Robust air-to-fuel ratio and boost pressure controller design for EGR and VGT systems using QFT method Inseok Park Advised by prof. Myoungho Sunwoo November,

Robust air-to-fuel ratio and boost pressure controller design for EGR

and VGT systems using QFT method

Inseok Park

Advised by prof. Myoungho SunwooNovember, 2012

Department of Automotive Engineering, Hanyang university

- 2 -

Copyright @ ACE Lab, All rights reserved

▶ Introduction

▶ Part I. Robust feedback design Control loops design using QFT method Decoupler design

▶ Part II. Model-based feed-forward design Mean-value engine model Feedforward design using model inversion technique

▶ Conclusions

Contents

- 3 -


▶ Increasing complexity of clean diesel engine control system

Background

DPF 제어

고압EGR 제어

커먼레일 제어

터보차저제어

고압 EGR 제어

커먼레일 제어

EURO-5 EURO-6 and FurtherEURO-4

NOx [g/km]

PM [g/km]

0.25

0.18

0.0250.005

0.08

0.05

0.50EURO-3 (2000)

EURO-6 (2014)

EURO-5 (2009)

EURO-4 (2005)

EUROComplexity

커먼레일 제어

연소압력기반 제어

고압 EGR 제어

저압 EGR 제어

SCR 제어

터보차저 제어

DPF 제어

LNT 제어

피에조인젝터 제어

- 4 -


▶ Exhaust gas recirculation (EGR)

Background

uEGR

WEGR

- 5 -


▶ Exhaust gas recirculation (EGR)

Background

NOx reduction- Combustion temperature ▼- Oxygen availability ▼

Excessive EGR- NOx vs. PM tradeoff - Combustion instability

Fresh charge

Fresh charge

Burned gas

- 6 -


▶ Variable geometry turbocharger (VGT)

Background

uVGT

Pint

- 7 -


▶ Variable geometry turbocharger (VGT)

Background

Power increase- Fresh charge ▲

- Fuel mass ▲

Slow response- Smoke limit function

- Limitation of driv-ability

Fresh charge

Fuel mass

- 8 -


▶ Difficulties in EGR and VGT control problems

Background

Two feedback loops be-tween exhaust and intake

manifolds

Mass flow path(Pressure ratio, ef-fective valve area)

Power path(T/C dynam-

ics)

- 9 -


▶ EGR rate* Direct measurement / unmeasurable Accuracy & reliability problems of estimator

▶ Mass air flow rate measured from HFM sensor Indirect measurement / measurable (on-board sensor) Drift problems / poor SNR*

▶ Air-to-fuel ratio Indirect measurement / measurable (on-board sensor) Robust to HFM, Injector drift Good SNR*

Related works - Performance variables for EGR

*EGR rate = Wegr / (Wcomp + Wegr), SNR: signal to noise ratio

- 10 -


▶ Model-based controller design (Sliding mode, Hinf, …) Limited access of on-line calibration

▶ Model-predictive approach High computational loads / unknown future disturbance Limited access of on-line calibration

▶ Soft-computing approach (Artificial neural-network) High computational loads / Limited access of on-line calibration

Related works - Control approach

There is still a large gap between theory and industry ap-

plicationsUse Gain-scheduled PID structure

How to design PID gains ?

How to compensate non-linearity and cross-coupling

effect?

- 11 -


▶ Proposition of design methodology for robust air-to-fuel ratio and boost pressure controller of EGR and VGT system

▶ Problem formulation Performance variables:

Air-to-fuel ratio(AFRexh), Boost pressure (Pint) Controller structure: Gain-scheduled PID structure

▶ Approaches Uncertainty problems: Quantitative feedback theory Cross-coupled problems: Static forward path decoupler Non-linearity compensation: Model-based feedforward design

Research objectives

- 12 -


Part I. Robust feedback design

- Control loops design using QFT method - Forward path decoupler design

- 13 -


▶ Multi-input multi-output control problem

Problem formulation

Air system Set-point generator

Air system MIMO

controller

Wf

Ne

AFRexh,des

Pint,des

Diesel engine

AFRexh

Pint

EGR valveLift controller

uEGR,desuEGREGR

valve

VGT vaneangle controller

uVGT,desuVGTVGT

vane

Scope

In-house developed con-troller

Smart actuator

11 12

int 21 22

( ) ( )

( ) ( )exh EGR

VGT

AFR uG s G s

P uG s G s

- 14 -


▶ Linear approximation of non-linear system Potentially large uncertainty Robustness problem

Problem statement (1)

Stationary measurements of G11, G22 @ 1750 rpm, 20 mg/str

Static gain contour (Ne =1750 [rpm],W

f =20 [mg/str])

55 60 65 70 75 80 85 90 95 100 10515

20

25

30

35

40

45

uEGR

[%, Close]

AF

Rex

h [

-]

uEGR

to AFRexh

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 10015

20

25

30

35

40

45

uVGT

[%, Close]

AF

Rex

h [

-]

uVGT

-> AFRexh

u

EGR =100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

55 60 65 70 75 80 85 90 95 100 105110

120

130

140

150

160

170

uEGR

[%, Close]

Pin

t [kP

a]

uEGR

to Pint

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 100110

120

130

140

150

160

170

uVGT

[%, Close]

Pin

t [kP

a]

uVGT

to Pint

uEGR

=100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

Static gain contour (Ne =1750 [rpm],W

f =20 [mg/str])

55 60 65 70 75 80 85 90 95 100 10515

20

25

30

35

40

45

uEGR

[%, Close]

AF

Rex

h [

-]

uEGR

to AFRexh

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 10015

20

25

30

35

40

45

uVGT

[%, Close]

AF

Rex

h [

-]

uVGT

-> AFRexh

u

EGR =100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

55 60 65 70 75 80 85 90 95 100 105110

120

130

140

150

160

170

uEGR

[%, Close]

Pin

t [kP

a]

uEGR

to Pint

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 100110

120

130

140

150

160

170

uVGT

[%, Close]

Pin

t [kP

a]

uVGT

to Pint

uEGR

=100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

- 15 -




1000

2000

3000

4000

0

20

40

60

800

100

200

300

Ne [rpm] W

f [mg/str]

Pin

t [kP

a]

1000

2000

3000

4000

0

20

40

60

800

100

200

300

Ne [rpm] W

f [mg/str]

Pin

t [kP

a]1000

2000

3000

4000

020

4060

800

20

40

60

80

Ne [rpm] W

f [mg/str]

AF

Rex

h [

-]

1000

2000

3000

4000

020

4060

800

20

40

60

80

Ne [rpm] W

f [mg/str]

AF

Rex

h [

-]

Pint set-point LUTAFRexh set-point LUT

- 16 -




Static gain contour of G11(s), G22(s) @ 1750 rpm, 20 mg/str

0.6

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to AFRexh

)

70 80 90 10070

75

80

85

90

95-0.8

0 0.2

0.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to AFRexh

)

60 70 80 90 10070

75

80

85

90

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to Pint

)

70 80 90 10070

75

80

85

90

95

0.8

1 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to Pint

)

60 70 80 90 10070

75

80

85

90

0.6

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to AFRexh

)

70 80 90 10070

75

80

85

90

95-0.8

0 0.2

0.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to AFRexh

)

60 70 80 90 10070

75

80

85

90

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to Pint

)

70 80 90 10070

75

80

85

90

95

0.8

1 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to Pint

)

60 70 80 90 10070

75

80

85

90

- 17 -


▶ Large parameter uncertainty problem

Design of two SISO control loops using QFT, independently▶ Cross-coupled dynamics problem

Design of forward path static decoupler

▶ Target engine operating points

Design overview

0 200 400 600 800 10000

500

1000

1500

2000

2500

Ne [

rpm

]

time[sec]0 200 400 600 800 1000

0

5

10

15

20

25

30

35

40

45

Wf [

mg

/str

]

500 1000 1500 2000 25000

5

10

15

20

25

30

35

40

45

Ne [rpm]

Wf [

mg

/str

]

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

NEDC trajectoryDesign operation points

Sample design point(1750 rpm, 20 mg/str)

Ne and Wf trajectories of NEDC

- 18 -


▶ Design framework for robust controller design Parametric uncertainty mapped on Nichols chart Bounds of controller requirements on Nichols chart

Quantitative feedback theory

0.40.6

0.81

1.2

0.3

0.35

0.4

0.45

0.5

0.55

0.60

0.2

K

Td

Structure parameter uncer-tainty

( )1

dsTK

G s es

Template on Nichols chart

-280 -260 -240 -220 -200 -180 -160

-22

-21

-20

-19

-18

-17

-16

-15

-14

-13

-20 dB

2.00 [Hz]

- 19 -


▶ Two DOF controller structure Compensator, Prefilter

▶ Straight-forward design process

Quantitative feedback theory

- 20 -


▶ Plant model: 1st order plus time-delay (FOPTD)

▶ Measurement conditions for parameter identification

Parameter identification

Input variables Stationary condition Dynamic condition

uEGR70 ~ 100 (grid size: 5)

[%, close] 24 Step patterns

uVGT70 ~ 95 (grid size:5)

[%, close] 24 Step patterns

( )1

dsTK

G s es

- 21 -


▶ Stationary measurements results


60 70 80 90 100

20

25

30

35

40

45

uEGR

[%, Close]

AF

Rex

h [-]

K11

(uEGR

to AFRexh

)

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 10015

20

25

30

35

40

45

uVGT

[%, Close]

AF

Rex

h [-]

K12

(uVGT

to AFRexh

)

u

EGR =100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

60 70 80 90 100110

120

130

140

150

160

170

uEGR

[%, Close]

Pin

t [kP

a]

K21

(uEGR

to Pint

)

uVGT

=70

uVGT

=75

uVGT

=80

uVGT

=85

uVGT

=90

uVGT

=95

65 70 75 80 85 90 95 100110

120

130

140

150

160

170

uVGT

[%, Close]

Pin

t [kP

a]K

22 (u

VGT to P

int)

uEGR

=100

uEGR

=95

uEGR

=90

uEGR

=85

uEGR

=80

uEGR

=75

uEGR

=70

uEGR

=65

uEGR

=60

- 22 -


▶ Stationary measurements results


0.2

0.4

0.6

0.6

0.81 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to AFRexh

)

70 80 90 10070

75

80

85

90

95-0.8

-0.2

0 0.2

0.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to AFRexh

)

60 70 80 90 10070

75

80

85

90

0.2

0.2

0.4

0.81 1.2

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to Pint

)

70 80 90 10070

75

80

85

90

950

0.2

0.4

0.60.8

1 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

] Static gain (u

VGT to P

int)

60 70 80 90 10070

75

80

85

90

- 23 -


▶ Identification results at sample design operating point


PlantModel Parameter Value range Nominal value

G11 (s)

K11 0.23 ~ 0.64 0.51

0.4329 ~ 0.4971 0.4971

Td11 0.1229 ~ 0.2429 0.2429

G12 (s)

K12 -0.38 ~ 0.13 -0.29

0.2573 ~ 0.4913 0.4913

Td12 0.114 ~ 0.16 0.16

G21 (s)

K21 0.30 ~ 1.23 0.92

0.7343 ~ 0.8986 0.8986

Td21 0.0357 ~ 0.05 0.05

G22 (s)

K22 0.14 ~ 1.29 0.35

0.91 ~ 1.0138 1.0138

Td22 0.1038 ~ 0.1408 0.1408

1st Loop design using QFT method

2nd Loop design using QFT method

uEGR linearization range: 70 ~ 95 [%,-close]

uVGT linearization range: 75 ~ 95 [%, close]

- 24 -


▶ Point-wise frequency response analysis

Step1: Frequency vector

Analysis of ROI Freq. array

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

time[s]

[rpm

]

Engine speed

0 200 400 600 800 1000 12000

5

10

15

20

25

time[s]

[-]

0 1 2 3 4 50

1

2

3

4

5

6

Frequency[Hz]

Mag

nitu

de

FFT of

1 2 3 4 5 6 7 82

2 0.01 0.05 0.1 0.2 0.4 0.5 1 2

f f f f f f f f

Power spectrum analysis of AFR during NEDC ex-periment

- 25 -


▶ Robust stability specification Peak response of complementary sensitivity function(T) for all freq.

Step2: Desired controller specifications (1)

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

Step Response

time (sec)

am

plit

ud

e

Mp= 1.1 (GM = 5.61 dB, PM = 54 deg)*

*Maximum peak criteria

, [0, )1

where, is a peak responsein magnitude

p

p

G j C jT j M

G j C j

M

- 26 -


▶ Robust stability bound on Nichols chart


- 27 -


▶ Robust reference tracking specification Design of acceptable time responses models

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

Tracking bound model

time (sec)

am

plit

ud

e

TR

U

TR

L


- 28 -


▶ Robust reference tracking specification Upper bound model: %OS (10%), Tr (0.7 sec), Min Td (0.13 sec) Lower bound model: Ts (3.5 sec), Max Td (0.25 sec)


0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

Tracking bound model

time (sec)

am

plit

ud

e

TR

U

TR

L

1

0.132

1.017 5.087

2.667 5.087U sR

sT s e

s s

1

0.253 2

21.95

12.67 28.86 21.95L sRT s e

s s s

- 29 -


▶ Robust reference tracking bounds on Nichols chart


Higher than solid lines

Lower than dashed lines

- 30 -


-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

Nichols Chart

Open-Loop Phase (deg)

Ope

n-Lo

op G

ain

(dB

)

▶ Composite bounds and nominal plant responses

Step3: Loop shaping

Nominal plant, G11,0(s)

- 31 -


-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

▶ Off-line tuning of PID gains using bounds on Nichols chart

Step3: Loop shaping

-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

0.01[Hz]

0.05[Hz]

0.10[Hz]

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]

0.40[Hz]0.50[Hz]

1.00[Hz]2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)


1

4.2( ) 2.04 0.24C s s

s

Nominal Loop func-tion, L11,0(s) = G11,0(s)C1(s)

- 32 -


-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

▶ Off-line tuning of PID gains using bounds on Nichols chart

Step3: Loop shaping

-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

0.01[Hz]

0.05[Hz]

0.10[Hz]

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]

0.40[Hz]0.50[Hz]

1.00[Hz]2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

Nominal Loop func-tion, L11,0(s) = G11,0(s)C1(s)

GM: 10.96 dB

PM: 68.98 deg


1

4.2( ) 2.04 0.24C s s

s

- 33 -


-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

▶ Design tradeoff between performance and robustness

Step3: Loop shaping

-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

0.01[Hz]

0.05[Hz]

0.10[Hz]

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]

0.40[Hz]0.50[Hz]

1.00[Hz]2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

-315 -270 -225 -180 -135 -90 -45 0-40

-30

-20

-10

0

10

20

30

40

50

60

0.01[Hz]

0.05[Hz]

0.10[Hz]

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

-40 dB

0.20[Hz]0.40[Hz]

0.50[Hz]1.00[Hz]

2.00[Hz]

0.01[Hz]

0.05[Hz]

0.10[Hz]

0.20[Hz]

0.40[Hz]0.50[Hz]

1.00[Hz]2.00[Hz]

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

GM: 7.86 dB

PM: 64.74 deg

Nominal Loop func-tion, L11,0(s) =

G11,0(s)C1(s) (High gain case)

1

6( ) 2.9 0.3C s s

s

- 34 -


▶ Fragility analysis within parameter uncertainty

Step3: Loop shaping

-360 -315 -270 -225 -180 -135 -90 -45 0-20

-10

0

10

20

30

40

6 dB

3 dB

1 dB

0.5 dB

0.25 dB

0 dB

-1 dB

-3 dB

-6 dB

-12 dB

-20 dB

Nichols Chart


Ope

n-Lo

op G

ain

(dB

)

0.01 [Hz]0.05 [Hz]0.10 [Hz]0.20 [Hz]0.40 [Hz]0.50 [Hz]1.00 [Hz]2.00 [Hz]

- 35 -


▶ F1(s) design with min/max closed-loop responses in bode plot

Step4: Prefilter design

1 3 2

0.2738 1

0.01878 0.1994 0.7658 1

sF s

s s s

Bode plot of T1(s)

10-1

100

101

-25

-20

-15

-10

-5

0

5

Mag

nitu

de

(dB

)

Frequency (rad/sec)

Nichols plot

11 11 1min,max

11 1 min,max

( ) ( )( )

1 ( ) ( )

G s C sT s F s

G s C s

CL response w/o prefilter

10-1

100

101

-25

-20

-15

-10

-5

0

5

Mag

nitu

de

(dB

)

Frequency (rad/sec)

Nichols plot

Tracking bounds

CL resp. with prefilter

- 36 -


▶ F1(s) design with min/max closed-loop response in bode plot

Step4: Prefilter design

1 3 2

0.2738 1

0.01878 0.1994 0.7658 1

sF s

s s s

11 11 1min,max

11 1 min,max

( ) ( )( )

1 ( ) ( )

G s C sT s F s

G s C s

Step responses within parameter uncertainty region

0 1 2 3 4 5 6-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (sec)

Nichols plot

Tracking bounds

- 37 -


▶ Frequency vector

▶ Desired controller specifications Robust stability (Same as 1st loop)

– Complementary sensitivity function’s peak response Mp: 1.1

– GM: 5.61db, PM: 54 deg

Robust reference tracking (Slower than 1st loop)– Upper bound: %OS (6%), Tr (0.95 sec)– Lower bound: Ts (5.8 sec)

2nd Loop design (1)

2 1 2 3 4 5 62

2 0.01 0.05 0.1 0.2 0.4 0.5

f f f f f f

2

0.12

0.8295 3.733

2.667 3.733U sR

sT s e

s s

2

0.153 2

2.37

4.6 5.59 2.37L sRT s e

s s s

- 38 -


▶ Loop shaping results:

2nd Loop design (2)

C2(s)’s Loop shaping re-sults

C2(s)’s Fragility analysis

2

4.5( ) 3.987 0.1973C s s

s

- 39 -


▶ Prefilter design results

2nd Loop design (3)

Bode plot of T2(s) with F2(s)

Step responses within parameter uncertainty region

2 3 2

0.2 1

0.054 0.3663 0.9922 1

sF s

s s s

- 40 -


Part I. Robust feedback design

- Control loops design using QFT method - Forward path decoupler design

- 41 -


▶ Static gain contour at Ne = 1750 rpm, Wf = 20 mg/str

Measurements of cross-coupling character-istics

0.2

0.4

0.6

0.6

0.81 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to AFRexh

)

70 80 90 10070

75

80

85

90

95-0.8

-0.2

0 0.2

0.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to AFRexh

)

60 70 80 90 10070

75

80

85

90

0.2

0.2

0.4

0.6

0.81 1.2

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uEGR

to Pint

)

70 80 90 10070

75

80

85

90

950

0.2

0.4

0.60.8

1 1.2

1.4

uEGR

[%, close]

uV

GT [

%, c

lose

]

Static gain (uVGT

to Pint

)

60 70 80 90 10070

75

80

85

90

*RNGA: Relative Normalized Gain Array

- 42 -


▶ RNGA* analysis result at sample design point Poor input-output paring condition

▶ RNGA analysis of entire operating points

Measurements of cross-coupling character-istics

*RNGA: Relative Normalized Gain Array

0.3260 0.6740

0.6740 0.3260

- 43 -


▶ Forward path static decoupler Attenuation of the off-diagonal gains using static gain inversion Decoupling interactions, approximately

Decoupler design

1

11,0 12,0

21,0 22,0

0 0 0

0 0 0

0.7860 0.65

2.0660 1.1453

G GW

G G

Control input scaling parame-ters

11 12 11 12

21 22 21 22ideal

G s G s W WTFM I

G s G s W W

- 44 -


▶ Repetition of proposed design steps for 15 operating points▶ Implementation results

LUT-based set-point generator and feed-forward controller Prefilters: (F1, F2)

Gain scheduled PID controllers (C1, C2)

Gain scheduled decouplers (W11, W12, W21, W22)

Implementation

- 45 -


Experimental results

- 46 -


▶ Target plant: Mass produced R2.2 Liter diesel engine

Experimental setup

Engine test cell

Common rail & Fuel injection

(MeUn*, PCV*, piezo in-jector)

Exhaust air path (VGT & EGR)

Intake air path(VSA* & ACV*)

MeUn*: Metering unitPCV*: Pressure control valve

RPS*: Rail pressure sensorVSA*: Variable swirl actuator

ACV*: Air control valve

- 47 -


▶ Test environment configuration

Experimental setup

- 48 -


▶ Implementation environment Engine management system (EMS) platform

Experimental setup

Hardware platform- Production type 32-bit microcontroller (MPC5554)- Target engine compatible I/O configuration

Software platform- Standardized architecture (AU-TOSAR-Lite)- Model-based SW development (Simulink)

- 49 -


▶ AFRexh step responses at Ne = 1750 rpm, Wf = 20 mg/str Three fixed VGT positions

Experimental results – SISO case

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.2

0.4

0.6

0.8

1

1.2

Time [sec]

No

rma

lize

d A

/Fe

xh [

-]

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

70

80

90

100

Time [sec]

uE

GR

[%

, c

los

e]

uVGT

= 85%

uVGT

= 90%

uVGT

= 95%

Filtered desired valueu

VGT = 85%

uVGT

= 90%

uVGT

= 95%

TR

U

, TR

L

Tracking bound models

- 50 -


▶ AFRexh step responses at Ne = 1750 rpm, Wf = 20 mg/str

Experimental results – MIMO case (1)

10 12 14 16 18 20

26

27

28

29

30

31

32

33

34

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20128

129

130

131

132

133

134

135

136

137

138

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2075

80

85

90

95

time[sec]

uV

GT[%

,clo

se]

TrackingBounds

Desired value

Prefiltered desired value

QFT design without decoupler

Desired valuePrefiltered desired value


10 12 14 16 18 20

26

27

28

29

30

31

32

33

34

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20128

129

130

131

132

133

134

135

136

137

138

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2075

80

85

90

95

time[sec]

uV

GT[%

,clo

se]

TrackingBounds

Desired value

Prefiltered desired value


Desired valuePrefiltered desired value


10 12 14 16 18 20

26

27

28

29

30

31

32

33

34

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20128

129

130

131

132

133

134

135

136

137

138

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2075

80

85

90

95

time[sec]

uV

GT[%

,clo

se]

TrackingBoundsDesired valuePrefiltered desired valueQFT design without decouplerQFT design with decouplerTuned by trial and error without decoupler

Desired valuePrefiltered desired valueQFT design without decouplerQFT design with decouplerTuned by trial and error without decoupler

- 51 -


▶ Pint step responses at Ne = 1750 rpm, Wf = 20 mg/str

Experimental results (2)

10 12 14 16 18 20

24

25

26

27

28

29

30

31

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20

131

132

133

134

135

136

137

138

139

140

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2080

85

90

95

100

time[sec]

uV

GT[%

,clo

se]

Desired value

Prefiltered desired valueQFT design without decoupler

TrackingBoundsDesired valuePrefiltered desired valueQFT design without decoupler

10 12 14 16 18 20

24

25

26

27

28

29

30

31

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20

131

132

133

134

135

136

137

138

139

140

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2080

85

90

95

100

time[sec]

uV

GT[%

,clo

se]

Desired valuePrefiltered desired valueQFT design without decouplerQFT design with decoupler

TrackingBoundsDesired valuePrefiltered desired valueQFT design without decouplerQFT design with decoupler

10 12 14 16 18 20

24

25

26

27

28

29

30

31

time[sec]

AF

Rex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se]

10 12 14 16 18 20

131

132

133

134

135

136

137

138

139

140

time[sec]

Pin

t [kP

a]

10 12 14 16 18 2080

85

90

95

100

time[sec]

uV

GT[%

,clo

se]

Desired valuePrefiltered desired valueQFT design without decouplerQFT design with decouplerTuned by trial and error without decoupler

TrackingBoundsDesired valuePrefiltered desired valueQFT design without decouplerQFT design with decouplerTuned by trial and error without decoupler

- 52 -


▶ AFRexh step responses of entire operating points


10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d A

FR

ex

h [

-]

10 12 14 16 18 2070

80

90

100

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

time [sec]

P

int [

kP

a]

10 12 14 16 18 2070

75

80

85

90

95

time [sec]

uV

GT [

%,

clo

se

]

Desired valuePrefiltered desired value1500 [rpm], 10 [mg/str]1500 [rpm], 15 [mg/str]1500 [rpm], 20 [mg/str]1500 [rpm], 25 [mg/str]1500 [rpm], 30 [mg/str]


10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d A

FR

ex

h [

-]

10 12 14 16 18 20

60

70

80

90

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-2

-1.5

-1

-0.5

0

0.5

time [sec]

P

int [

kP

a]

10 12 14 16 18 2070

75

80

85

90

95

time [sec]

uV

GT [

%,

clo

se

]



10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d A

FR

ex

h [

-]

10 12 14 16 18 2065

70

75

80

85

90

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

time [sec]

P

int [

kP

a]

10 12 14 16 18 2075

80

85

90

95

time [sec]

uV

GT [

%,

clo

se

]



- 53 -


▶ Pint step responses of entire operating points


10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

time [sec]

A

FR

ex

h [

-]

10 12 14 16 18 20

50

60

70

80

90

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d P

int [

-]

10 12 14 16 18 2080

85

90

95

100

time [sec]

uV

GT [

%,

clo

se

]



10 12 14 16 18 20

-2

-1

0

1

2

3

time [sec]

A

FR

ex

h [

-]

10 12 14 16 18 2060

70

80

90

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d P

int [

-]

10 12 14 16 18 2080

85

90

95

100

time [sec]

uV

GT [

%,

clo

se

]



10 12 14 16 18 20-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

time [sec]

A

FR

ex

h [

-]

10 12 14 16 18 2065

70

75

80

85

time [sec]

uE

GR

[%

, c

los

e]

10 12 14 16 18 20-0.2

0

0.2

0.4

0.6

0.8

1

time [sec]

No

rma

lize

d P

int [

-]

10 12 14 16 18 2085

90

95

100

time [sec]

uV

GT [

%,

clo

se

]



- 54 -


▶ Transient responses


0 10 20 30 40 50 60 70 80

20

25

30

35

40

45

time [sec]

AF

Re

xh [

-]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 90110

120

130

140

150

time [sec] P

int [

kP

a]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 9060

80

100

uE

GR

[%

, c

los

e]

time [sec]

0 10 20 30 40 50 60 70 80 9085

90

95

uV

GT [

%,

clo

se

]uEGR

uVGT0 200 400 600 800 1000

0

500

1000

1500

2000

2500

Ne [

rpm

]

time[sec]0 200 400 600 800 1000

0

5

10

15

20

25

30

35

40

45

Wf [

mg

/str

]

500 1000 1500 2000 25000

5

10

15

20

25

30

35

40

45

Ne [rpm]

Wf [

mg

/str

]

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

NEDC trajectoryDesign operation points

0 10 20 30 40 50 60 70 80 9020

25

30

35

40

45

50

time [sec]

AF

Rex

h [

-]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 90110

120

130

140

150

160

time [sec] P

int [

kP

a]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 9040

60

80

100

uE

GR

[%

, c

los

e]

time [sec]

0 10 20 30 40 50 60 70 80 9080

85

90

95

uV

GT [

%,

clo

se

]uEGR

uVGT

0 10 20 30 40 50 60 70 80 9020

25

30

35

40

45

50

time [sec]

AF

Re

xh [

-]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 90120

130

140

150

160

170

180

time [sec] P

int [

kP

a]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 9060

70

80

90

uE

GR

[%

, c

los

e]

time [sec]

0 10 20 30 40 50 60 70 80 9080

85

90

95

uV

GT [

%,

clo

se

]

uEGR

uVGT

- 55 -


▶ Transient responses Performance limitation

due to the phase lag of the EGR valve controller


0 10 20 30 40 50 60 70 80 9020

25

30

35

40

45

50

time [sec]

AF

Rex

h [

-]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 90110

120

130

140

150

160

time [sec] P

int [

kP

a]

Desired value

Measured value

0 10 20 30 40 50 60 70 80 9040

60

80

100

uE

GR

[%

, c

los

e]

time [sec]

0 10 20 30 40 50 60 70 80 9080

85

90

95

uV

GT [

%,

clo

se

]uEGR

uVGT

1750 rpm case

8 9 10 11 12 13 14 1530

35

40

45

time [sec]

AF

Re

xh [

-]

Desired value

Measured value

8 9 10 11 12 13 14 1550

60

70

80

time [sec]

uE

GR

[%

, c

los

e]

uEGR,des

uEGR

18 19 20 21 22 23 24 2525

30

35

time [sec]

AF

Re

xh [

-]

Desired value

Measured value

18 19 20 21 22 23 24 2565

70

75

80

85

time [sec]

uE

GR

[%

, c

los

e]

uEGR,des

uEGR

28 29 30 31 32 33 34 3522

24

26

28

time [sec]

AF

Re

xh [

-]

Desired value

Measured value

28 29 30 31 32 33 34 3575

80

85

90

time [sec]

uE

GR

[%

, c

los

e]

uEGR,des

uEGR

- 56 -


Part II. Model-based feed-forward design

- 57 -


▶ Why the feed-forward controller is required? Limited bandwidth of feedback controlled system due to slow, time-

delay dynamics of EGR and VGT system Compensating non-linear behavior

▶ Problems in designing feed-forward controller for EGR and VGT system Conventional: Look-up table based feed-forward design

– LUTs are obtained from steady state experiments– In transient, each actuator FF control input is generated without the consid-

erations of physical interactions

Proposed: Model-based feed-forward design– Physical model-based feedforward controller– In transient, physically acceptable EGR valve and VGT vane trajectories

are generated

Overview

- 58 -


▶ Structure of model-based feed-forward controller

Overview

, ,,FF EGR FF VGTu u

Desired val-ues

Measured val-ues

Estimated val-ues

, ,,exh des int desAFR P

int, , , ,e ic compN T W P

intˆ ˆ ˆ ˆ, , , ,egr exh exhT T P T

- 59 -


▶ MVEM of AFRexh path

MVEM modeling (1)

00

( )[ ] ,

, ( 1), ( ), 14.88,

where is a index of enginecycle

comp f fc rg rg egr egrcyl

comp f rg egr

compfc rg cyl egr cyl

f

W W W Wk

W W W W

Wk k t

W

k

In-Cylinder mass balance model

Energy balance of intake mani-fold

int

int

1

p egr egr p ic comp p ie

egr p ie p ic compp egr

c T W c T W c T W

W c T W c T Wc T

EGR Poppet valve model

1 1

2 11

exh int integr e

exh exhexh

P P PW A

P PRT

- 60 -


▶ MVEM of Pint path

MVEM modeling (2)

120vol d int e

turb f egrint

V P NW W W

RT

Mass balance of exhaust mani-fold

1

1comp p amb intcomp

comp amb

comp tc turb

W c T PPwr

P

Pwr Pwr

Compressor power model

Turbine power model 1

1 turbdnturb turb p exh turb

exh

PPwr W c T

P

1

2 1

exhturb VGT

amb

refexh amb amb

ref exh exh exh

PW a u b c d

P

TP P P

P T P P

VGT vane valve model

- 61 -


▶ Modeling region (225 operating points) Ne [rpm]: 1500, 1750, 2000

Wf [mg/str]: 15, 20, 25

uVGT [%,close]: 82.5 ~ 95

uEGR [%,close]: Nominal value ±5,10 %

Steady state evaluation (1)

0 50 100 150 2001400

1600

1800

2000

2200

Ne [

rpm

]

0 50 100 150 20015

20

25

Wf [

mg

/str

]

0 50 100 150 20075

80

85

90

95

uV

GT [

%,c

lose

]

0 50 100 150 20050

60

70

80

90

100

uE

GR

[%

,clo

se]

- 62 -


▶ Evaluation results of EGR path


0 50 100 150 20055

60

65

70

75

80

85

90

95

100

uE

GR

[%

, cl

ose

]

uFF,EGR

uEGR

0 50 100 150 200-5

0

5

10

15

Test case

Err

or

Error

± 5%

- 63 -


▶ Evaluation results of VGT path


0 50 100 150 20078

80

82

84

86

88

90

92

94

96

uV

GT [

%,

clo

se]

uFF,VGT

uVGT

0 50 100 150 200-5

0

5

Test case

Err

or

[%]

Error

± 5%

- 64 -


▶ Feedback controller: small PID gains without decoupler

Pint step response at Ne = 1750 rpm, Wf = 20mg/str (1)

10 20 30 40 5029

30

31

32

33

34

35

36

time[sec]

AF

Re

xh [

-]

Desired value

Measured value

0 20 40 6083

84

85

86

87

88

89

90

time[sec]

uE

GR

[%

, c

los

e]

uEGR

uFF, EGR

10 20 30 40 50136

138

140

142

144

146

148

150

time[sec]

Pin

t [k

Pa

]

Desired value

Measured value

10 20 30 40 50

84

86

88

90

92

94

96

98

time[sec]

uV

GT [

%,

clo

se

]

uVGT

uFF, VGT

Kp Ki Kd

QFT design 2 4.2 0.24

MBD-FF case 1 0.4 0

Kp Ki Kd

QFT design 4 4.5 0.2

MBD-FF case 1.2 0.6 0

AFRexh control loop

Pint control loop

- 65 -


▶ EGR path


5 10 15 20 25 30 35 40 45 508

8.5

9

9.5

10

time[sec]

Ma

ss f

low

ra

te [

g/s

]

5 10 15 20 25 30 35 40 45 500.8

0.82

0.84

0.86

0.88

0.9

Pre

ssu

re r

atio

[-]

Wegr,des

Pint,des

/ Pexh,hat

5 10 15 20 25 30 35 40 45 501.3

1.35

1.4

1.45

1.5

1.55

1.6x 10

-3

time[sec] E

ffe

cti

ve

are

a [

-]

Aegr, des

5 10 15 20 25 30 35 40 45 5084

85

86

87

88

89

90

time[sec]

uE

GR

[%

,clo

se

]

uFF, EGR

Wegr ①

WcompWie

② Pint / Pexh

③ Aegr

- 66 -


▶ VGT path


5 10 15 20 25 30 35 40 45 501.3

1.32

1.34

1.36

1.38

1.4

1.42

1.44

time[sec]

Po

we

r [k

W]

Pwrcomp, des

5 10 15 20 25 30 35 40 45 5026

26.5

27

27.5

time[sec]M

ass

flo

w r

ate

[g

/s]

5 10 15 20 25 30 35 40 45 50160

165

170

175

180

185

190

Pre

ssu

re [

kPa

]

Wturb,des

Pexh,des

5 10 15 20 25 30 35 40 45 5088

88.5

89

89.5

90

90.5

91

time[sec]

uV

GT [

%,c

los

e]

uFF, VGT

③ Pexh

① Pwrcomp②

Wie+WfWegr

Wturb

- 67 -


▶ Test condition Ne: 1750 rpm, Wf: 20 22.5 mg/str

Transient responses (1)

5 10 15 201650

1700

1750

1800

1850

time[sec]

Ne[r

pm

]

5 10 15 2018

20

22

24

time[sec]

Wf [

mg

/str

]

- 68 -


▶ LUT- FF + PID w/o decoupler vs. MBD-FF + PID w/o decoupler


5 10 15 2029

29.5

30

30.5

31

31.5

32

32.5

33

33.5

34

time[sec]

AF

Re

xh [

-]

5 10 15 20

70

80

90

time[sec]

uE

GR

[%

,clo

se

]

5 10 15 20138

140

142

144

146

148

150

time[sec]

Pin

t [k

Pa

]

5 10 15 2080

85

90

95

time[sec]

uV

GT[%

,clo

se

]

Desired valueLUT-FF case

MBD-FF case

LUT-FF case

MBD-FF case


MBD-FF case

LUT-FF case

MBD-FF case

- 69 -


▶ LUT- FF + PID w/o decoupler vs. MBD-FF + PID w/o decoupler


5 10 15 2029

29.5

30

30.5

31

31.5

32

32.5

33

33.5

34

time[sec]

AF

Re

xh [

-]

5 10 15 20

70

80

90

time[sec]

uE

GR

[%

,clo

se

]

5 10 15 20138

140

142

144

146

148

150

time[sec]

Pin

t [k

Pa

]

5 10 15 2080

85

90

95

time[sec]

uV

GT[%

,clo

se

]


MBD-FF case

LUT-FF case

MBD-FF case


MBD-FF case

LUT-FF case

MBD-FF case

5 10 15 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se

]

uEGR

: LUT case

uFF, EGR

: LUT case

5 10 15 2065

70

75

80

85

90

time[sec]

uE

GR

[%

,clo

se

]

uEGR

: MBD case

uFF, EGR

: MBD case

- 70 -


Conclusions

- 71 -


▶ In this dissertation, two kinds of controller design method for the EGR and VGT systems are proposed

▶ Approach 1. Robust MIMO feedback controller QFT design of two SISO control loops with regard to the parameter uncer-

tainty Mitigation of cross-coupled dynamics of the two loops by using forward path

decoupler

▶ Approach 2. Model-based feedforward controller Mean value modeling of the air-path systems Feedforward design using model inversion technique

Summary

- 72 -


▶ EGR and VGT system analysis Control-oriented modeling and identification

Potentially large uncertainty and cross-coupled dynamics are quantitatively evaluated

A good degree of physical insight is presented

▶ QFT-based MIMO controller design method Robust PID controller off-line tuning using QFT method Static feedforward design

Fast initial design without extensive calibration

Considerably calibration work can be reduced

▶ Model-based feed-forward controller Non-linear EGR and VGT system modeling EGR and VGT feedforward design

Solution for NL, MIMO control systems (e.g. LP-EGR or Two stage T/C)

Contributions

- 73 -


Thank you

Documents

Robust air-to-fuel ratio and boost pressure controller design for EGR and VGT systems using QFT method Inseok Park Advised by prof. Myoungho Sunwoo November,