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©20
08 T
he M
athW
orks
, Inc
.
® ®
Model-Based Design—Unpolished
591 /* Logic: ' <S3>/either ' */592 rtb_either = power_window_con_B.passenger_control_b 593 || power_window_con_B.passenger_control_a; 594 595 /* Logic: ' <S13>/allow_action ' incorporates:596 * Inport: ' <Root>/driver_up '597 * Logic: ' <S13>/overrule '598 */599 rtb_temp34 = power_window_con_U.driver_up 600 && (!(rtb_either));
Pieter J. Mostermanpieter.mosterman@mathworks.com
Senior Research ScientistThe MathWorks, Inc.
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
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3
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Elevator redundancy management
PFCU1
PFCU2
LOactuator
LIactuator
Hydraulics 2
LDL RDL
LIO RIO
Hydraulics 1
Elevator
RIactuator
ROactuator
Hydraulics 3
Elevator
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Reconfiguration requirements
If multiple failures are detected in left hydraulic pressure and actuator positions, isolate the fault by switching both the Left Outer actuator and the Left Inner actuator to the isolated mode. The following combinations trigger this condition:
• Failures in hydraulic pressure 1, and hydraulic pressure 2
• Failures in Left Outer actuator position sensor, and Left Inner actuator position sensor
� Failures in hydraulic pressure 1, and Left Inner actuator position sensor
• Failures in hydraulic pressure 2, and Left Outer actuator position sensor
2.1.15 Multiple failures on Left hydraulic and actuators
If multiple failures are detected in hydraulic pressure 1 or 2 systems and either the Left Outer actuator position sensor or the Left Inner actuator position sensor, isolate the fault by switching both the Left Outer actuator and the Left Inner Actuator to the isolate mode.
2.1.15 Multiple failures on Left hydraulics and actuators
If a failure is detected in both the hydraulic pressure 2 system and the Left Inner actuator position sensor, while there are no other failures, isolate the fault by switching the Left Inner actuator to the off mode.
2.1.12 Hydraulic pressure 2 and Left Inner actuator position failures
If a failure is detected in both the hydraulic pressure 1 system and the Left Outer actuator position sensor, while there are no other failures, isolate the fault by switching the Left Outer actuator to the off mode.
2.1.11 Hydraulic pressure 1 and Left Outer actuator position failures
reengineer
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Requirements traceability
2.1.5 Hydraulic pressure 3 failureIf a failure is detected in the hydraulic pressure 3 system, while there are no other failures, isolate the fault by switching the Right Outer actuator to the off mode.
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
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Control design architectures
controller plant
controller plantyur
controller plant
∆
yur e
yur e
en
plant
controller
environment
context
Feedforward control (experiment in pool room)
Feedback control (experiment in wine cellar)
Robust feedback control
system
reference
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® ®
A hydraulic cylinder
Rvalve
vpiston
ppump
Ccylinder
mpiston
Rcylinder
inherently (open loop) stable
second order model of dynamics
ideal picture model
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Feedback control system
rplant
pressure displacement
controller
error pressure
Scope
)()()(
)()()( sU
sGsHI
sGsHsY
+=
)(sH)(sG
pKsG =)(
s
KsKKs
sKs
KKsG
ipd
di
p
++=
++=
2
)(
straightforward:
position control
performance:
position-integral-derivative (PID) control
closed loop analysis
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Compensator pole placement
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+2%
-2%
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x 10-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Performance criteria
rise time
overshoot
settling time
10%
90%
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® ®
Stability classes
Lyapunov stable and
))()0()(0)(0)(0( εδδε <⇒<≥∀>∃>∀ txxt
)0)(lim)0()(0( =⇒<>∃∞→
txxt
δδ
))0()()0()(0)(0,,( textxxt βαδδβα −≤⇒<≥∀>∃
Lyapunov stable
Asymptotically stable
Exponentially stable
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® ®
Robustness analysis
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
8
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® ®
Adaptive control
controller plant
identification
yur
controller plant
adjustment
yur
referencemodel
2
2
1)( eJ =θ
θγ
θγ
θγθ
∂∂−=
∂∂
∂∂−=
∂∂−= e
ee
e
JJ
dt
d
model identification adaptive control
model reference adaptive control
my
θ
performance criterion:
adaptation strategy:
process
adapt: slow
feedback: fast
Principle
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® ®
First order system
buaydt
dy +−=
cmmmm ubya
dt
dy +−=
)()()( 21 tytutu c θθ −=
b
aab
b
m
m
−==
==
022
011
θθ
θθ
myye −= cubas
by
2
1
θθ++
=
ybas
bu
bas
be
ubas
be
c
c
22
2
12
2
21
)( θθθ
θ
θθ
++−=
++−=
∂∂
++=
∂∂
masbas +≈++ 2θ
eyas
a
dt
d
euas
a
dt
d
m
m
cm
m
+=
+−=
γθ
γθ
2
1
plant
reference model
controller
ideal parameters
error
approximate
adaptation
reference model
uc ym
rplant
u y
monitor
control
th2
th1
uc
y
u
adaptation
uc
ym
y
th1
th2
25.0
12
45.0
2
2
1
=−=
==
θ
θ
9
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® ®
Switched control
control1: stable
plantyur e
supervisor chooses control law
control1
control2
control2: stable switched control: unstable
supervisor
the act of switching may cause unstable compound behavior
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
10
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® ®
A B
S P T
Hierarchy in control
man machine interface
supervisory control
control law
plant
data
analysis
data
analysis
sensor actuator
PFCU1
PFCU2
LOactuator
LIactuator
Hydraulics 2
LDL RDL
LIO RIO
Hydraulics 1
Elevator
RIactuator
ROactuator
Hydraulics 3
Elevator
deflection
valve
opening
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
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® ®
Control synthesis
),,()(
),,(0
),,()(
tuxhty
tuxg
tuxftx
==
=&
)()( txKtu iii =
+=+=
+=+=
)()()(
)()()(
)()()(
)()()(
00000
00000
tuDtxCty
tuBtxAtx
tuDtxCty
tuBtxAtx
nnnnn
nnnnn&
M
&
−=−=
)()()(
)()()(
txKDCty
txKBAtx
iiiii
iiiii&
Rvalve
vpiston
ppump
Ccylinder
mpiston
Rcylinder
model phenomena of interest
derive representation amenable to synthesis
design control law
validate control
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® ®
Functional control design stages
+=+=
)()()(
)()()(
tDutCxty
tButAxtx&
−−
−−+
−−
−−
11
11
)2
(2
)2
(
)2
(4
)2
)(2
(
AT
IDT
AT
ICT
AT
IBTT
kA
TIA
TI
+=
+=+
)(~
)(~
)(
)(~
)(~
)( 1
kkk
kkk
tuDtxCty
tuBtxAtx
discretize
0.0 …
output:
update: Du…
FoEoDoAoBo FoEoAo
0.0 0.1 0.2 …
output:
update: FuEu
FoEoAo
…FuEu
1 se
con
dbl
ocks
0.1
seco
nd
bloc
ks
FuEu
Co
task assignment
2.1.15 Multiple failures on Left hydraulics and actuatorsIf multiple failures are detected in hydraulic pressure 1 or 2 systems and either the Left Outer actuator position sensor or the Left Inner actuator position sensor, isolate the fault by switching both the Left Outer actuator and the Left Inner Actuator to the isolate mode.
verif
y
validate
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® ®
Specifications become requirements
2.1.15 Multiple failures on Left hydraulics and act uatorsIf multiple failures are detected in hydraulic pressure 1 or 2 systems andeither the Left Outer actuator position sensor or the Left Inner actuator position sensor, isolate the fault by switching both the Left Outer actuator and the Left Inner Actuator to the isolate mode.
PFCU1
PFCU2
LOactuator
LIactuator
Hydraulics 2
LDL RDL
LIO RIO
Hydraulics 1
Elevator
RIactuator
ROactuator Hydraulics 3
Elevator
plantyur e
control1
control2
supervisor
+=+=
)()()(
)()()(
tuDtxCty
tuBtxAtx
iiiii
iiiii&
+=
+=+
)(~
)(~
)(
)(~
)(~
)( 1
kkk
kkk
tuDtxCty
tuBtxAtx
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® ®
Agenda
� Requirements engineering� Feedback control
� Control law design� Evaluation criteria
� Adaptive control� Parameter adaptation� Switched control
� Hierarchical control� Design
� Functional control design flow� Implementation� Platform based design
� Wrap up
13
25
® ®
What can we learn?
� Standard input performance excitation� Step input
� Standard architectures and terminology� Standard design representations
� Root locus� Bode plots� Practitioners can relate to theory (relatively) easy
� Well-defined analyses� Stability� Robustness
� Focused design stages� Strict separation
� …
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Wrap up
� Offline design is very involved� Some aspects highlit
� Adaptation does some design online� Which aspects of design can be automated?
� To be continued …
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