robust air-to-fuel ratio and boost pressure controller design for egr and vgt systems using qft...
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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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Exhaust gas recirculation (EGR)
Background
uEGR
WEGR
- 5 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Variable geometry turbocharger (VGT)
Background
uVGT
Pint
- 7 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
Part I. Robust feedback design
- Control loops design using QFT method - Forward path decoupler design
- 13 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Linear approximation of non-linear system Potentially large uncertainty Robustness problem
Problem statement (2)
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 -
Copyright @ ACE Lab, All rights reserved
▶ Linear approximation of non-linear system Potentially large uncertainty Robustness problem
Problem statement (3)
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Two DOF controller structure Compensator, Prefilter
▶ Straight-forward design process
Quantitative feedback theory
- 20 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Stationary measurements results
Parameter identification
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 -
Copyright @ ACE Lab, All rights reserved
▶ Stationary measurements results
Parameter identification
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 -
Copyright @ ACE Lab, All rights reserved
▶ Identification results at sample design operating point
Parameter identification
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Robust stability bound on Nichols chart
Step2: Desired controller specifications (1)
- 27 -
Copyright @ ACE Lab, All rights reserved
▶ 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
Step2: Desired controller specifications (2)
- 28 -
Copyright @ ACE Lab, All rights reserved
▶ 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)
Step2: Desired controller specifications (2)
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 -
Copyright @ ACE Lab, All rights reserved
▶ Robust reference tracking bounds on Nichols chart
Step2: Desired controller specifications (2)
Higher than solid lines
Lower than dashed lines
- 30 -
Copyright @ ACE Lab, All rights reserved
-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 -
Copyright @ ACE Lab, All rights reserved
-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
)
▶ 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
Open-Loop Phase (deg)
Ope
n-Lo
op G
ain
(dB
)
Nominal plant, G11,0(s)
1
4.2( ) 2.04 0.24C s s
s
Nominal Loop func-tion, L11,0(s) = G11,0(s)C1(s)
- 32 -
Copyright @ ACE Lab, All rights reserved
-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
)
▶ 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
Open-Loop Phase (deg)
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
Nominal plant, G11,0(s)
1
4.2( ) 2.04 0.24C s s
s
- 33 -
Copyright @ ACE Lab, All rights reserved
-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
)
▶ 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
Open-Loop Phase (deg)
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
Open-Loop Phase (deg)
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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
Open-Loop Phase (deg)
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
Part I. Robust feedback design
- Control loops design using QFT method - Forward path decoupler design
- 41 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
Experimental results
- 46 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Test environment configuration
Experimental setup
- 48 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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
QFT design without decoupler
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
QFT design without decoupler
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ AFRexh step responses of entire operating points
Experimental results (3)
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]
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
]
Desired valuePrefiltered desired value1750 [rpm], 10 [mg/str]1750 [rpm], 15 [mg/str]1750 [rpm], 20 [mg/str]1750 [rpm], 25 [mg/str]1750 [rpm], 30 [mg/str]
Desired valuePrefiltered desired value1750 [rpm], 10 [mg/str]1750 [rpm], 15 [mg/str]1750 [rpm], 20 [mg/str]1750 [rpm], 25 [mg/str]1750 [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 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
]
Desired valuePrefiltered desired value2000 [rpm], 10 [mg/str]2000 [rpm], 15 [mg/str]2000 [rpm], 20 [mg/str]2000 [rpm], 25 [mg/str]2000 [rpm], 30 [mg/str]
Desired valuePrefiltered desired value2000 [rpm], 10 [mg/str]2000 [rpm], 15 [mg/str]2000 [rpm], 20 [mg/str]2000 [rpm], 25 [mg/str]2000 [rpm], 30 [mg/str]
- 53 -
Copyright @ ACE Lab, All rights reserved
▶ Pint step responses of entire operating points
Experimental results (4)
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
]
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]
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
-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
]
Desired valuePrefiltered desired value1750 [rpm], 10 [mg/str]1750 [rpm], 15 [mg/str]1750 [rpm], 20 [mg/str]1750 [rpm], 25 [mg/str]1750 [rpm], 30 [mg/str]
Desired valuePrefiltered desired value1750 [rpm], 10 [mg/str]1750 [rpm], 15 [mg/str]1750 [rpm], 20 [mg/str]1750 [rpm], 25 [mg/str]1750 [rpm], 30 [mg/str]
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
]
Desired valuePrefiltered desired value2000 [rpm], 10 [mg/str]2000 [rpm], 15 [mg/str]2000 [rpm], 20 [mg/str]2000 [rpm], 25 [mg/str]2000 [rpm], 30 [mg/str]
Desired valuePrefiltered desired value2000 [rpm], 10 [mg/str]2000 [rpm], 15 [mg/str]2000 [rpm], 20 [mg/str]2000 [rpm], 25 [mg/str]2000 [rpm], 30 [mg/str]
- 54 -
Copyright @ ACE Lab, All rights reserved
▶ Transient responses
Experimental results (4)
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 -
Copyright @ ACE Lab, All rights reserved
▶ Transient responses Performance limitation
due to the phase lag of the EGR valve controller
Experimental results (5)
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 -
Copyright @ ACE Lab, All rights reserved
Part II. Model-based feed-forward design
- 57 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ Evaluation results of EGR path
Steady state evaluation (2)
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 -
Copyright @ ACE Lab, All rights reserved
▶ Evaluation results of VGT path
Steady state evaluation (3)
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ EGR path
Pint step response at Ne = 1750 rpm, Wf = 20mg/str (2)
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 -
Copyright @ ACE Lab, All rights reserved
▶ VGT path
Pint step response at Ne = 1750 rpm, Wf = 20mg/str (3)
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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ LUT- FF + PID w/o decoupler vs. MBD-FF + PID w/o decoupler
Transient responses (2)
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
Desired valueLUT-FF case
MBD-FF case
LUT-FF case
MBD-FF case
- 69 -
Copyright @ ACE Lab, All rights reserved
▶ LUT- FF + PID w/o decoupler vs. MBD-FF + PID w/o decoupler
Transient responses (2)
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
Desired valueLUT-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 -
Copyright @ ACE Lab, All rights reserved
Conclusions
- 71 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
▶ 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 -
Copyright @ ACE Lab, All rights reserved
Thank you
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