H Multi-objective and Multi-Model MIMO control design for Broadband noise … · 2016-03-16 ·...
Transcript of H Multi-objective and Multi-Model MIMO control design for Broadband noise … · 2016-03-16 ·...
H∞ Multi-objective and Multi-Model MIMOcontrol design for Broadband noise
attenuation in a 3D enclosure
Paul LOISEAU, Philippe CHEVREL, Mohamed YAGOUBI, Jean-Marc DUFFAL
Mines Nantes, IRCCyN & Renault SAS
March 2016
Content
1 IntroductionGeneral contextPhD objectiveState of ArtScope of the presentation
2 System to control
3 Control Strategy
4 Results
5 Conclusions and Perspectives
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General ContextBrief ANC overview
Duct
I Propagative wavesI Feedforward + feedback
Headphone
I SISO controlI Co-located actuator and sensor
Headrest
I SISO controlI Co-located actuator and sensor
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General ContextActive Noise Control (ANC) in a cavity
Cavity
Feedback
Feedforward
Sensor
Feedback
Feedforward
Cavity
Sensor
Characteristics of ANC in a cavityI Stationary wavesI Actuators and sensors co-located or notI feedback or feedback + feedforwardI d narrow or broadband noiseI SISO or MIMO control
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PhD objectiveActive control of broadband low frequency noise in car cabin
Engine noise
Aeroacoustic noise
ROAD noise
(Line spectrum)
(Low frequency, Broadband spectrum)
(Mainly in high frequency)
I Passive treatments for low frequency noise ⇒ Addition of weightI Active Noise Control (ANC) is a great opportunity to simultaneously:
I Reduce road noiseI Achieve car weight reduction
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PhD objectiveActive Noise Control of broadband noise
Cavity
Feedback Feedback
Cavity
ANC problem characteristicsI 3D enclosureI Actuators and sensors not co-locatedI No measure of w is availableI d broadband low frequency noise
Limitations involvedI Waterbed effect (Bode integral)I Non minimum phase zeros
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State of ArtAdaptive feedforward control (FxLMS)
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1T. Sutton, S. J. Elliott, M. McDonald, et al., “Active control of road noiseinside vehicles”, Noise Control Engineering Journal, vol. 42, no. 4,pp. 137–147, 1994.
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State of ArtInternal Model Control (feedback)
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2J. Cheer, “Active control of the acoustic environment in an automobilecabin”, PhD thesis, University of Southampton, Southampton, 2012, p. 346.
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Scope of the presentation
Feedback
Cavity ProblemI Attenuate broadband low frequency noise;I In a closed cavity;I by feedback.
Goal of the presentationCompare SISO and MIMO achievable performances.
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Content
1 IntroductionGeneral contextPhD objectiveState of ArtScope of the presentation
2 System to controlExperimental Set upIdentification
3 Control StrategyControl problem formulationMulti-objective optimizationController StructureInitialization
4 Results
5 Conclusions and Perspectives
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Content
1 Introduction
2 System to controlExperimental Set upIdentification
3 Control Strategy
4 Results
5 Conclusions and Perspectives
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Experimental set up
Top view of the cavity
RC filter
Preamplifier
ADC DAC
Amplifier
Acquisition CardNI PCIe 6259 Cavity characteristics
I One predominant dimension: 1D acoustic field in low frequency;I One biased side: Attenuation of the first longitudinal mode;I Frequency complexity: Similar to vehicle one.
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MIMO IdentificationFrequency Domain, Continuous time model
IdentificationI Algorithm: Subspace;I Model structure: Modal;I Frequency range: [20-1000]Hz;I Order: 80.
Fit indicatorLS1 LS2 LS3
M1 86.2326 84.1038 91.1196M2 84.6231 88.8484 91.1542
Remark: SISO transfers contain RHP zeros.
−20
0
20
40
60
From: LS2 To: M
1
Magnitude (
dB
)
200 400 600 800 1000 1200 1400 1600 1800 2000−180
−90
0
90
180
Phase (
deg)
Bode Diagram N = 80 (FIT : 84.1038)
Frequency (Hz)
Measure
Model
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Content
1 Introduction
2 System to control
3 Control StrategyControl problem formulationMulti-objective optimizationController StructureInitialization
4 Results
5 Conclusions and Perspectives
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Control problem formulation
|W1|
fmin fmax
1|W2|
fmaxG
Optimization problem
minK
∥∥W1Tw→e1
∥∥∞
subject to
∥∥W2Tw→ui
∥∥∞
< 1∥∥∥W3Td′j →ei
∥∥∥∞
< 1
|piK | < fe/N
Re(piK ) < 0
i = 1, 2 and j = 1, 2
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Control problem formulationAdditional robustness needed
Environment conditions modify acoustic transfers
−10
0
10
20
30
40
50
Magnitude (
dB
)
100 200 300 400 500 600 700 800 900 1000−180
−90
0
90
180
Phase (
deg)
Measured frequency responses from LS2 to M1
Frequency (Hz)
FRF1
FRF2
FRF3 (nominal plant)
A multi-model approach was used to tackle system variations16
Control problem formulation
|W1|
fmin fmax
1|W2|
fmaxG
Optimization problem
minK
max1,...,N
∥∥W1Tw→e1
∥∥∞
subject to
max1,...,N
∥∥W2Tw→ui
∥∥∞
< 1
max1,...,N
∥∥∥W3Td′j →ei
∥∥∥∞
< 1
|piK | < fe/N
Re(piK ) < 0
i = 1, 2 and j = 1, 2
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Multi-objective and Multi-model optimization
MotivationsI Be able to consider various constraints without pessimism;I Clearly distinguish objective and constraints;I Have the possibility to mix H2 and H∞ objectives, if needed;I Be able to structure the controller;I Be able to consider reduce order controller.
Optimization tool: systuneI Specialized in tuning fixed-structure control systems;I Based on non smooth optimization;I P. Apkarian, “Tuning controllers against multiple design
requirements”, in American Control Conference (ACC),Washington, 2013, pp. 3888–3893
DrawbackI May lead to local optima;I Necessity of ”good” initialization and controller structure.
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Controller StructureState feedback observer
Model of the systemI No real time measure of wI Gp is known{
x = Ax + Buu + Bw we = Cx + Duu + Dw w
Model of the controller{˙x = Ax + Buu + Kf (e − e)u = −Kcx
RemarksI Kf : observation gainI Kc : state feedback gainI full order controller
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InitializationLQG
LQ criteria
JLQ = minKc‖WLQe‖2
2 + ρ‖u‖22
I WLQ is a bandpass filter (attenuation frequency range)I ρ manages trade-off between performances and control energy
Kalman filter {xa = Aaxa + Bua u + Bwa we = Caxa + Dua u + Dwa w + v
I Tuning parameters are the covariances of noises v and w
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Content
1 Introduction
2 System to control
3 Control Strategy
4 Results
5 Conclusions and Perspectives
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ResultsNarrow attenuation: [190-220] Hz
150 160 170 180 190 200 210 220 230 240 250
−10
0
10
20
30
40
50M
ag
nitu
de
(d
B)
Transfer e1w [190-220] Hz (SIMULATION)
Frequency (Hz)
Open loop
SISO (LS1)
SISO (LS2)
MISO
MIMO
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ResultsNarrow attenuation: [190-300] Hz
150 200 250 300 350−5
0
5
10
15
20
25
30
35
40
45M
ag
nitu
de
(d
B)
Transfer e1w [190-300] Hz (SIMULATION)
Frequency (Hz)
Open loop
SISO (LS1)
SISO (LS2)
MISO
MIMO
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ResultsExperimentation: 190-300 Hz (MIMO)
50 100 150 200 250 300 350 400 450 500−20
−10
0
10
20
30
40
50From: w To: e1
Ma
gn
itu
de
(d
B)
Transfer e1w [190-300] Hz (MIMO)
Frequency (Hz)
Simulation (nominal Plant)
Experimentation
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Content
1 Introduction
2 System to control
3 Control Strategy
4 Results
5 Conclusions and Perspectives
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Conclusions and Perspectives
ConclusionsI A general framework (for identification and control) was presented;I It allows to quantify and compare SISO and MIMO achievable performances
according to :I Frequency range of attenuation ;I Actuators and sensors position ;I Cavity geometryI . . .
Ongoing workI Compare feedback and feedforward controlI Apply methodology to the industrial problem where:
I Gp is unknownI System order and dimensions are higher
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