Dynamics and Vibration Control of Flexible Systems

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1 The 9th Workshop on Control of Distributed Parameter Systems IEEE ICAL 2009, Shenyang Dynamics and Vibration Control of Flexible Systems Wei He 1 and Shuzhi Sam Ge 2 1 School of Automation & Electrical Engineering, University of Science and Technology Beijing 2 Department of Electrical & Computer Engineering, National University of Singapore 3 rd July

2 Outline 1. Overview and Background 2. Flexible String and Its Applications 3. Euler-Bernoulli Beam and Its Applications 4. Conclusion and Future Work 2

3 Motivation The advantages of flexible structures greatly motivate the applications of flexible structures in the fields of aerospace, robotics, offshore engineering, etc. Objective To develop modeling and control methods of the flexible systems with guaranteed stability. Challenges Infinite dimensions of the system due to the flexibility; Dynamic modeling and boundary control design of the flexible systems; Stability analysis for the closed-loop systems. 3

4 Control methods for flexible systems Distributed control: by using distributed sensors and actuators; Boundary control: based on PDE model of the system. Advantages of boundary control Avoid spillover instability due to model truncation; Require fewer sensors and actuators; 4

5 Outline 1. Overview and Background 2. Flexible String and Its Applications 3. Euler-Bernoulli Beam and Its Applications 4. Conclusions and Future Work 5

6 Applications for the Flexible String Installation System Ocean Mooring System Crane System 6

7 2. 1 Installation System Accurate placement Vibration suppression 7

8 Dynamics of the Installation System Nomenclature Definition Subsea installation system 8

9 Modeling Governing equation Boundary conditions Challenges: position the payload and reduce vibrations of the cable at the same time. 9

10 Control Design where The adaptation law is proposed as 10

11 Stability Analysis 11

12 Simulation Platform for Flexible Systems 12

13 Simulation 13

14 Simulation Position of the cable without control Position of the cable with robust adaptive boundary control 14

15 Video for the marine installation system without control Video for the marine installation system with the proposed control 15

16 2.2 Floating Platforms with Mooring System Shuttle Tanker Tension Leg Platform Mooring System FPSO vessel Umbilical Risers Mooring lines Drag Anchors Suction Anchors Courtesy of Atlantis 16

17 Dynamics of the Mooring system Nomenclature A FPSO vessel with the thruster assisted position mooring system 17

18 Modeling Governing equations Boundary conditions 18

19 Control Design 19

20 Stability Analysis 20

21 Simulation 21

22 Simulation Snapshots of the mooring system movements without control 22

23 Simulation Video of the mooring system without control 23

24 Simulation Snapshots of the mooring system movements with the proposed control 24

25 Simulation Video of the mooring system with the proposed control 25

26 2. 3 Crane System Overhead crane Crane cables 26

27 Dynamics of a Crane System Governing equation Boundary conditions Constraint Schematic of a flexible crane system. 27

28 Control Design The boundary control Barrier Lyapunov Function 28

29 Simulation (a) Without control, (b) with the IBLF-based adaptive control, (c) with boundary control without barrier term, and (d) with the PD control 29

30 Simulation Constraint (a) Without control, (b) with the IBLF-based adaptive control, (c) with boundary control without barrier term, and (d) with the PD control 30

31 Outline 1. Overview and Background 2. Flexible String and Its Applications 3. Euler-Bernoulli Beam and Its Applications 4. Conclusion and Future Work 31

32 Applications for the Euler-Bernoulli Beam Flexible Robotic Manipulator Robotic Aircraft with Flexible Wings Marine Riser System 32

33 3.1 Flexible Robotic Manipulator System Flexible manipulator in the outer space 33

34 3. 1 Dynamics of the Flexible Robotic Manipulator A flexible robotic manipulator 34

35 Modeling Governing equations Boundary conditions Motion of the angular position 35

36 Control Design The torque control law Block diagram of control design for flexible robotic manipulator 36

37 Simulation 37

38 Simulation Displacement of flexible system without control Displacement of flexible system with boundary control 38

39 Simulation Displacement of flexible manipulator system without control Displacement of flexible manipulator system with boundary control 39

40 Simulation Angular position of flexible system without control Angular position of flexible system with boundary control 40

41 Experimental Platform 41

42 Experimental Platform Diagram of flexible Robotic Manipulator 42

43 Programming Simulink implementation diagram with boundary control 43

44 Experimental results Video for the flexible robotic manipulator without control Video for the flexible robotic manipulator with the proposed control 44

45 3.2 Robotic Aircraft with Flexible Wings Robot with flexible wings Robotic aircraft concept Wing flexibility not only improves aircraft performance and stability passively, but can also be actuated actively for control. 45

46 Dynamics of the Robotic Aircraft with Flexible Wings Governing equation Boundary conditions 46

47 Control Design We design auxiliary signals: We design the control laws as 47

48 Simulation Parameters of the robotic aircraft with flexible wings Mass 44.00g Length of the wing Mass per unit span Bending stiffness 41.80cm 10 kg/m 0:12 Nm^2 48

49 Simulation Bending displacement of the system w(x,t) 49

50 Simulation Bending displacement of the system Ɵ(x,t) 50

51 3.3 Marine Riser System A flexible marine riser system The structure of the riser 51

52 Dynamics of the marine riser Nomenclature A typical marine flexible riser system 52

53 Modeling Governing equations Boundary conditions Challenges: nonlinear PDEs 53

54 Control Design The control is independent of system parameters, thus possessing robustness to variations in system parameters. All the signals during the control process can be measured through position sensors at the top boundary of the riser. The control system requires fewer sensors and actuators. 54

55 Stability Analysis 55

56 Simulation 56

57 Simulation Ocean surface current U(t) 57

58 Simulation Displacement of the riser without control 58

59 Simulation Displacement of the riser with the proposed control 59

60 Overlay of riser profiles with control and without control 60

61 Simulation Top transverse displacement Transverse control input Top longitudinal displacement Longitudinal control input 61

62 Outline 1. Overview and Background 2. Flexible String and Its Applications 3. Euler-Bernoulli Beam and Its Applications 4. Conclusion and Future Work 62

63 Conclusions Investigations of dynamical characteristics for a)flexible string: installation system, mooring system, crane system; b)flexible beam: marine riser, robot with flexible wing. Control design for a)flexible string system; b)flexible beam system. Stability analysis of different types of PDE systems for a) Linear PDE: mooring system, installation system, etc.; b) nonlinear PDE: riser system, etc. 63

64 Conclusions Dynamical modeling for several classes of the flexible systems has been discussed. Boundary control for the flexible systems have been developed. Vibration suppression and stability analysis of the flexible systems have been studied. Simulation and experimental results have been provided to verify the effectiveness and the performance of the proposed method. 64

65 Future Work Control of vibrations in the three-dimensional space. 65

66 Future Work Control of the tension for the mooring lines. Shuttle Tanker Tension Leg Platform Mooring System FPSO vessel Umbilical Risers Mooring lines Suction Anchors Drag Anchors Courtesy of Atlantis 66

67 Future Work System Design for the Robotic Aircraft with Flexible Wings 67

68 Thank you very much! 68

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