1. Eurotev 22-06-051 Feedback Loop for the mechanical Stabilisation Jacques Lottin* (jacques.lottin@univ-savoie.fr) Laurent Brunetti* (laurent.brunetti@univ-savoie.fr) Mihai Corduneanu** Vlad Cozma ** *LISTIC-ESIA, Université de Savoie, Annecy, France **Universitatea Politehnica, Bucuresti, Romania

2. Eurotev 22-06-052 Overview : - Presentation of active vibration reduction - Principle of rejection - Control scheme - Programs - Experiments - Results - Conclusion Collaboration with and

3. Eurotev 22-06-053 Mechanical part control Measurement : (continuous + resonances) Disturbance :-ground: cultural noise… -equipment: motors, flows… Excitation : (strength applied with actuators…) Presentation of Active Vibration Reduction

4. Eurotev 22-06-054 Principle of rejection Assumptions: - There are a few resonances which are independent small amplitudes, linearity, … - amplitude and phase of each resonance are constant or slowly varying with respect to the signal period - frequency of each resonance is known computed by means of Fourier transform - there is no accurate model available

5. Eurotev 22-06-055 Principle of rejection Current objectives: Independently reduce the main resonances For example, an identification of one mock-up…

6. Eurotev 22-06-056 Principle of rejection - rule 2: make the components of excitation converge to values such that the global effect of disturbance and excitation is null at sensor location lumped / distributed - rule 1: decompose each resonance as a weighted combination of sine and cosine measurement, disturbance, excitation with:

7. Eurotev 22-06-057 Principle of rejection An exact direct compensation would require the knowledge of eight elementary transfer functions: at least at one frequency Mechanical part disturbance excitation measurement pcpc psps fcfc fsfs ycyc ysys Disturbance is not well defined Measurement/Excitation transfers are badly known

8. Eurotev 22-06-058 Model (State space representation for one frequency): Control scheme Disturbance With the different components are decomposed in sine and cosine: Input (Strength) State (1)

9. Eurotev 22-06-059 A n : represents the dynamic of the system. Control scheme Dynamic response open loop : first order -> Setting time = 3 * time-constant  : time-constant

10. Eurotev 22-06-0510 Control scheme B n, G n : Transfer’s matrix of the strength and the disturbance. (1) Steady state then : 1 st case: disturbance = 0 y = k yf ( f s sin (  t +  yf ) + f c cos (  t +  yf ) ) (2) (2) & (4): (3) also: (4) (5) (6)

11. Eurotev 22-06-0511 Estimation of the disturbance using a state observer : Control scheme Requirement: the new model should include the disturbance in the components of the state: The new state vector: The model: (7) (8)

12. Eurotev 22-06-0512 State observer: Control scheme Where: Final relation: (9) (10) (Luenberger)

13. Eurotev 22-06-0513 Control law: Control scheme State feedback control : (1) => To reject the disturbance: (11) (12) (13)

14. Eurotev 22-06-0514 Control scheme Mechanical part spectral analysis signal processing observer state feedback signal rebuilding actuator sensor y c (w i ) y s (w i ) f c (w i ) f s (w i ) y(w i ) f

15. Eurotev 22-06-0515 Program Main program: (Matlab / Simulink / XPC Target toolboxes) Analog Input board Analog Output board Control of disturbances Summation of each command Algorithm for one frequency

16. Eurotev 22-06-0516 Program Program for one frequency : (Matlab / Simulink / XPC Target toolboxes) State feedback State observer Signal processing Band-pass filter for the disturbance Sensor command rebuilding Actuator Algorithm for one frequency :

17. Eurotev 22-06-0517 « a steel beam » 2 loudspeakers 2 opposite PZT Accelerometer (only for monitoring) Experiments Mock-up:

18. Eurotev 22-06-0518 Experiments Mock-up: Sensor PZT (bottom) Actuator PZT (on top)

19. Eurotev 22-06-0519 Experiments Layout : Development PC (host) Matlab + Simulink + XPC Target Toolboxes Dedicated PC (target) XPC Target Ethernet network Input / Output analog board Texas Instruments Plant Sample time : 0.0007 s

20. Eurotev 22-06-0520 Results Rejection of 6 resonances : (without and with rejection) Resonances of :-beam -support

21. Eurotev 22-06-0521 Results Some zooms… Without rejection With rejection

22. Eurotev 22-06-0522 Results Rejection of 6 resonances : (disturbances and control) Resonances of : -beam -support Disturbances Control

23. Eurotev 22-06-0523 Results Phase robustness of  yf (matrix B n ) : 1 st resonance : margin of  /2 Robustness OK : Identified phase Stability limit : Identified phase +2  /20 Identified phase -8  /20 Without rejection

24. Eurotev 22-06-0524 Results Gain robustness of k yf (matrix B n ) : 1 st resonance : factor 10. Identified gain Identified gain * 0.1 Identified gain * 10 Beginning of control Worse in setting time Time Right convergence in steady time (stability limit…)

25. Eurotev 22-06-0525 Conclusion Status: - Validation is OK - Robustness is ~OK Current and future works: -Spectral analysis of the disturbance in real time -Translation of the last studies on a new model with a parallelepiped beam (2.5 meters long). (testing the algorithm and choosing the appropriate actuators….) Jacques LOTTIN : jacques.lottin@univ-savoie.fr Laurent BRUNETTI : laurent.brunetti@univ-savoie.fr