H Multi-objective and Multi-Model MIMO control design for Broadband - PowerPoint PPT Presentation

H ∞ Multi-objective and Multi-Model MIMO control 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 Introduction General context PhD objective State of Art Scope of the presentation 2 System to control 3 Control Strategy 4 Results 5 Conclusions and Perspectives 2

General Context Brief ANC overview Duct ◮ Propagative waves ◮ Feedforward + feedback Headphone Headrest ◮ SISO control ◮ SISO control ◮ Co-located actuator and sensor ◮ Co-located actuator and sensor 3

General Context Active Noise Control (ANC) in a cavity Sensor Sensor Cavity Cavity Feedback Feedback Feedforward Feedforward Characteristics of ANC in a cavity ◮ Stationary waves ◮ Actuators and sensors co-located or not ◮ feedback or feedback + feedforward ◮ d narrow or broadband noise ◮ SISO or MIMO control 4

PhD objective Active control of broadband low frequency noise in car cabin Aeroacoustic noise (Mainly in high frequency) Engine noise (Line spectrum) ROAD noise (Low frequency, Broadband spectrum) ◮ Passive treatments for low frequency noise ⇒ Addition of weight ◮ Active Noise Control (ANC) is a great opportunity to simultaneously: ◮ Reduce road noise ◮ Achieve car weight reduction 5

PhD objective Active Noise Control of broadband noise Cavity Cavity Feedback Feedback ANC problem characteristics ◮ 3D enclosure Limitations involved ◮ Waterbed effect (Bode integral) ◮ Actuators and sensors not co-located ◮ No measure of w is available ◮ Non minimum phase zeros ◮ d broadband low frequency noise 6

State of Art Adaptive feedforward control (FxLMS) 1 1 T. Sutton, S. J. Elliott, M. McDonald, et al. , “Active control of road noise inside vehicles”, Noise Control Engineering Journal , vol. 42, no. 4, pp. 137–147, 1994. 7

State of Art Internal Model Control (feedback) 2 2 J. Cheer, “Active control of the acoustic environment in an automobile cabin”, PhD thesis, University of Southampton, Southampton, 2012, p. 346. 8

Scope of the presentation Problem Cavity ◮ Attenuate broadband low frequency noise; ◮ In a closed cavity; ◮ by feedback. Feedback Goal of the presentation Compare SISO and MIMO achievable performances. 9

Content 1 Introduction General context PhD objective State of Art Scope of the presentation 2 System to control Experimental Set up Identification 3 Control Strategy Control problem formulation Multi-objective optimization Controller Structure Initialization 4 Results 5 Conclusions and Perspectives 10

Content 1 Introduction 2 System to control Experimental Set up Identification 3 Control Strategy 4 Results 5 Conclusions and Perspectives 11

Experimental set up Top view of the cavity RC fi lter Ampli fi er Preampli fi er ADC DAC Acquisition Card Cavity characteristics NI PCIe 6259 ◮ One predominant dimension: 1D acoustic field in low frequency; ◮ One biased side: Attenuation of the first longitudinal mode; ◮ Frequency complexity: Similar to vehicle one. 12

MIMO Identification Frequency Domain, Continuous time model Identification Fit indicator ◮ LS 1 LS 2 LS 3 Algorithm: Subspace; M 1 86.2326 84.1038 91.1196 ◮ Model structure: Modal; M 2 84.6231 88.8484 91.1542 ◮ Frequency range: [20-1000]Hz; ◮ Order: 80. Remark: SISO transfers contain RHP zeros. Bode Diagram N = 80 (FIT : 84.1038) From: LS 2 To: M 1 60 40 Magnitude (dB) 20 0 −20 180 Measure Model 90 Phase (deg) 0 −90 −180 200 400 600 800 1000 1200 1400 1600 1800 2000 Frequency (Hz) 13

Content 1 Introduction 2 System to control 3 Control Strategy Control problem formulation Multi-objective optimization Controller Structure Initialization 4 Results 5 Conclusions and Perspectives 14

Control problem formulation | W 1 | f min f max 1 | W 2 | f max G Optimization problem � �  � W 2 T w → ui < 1 � ∞    � �   � �  � W 3 T d ′ < 1 � � j → ei � min � W 1 T w → e 1 subject to i = 1 , 2 and j = 1 , 2 � ∞ K ∞   | p iK | < f e / N     Re ( p iK ) < 0 15

Control problem formulation Additional robustness needed Environment conditions modify acoustic transfers Measured frequency responses from LS 2 to M 1 50 40 Magnitude (dB) 30 20 10 FRF1 0 FRF2 FRF3 (nominal plant) −10 180 90 Phase (deg) 0 −90 −180 100 200 300 400 500 600 700 800 900 1000 Frequency (Hz) A multi-model approach was used to tackle system variations 16

Control problem formulation | W 1 | f min f max 1 | W 2 | f max G Optimization problem � �  max 1 ,..., N � W 2 T w → ui < 1 �  ∞   � �   max 1 ,..., N � � W 3 T d ′ � < 1  j → ei � � � min max � W 1 T w → e 1 subject to i = 1 , 2 and j = 1 , 2 � ∞ K 1 ,..., N ∞  | p iK | < f e / N      Re ( p iK ) < 0 17

Multi-objective and Multi-model optimization Motivations ◮ Be able to consider various constraints without pessimism ; ◮ Clearly distinguish objective and constraints; ◮ Have the possibility to mix H 2 and H ∞ objectives, if needed; ◮ Be able to structure the controller; ◮ Be able to consider reduce order controller. Optimization tool: systune ◮ Specialized in tuning fixed-structure control systems; ◮ Based on non smooth optimization; ◮ P. Apkarian, “Tuning controllers against multiple design requirements”, in American Control Conference (ACC) , Washington, 2013, pp. 3888–3893 Drawback ◮ May lead to local optima; ◮ Necessity of ”good” initialization and controller structure. 18

Controller Structure State feedback observer Model of the system ◮ No real time measure of w ◮ G p is known � ˙ x = Ax + B u u + B w w e = Cx + D u u + D w w Model of the controller � ˙ ˆ x = A ˆ x + B u u + K f ( e − ˆ e ) u = − K c ˆ x Remarks ◮ K f : observation gain ◮ K c : state feedback gain ◮ full order controller 19

Initialization LQG LQ criteria � W LQ e � 2 2 + ρ � u � 2 J LQ = min 2 K c ◮ W LQ is a bandpass filter (attenuation frequency range) ◮ ρ manages trade-off between performances and control energy Kalman filter � ˙ x a = A a x a + B u a u + B w a w e = C a x a + D u a u + D w a w + v ◮ Tuning parameters are the covariances of noises v and w 20

Content 1 Introduction 2 System to control 3 Control Strategy 4 Results 5 Conclusions and Perspectives 21

Results Narrow attenuation: [190-220] Hz Transfer e 1 w [190-220] Hz (SIMULATION) 50 40 30 Magnitude (dB) 20 10 Open loop SISO (LS 1 ) SISO (LS 2 ) 0 MISO MIMO −10 150 160 170 180 190 200 210 220 230 240 250 Frequency (Hz) 22

Results Narrow attenuation: [190-300] Hz Transfer e 1 w [190-300] Hz (SIMULATION) 45 Open loop 40 SISO (LS 1 ) SISO (LS 2 ) 35 MISO 30 MIMO Magnitude (dB) 25 20 15 10 5 0 −5 150 200 250 300 350 Frequency (Hz) 23

Results Experimentation: 190-300 Hz (MIMO) Transfer e 1 w [190-300] Hz (MIMO) From: w To: e1 50 Simulation (nominal Plant) Experimentation 40 30 Magnitude (dB) 20 10 0 −10 −20 50 100 150 200 250 300 350 400 450 500 Frequency (Hz) 24

Content 1 Introduction 2 System to control 3 Control Strategy 4 Results 5 Conclusions and Perspectives 25

Conclusions and Perspectives Conclusions ◮ A general framework (for identification and control) was presented; ◮ It allows to quantify and compare SISO and MIMO achievable performances according to : ◮ Frequency range of attenuation ; ◮ Actuators and sensors position ; ◮ Cavity geometry ◮ . . . Ongoing work ◮ Compare feedback and feedforward control ◮ Apply methodology to the industrial problem where: ◮ G p is unknown ◮ System order and dimensions are higher 26