other component considerations.

From equation 2.4, the engine torque is given by


64/80

57

( ) ( )

eng

cylT

comb

SPIAFImCTQ

=

(5.41)

One option for this problem is to split it into two parts. First, the throttle can be

controlled to achieve the air flow required to achieve the desired torque. For this

control, it can be assumed that the effects of air to fuel ratio and ignition timing

are constant. The difference between the actual driveline torque and the desired

driveline torque (TQ) will be controlled to zero using the ignition timing and the

air to fuel ratio.

The desired effects of the ignition timing and the air to fuel ratio on engine torque

are calculated using the relationship

xTQTQoptimal,comb

==

(5.42)

Using the known functions of SPI() and AFI(), the desired ignition timing and

air to fuel ratio could be calculated to achieve the desired value for x.

However, it would seem that, as with the idle speed control problem, what is

really desired is to use and to maintain engine speed (or acceleration)

through the transient. Using the sliding mode control methodology discussed in

section 5.2, a sliding surface is defined as

desS = (5.43)

where des is taken to be the engine speed before the strategy is started. Thederivative of the sliding surface, assuming a constant desired engine speed, is

given by


65/80

58

( )

( ) ( ) ( )

( )

+

=

=

=

=

impacc2eng1

mexhm,

disp

eng

cylT

eng

impaccfricpumpcomb

eng

des

TQTQCC

PP4

V

SPIAFImC

I

1

TQTQTQTQTQI

1

S

(5.44)

In equation 5.44, the desired engine acceleration is assumed to be zero. This is

not a requirement for the strategy.

The control goal is to use the ignition timing, , and the air to fuel ratio, , tocontrol the engine speed. However, these control inputs will not be used in

tandem. First, the ignition timing, , will be used to control the engine speed. If

reaches some predefined limit, will be used to control engine speed with left

at the saturated value. Thus, this is not a true multi-input control problem, but a

system that can be decoupled. The individual controllers for ignition timing and

air to fuel ratio are derived using equation 5.44 and are given by

( )[ ]

( )

++

++

= 1

AFImC

TQTQTQ

TQSsgnI

0.00015

1

stoiccylT

eng

pumpfricacc

impeng

(5.45)

and

( )[ ]

( )

++

++

+= 1

SPImC

TQTQTQ

TQSsgnI

0.0156

113.6

satcylT

eng

pumpfricacc

impeng

(5.46)

where stoic is the stoichiometric air to fuel ratio, and sat is the saturated value of

the ignition timing.


66/80

59

5.5.2 Selection of Pressure Control or Torque Control Strategy

Control strategies for manifold pressure and driveline torque were derived in

sections 5.3 and 5.4. Before the torque management strategy can be

implemented, a torque control strategy must be selected.

For the driveline torque control strategy, the engine torque sensor has been

assumed to measure crankshaft torque. This measurement includes the effects

of the engine combustion torque, friction torque, pumping torque, and all

accessory loads. As stated, in this derivation of the torque management

strategy, and are used to control the engine speed. Maintaining engine

speed is equivalent to maintaining constant torque at the driveline. So, if the

throttle is used to control the driveline torque and and are actuated to control

engine speed, the error between desired and actual driveline torque is

eliminated. Thus, there is no error to drive the throttle. This would lead to and

remaining away from the optimal ranges for long periods of time. This is

unacceptable performance. Thus, the torque control is not a legitimate option for

the torque management strategy derived here.

If instead, the throttle is used to control manifold pressure, the effect of ignition

timing and air to fuel ratio on combustion torque does effect the throttle control.

Thus, the pressure control strategy is proper for implementing the torque

management strategy. Also, use of this strategy will not require a torque sensor.

The disadvantage is a larger amount of calibration required to get a proper

conversion from desired torque to desired manifold pressure for all engine

operating conditions.


67/80

60

5.5.3 Results

Figures 32 to 34 show the results of the torque management strategy when a 7

N.m accessory load is removed from the engine. In this case, the ignition timing

has enough control authority to achieve the objective. At two seconds, the

accessory load is removed from the engine. The pressure setpoint immediately

changes. Over a third of a second, the throttle adjusts to achieve the desired

manifold pressure. As desired, the engine speed (shown in Figure 33) remains

approximately constant through the transient. However, Figure 34 shows the

control input required to achieve this response. This type of rapid chatter in the

control input is undesirable and unrealizable in implementation.

This chatter is due to the high gain used in the engine speed control. Since this

strategy requires strict control of engine speed, a high gain is used to rapidly

drive the system to the control surface. As shown in Figure 34, the ignition timing

saturates for a short period of time at 20 degrees. During this time, the system

has not reached the control surface. Once the control surface is reached, the

control input begins to chatter rapidly. A reduction of the control gain would

reduce the peak to peak value of the chatter, but would cause the system to take

longer to reach the control surface.


68/80

61

Figure 32. Torque management with discontinuous ignition timing control law throttle and accessory.

Figure 33. Torque management with discontinuous ignition timing control law pressure and speed.


69/80

62

Figure 34. Torque management with discontinuous ignition timing control law ignition timing.

In order to eliminate the chatter, a smooth sliding mode control law is

investigated. In this case, a smooth control law is chosen such that

2SSS (5.48)

Although perfect tracking will not be achieved, the high frequency chatter will be

reduced with this control law.

Figures 35 and 36 show the results using the smooth control law. As shown, the

performance is similar to the discontinuous control law. However, the chatter of

the ignition timing is greatly reduced. Also, since the control gain is still high, the

time that it takes the system to reach the control surface remains the same.


70/80

63

Figure 35. Torque management with smooth ignition timing control law pressure and speed.

Figure 36. Torque management with smooth ignition timing control law ignition timing.


71/80


72/80

65

Figure 38. Torque management results using only ignition timing to controlengine speed ignition timing and air to fuel ratio.

Figures 39 and 40 show the response to a 10 N.m load being removed from the

engine. Again, smoothed control laws are used both for the ignition timing and

the air to fuel ratio control. As shown, during the portion of time the ignition

timing is saturated, the air to fuel ratio is controlled. Once the system has

approached the control surface to a point at which air to fuel ratio control is

unnecessary, the air to fuel ratio is set to its optimal value and ignition timing is

used to achieve the control goal. As shown, engine speed is maintained

approximately constant throughout the transient.


73/80

66

Figure 39. Torque management results using both ignition timing and air to fuelratio to control engine speed pressure and speed.

Figure 40. Torque management results using both ignition timing and air to fuelratio to control engine speed ignition timing and air to fuel ratio.


74/80

67

6 Application to the MoBIES Project

The goal of the Model Based Integration of Embedded Systems (MoBIES)

program is to develop tools to aid the control developer in moving from a

controller implemented in a simulation environment to a controller implemented

on a target platform. The end goals are to have greater re-use of code and a

decrease in implementation time. The tools under development for this program

include tools that perform hybrid system verification analysis, timing and

schedulability analysis, and automatic code generation tools. The Ford Taurus

engine was used as an open experimental platform on which to test the

generated control code before and after all analyses had been performed. This

was used as a way to test the usability and applicability of the developed tools.

The air to fuel ratio and torque management problems were used as test cases

for the MoBIES technologies. The MoBIES program and the model based

methodology for embedded system design are discussed in detail in [13].

7 Future Work

The sliding mode control laws have been derived using discontinuous control. If

this method of engine torque management is found to be useful, an investigation

into the use of smoothed control laws or other control methodologies may be

useful. In particular, some introductory work has been done in applying linear

robust control methodologies, such as HHHH [3] to this problem. Initial work in this

area has been done by Ingram et. al. [9]. It is believed that use of these types of

linear control methodologies could provide excellent performance even in the

presence of model uncertainty.

As stated, the plant model used throughout this derivation does not include the

effects of EGR. Since EGR would act to displace air in the intake manifold, this

effect would significantly change the model, the estimators for cylinder flow, and


75/80

68

the controller derivations. Extending the torque management strategy to deal

with these types of engines would be beneficial.

This analysis has showed the benefits of torque management and introduced a

strategy for implementation. At this point the strategy should be expanded to

include the complete operating range of the engine. This would require

additional calibration and a map of pedal position to desired engine torque must

be selected. It is probable that the desired engine torque would be a function of

engine speed. This adds to the complexity, but does not change the form of the

control strategy.

As stated, most of the control derivations assume a perfect model of the plant

with only parameter uncertainty. While a complete uncertainty analysis can be

made for each control law, it is believed that the control strategy should be tested

on a more complete engine model and eventually an actual engine. The engine

model used in this control derivation is a simple model which eliminates some of

the complex behavior of the engine. While this type of model is useful for

implementation in real time, the engine has much more complex dynamics. The

performance of the controller will depend more on the unmodeled, or simplified,dynamics than the parameter uncertainty of the model.

Finally, a complete test of the control logic should be made. If possible, hybrid

system verification tools (such as those developed in the MoBIES program)

should be used to guarantee proper operation of the control logic for all engine

operating conditions. At the very least, potential problems should be seen when

the complete strategy is run over the entire engine operating range.


76/80

69

8 Summary

It was shown that, in the presence of model uncertainty, an open loop estimate of

the cylinder air flow using a mass air flow sensor was more accurate than one

using a manifold pressure sensor. A closed loop observer for the cylinder air

flow, using both a throttle flow sensor and a manifold pressure sensor, was

developed to obtain a better estimate in the presence of model uncertainty. The

sliding observer achieved excellent tracking in the presence of some types of

uncertainty. However, error in the cylinder pumping model leads to a

degradation of the estimator performance as compared to the open loop

estimator using a throttle flow sensor.

Two torque control strategies were developed. These control strategies used the

electronic throttle actuator to control the manifold pressure and the driveline

torque. Control of torque would require either a torque sensor or some torque

estimation algorithm. Both control strategies were similar in operation although

the pressure control was more direct in that pressure is a system state and thus

its derivative is readily available. However, by controlling torque directly, model

uncertainty in the combustion torque model is directly accounted for in thecontrol. An adaptive controller was developed to adapt on the engine torque

constant.

A torque management strategy was developed using the ignition timing and the

air to fuel ratio. It was shown that using the pressure control as a means of

controlling engine torque is more easily implemented in the torque management

strategy. Also, smooth sliding control laws were derived for both ignition timing

and air to fuel ratio control. It was found that the smoothed controllers gave

acceptable performance in controlling engine speed.


77/80

70

9 Ackno

lamberson ms thesis

Documents