H Multi-objective and Multi-Model MIMO control design for Broadband noise attenuation in a 3D enclosure

Transcription

1 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

2 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

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

4 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

5 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

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

7 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 ,

8 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

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

10 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

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

12 Experimental set up Top view of the cavity RC filter Preamplifier Amplifier ADC DAC Acquisition Card NI PCIe 6259 Cavity characteristics 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

13 MIMO Identification Frequency Domain, Continuous time model Identification Algorithm: Subspace; Model structure: Modal; Frequency range: [ ]Hz; Order: 80. Fit indicator LS 1 LS 2 LS 3 M M Remark: SISO transfers contain RHP zeros. Bode Diagram N = 80 (FIT : ) 60 From: LS 2 To: M 1 Magnitude (db) Phase (deg) Measure Model Frequency (Hz) 13

14 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

15 Control problem formulation W 1 f min f max 1 W2 f maxg Optimization problem min W1 T w e1 K subject to W2 T w ui < 1 W 3 T d j e i < 1 p ik < f e /N Re(p ik ) < 0 i = 1, 2 and j = 1, 2 15

16 Control problem formulation Additional robustness needed Environment conditions modify acoustic transfers 50 Measured frequency responses from LS2 to M1 40 Magnitude (db) FRF1 FRF2 FRF3 (nominal plant) Phase (deg) Frequency (Hz) A multi-model approach was used to tackle system variations 16

17 Control problem formulation W 1 f min f max 1 W2 f maxg Optimization problem max 1,...,N W2 T w ui < 1 min K max 1,...,N W1 T w e1 subject to max 1,...,N W 3 T d j e i < 1 p ik < f e /N Re(p ik ) < 0 i = 1, 2 and j = 1, 2 17

18 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 Drawback May lead to local optima; Necessity of good initialization and controller structure. 18

19 Controller Structure State feedback observer Model of the system No real time measure of w G p is known { ẋ = Ax + Buu + B w w e = Cx + D uu + D w w Model of the controller { ˆx = Aˆx + Buu + K f (e ê) u = K cˆx Remarks K f : observation gain K c : state feedback gain full order controller 19

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

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

22 Results Narrow attenuation: [ ] Hz 50 Transfer e1 w [ ] Hz (SIMULATION) Magnitude (db) Open loop SISO (LS 1 ) SISO (LS ) 2 MISO MIMO Frequency (Hz) 22

23 Results Narrow attenuation: [ ] Hz 45 Transfer e1 w [ ] Hz (SIMULATION) Open loop SISO (LS 1 ) SISO (LS 2 ) MISO MIMO Magnitude (db) Frequency (Hz) 23

24 Results Experimentation: Hz (MIMO) Transfer e1 w [ ] Hz (MIMO) From: w To: e1 Simulation (nominal Plant) Experimentation 30 Magnitude (db) Frequency (Hz) 24

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

26 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