1. Semi Active Control of
Magnetorheological Damper for
Structures
Umair Najeeb Mughal
Supervisors:
Prof. Robert Gri˜o
n´
Prof. Fay¸al Ikhouane
c
Institute of Industrial and Control Engineering
Universitat Politecnica De Catalunya, BarcelonaTECH,
Barcelona, Spain 08034
umair.mughal@upc.edu
July 15, 2011

2. Outline Introduction State of the Art My Present Status Future Goals/Milestones
1 Introduction
2 State of the Art
3 My Present Status
4 Future Goals/Milestones
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 2 / 40

3. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Outline
1 Introduction
Motivation and Objective
2 State of the Art
3 My Present Status
4 Future Goals/Milestones
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 3 / 40

4. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Motivation and Objective
Introduction
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 4 / 40

5. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Motivation and Objective
Introduction
Motivation
Earthquake Resilient Structures
Life Safety
Inventory Safety
Open Problems
Actuator Dynamics
Closed Loop Stability
Objective
Nonlinear Control Law
Mathematical Proof
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 4 / 40

6. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Outline
1 Introduction
2 State of the Art
Smart Materials
Smart Materials
Magnetorheological Materials
Non Newtonian
Classifications of Fluids
Mathematical Models
Structural Control
MR Damper Models and Control Techniques
MR Damper Models
MR Damper Semi Active Control Techniques
3 My Present Status
4 Future Goals/Milestones
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 5 / 40

7. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Smart Materials
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 6 / 40

8. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Smart Materials
Shape Memory Alloys
Piezoelectric Materials
Magnetostrictive Materials
Magnetorheological Materials
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 6 / 40

9. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Magnetorheological Materials
What is it and how does it work?
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 7 / 40

10. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Magnetorheological Materials
What is it and how does it work?
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 7 / 40

11. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Magnetorheological Materials
Various Modes
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 8 / 40

12. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Smart Materials
Magnetorheological Materials
Various Modes
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 8 / 40

13. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Classifications of Fluids
Response to normal stress
Compressible (typically gases)
Incompressible (typically liquids)
Response to shear stress
·
Newtonion τyx = µγ yx
Non Newtonian ·
γ yx = f (τyx )
Time Independent Fluids
Time Dependent Fluids
or
Viscoelastic Fluids ·
τyx = f1 (γ yx )
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 9 / 40

14. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids Behavior
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 10 / 40

15. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids Behavior
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 10 / 40

16. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Shear Thinning Fluids
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 11 / 40

17. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Shear Thinning Fluids
Power Law Cross Viscosity Model
τyx ·
µ − µ∞ 1
µ= = m(γ yx )n−1 =
·
γ yx · n.
µ0 − µ∞ 1 + k(γ yx )
Carreau Viscosity Model Ellis Fluid Model
n−1
µ − µ∞ · 2 µ0
= 1 + (λγ yx )2 µ= α−1
µ0 − µ∞ τyx
1+ τ1
2
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 11 / 40

18. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Viscoplastic
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 12 / 40

19. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Viscoplastic
Bingham Plastic
·
B
τyx = τ0 + µB (γ yx ) for B
|τyx | > τ0 ,
·
γ yx = 0 for B
|τyx | < τ0 .
Hurshchel Bulkley Fluid
·
τyx = τ0 + m(γ yx )n
H for B
|τyx | > τ0 ,
·
γ yx = 0 for B
|τyx | < τ0 .
Casson Fluid Model
1
1 1 · 2
(|τyx |) 2 = C
τ0 2
+ µC γ yx for C
|τyx | > τ0 ,
·
γ yx = 0 for C
|τyx | < τ0 .
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 12 / 40

20. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Shear Thickening
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 13 / 40

21. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Independent Fluids
Shear Thickening
Power Law
τyx ·
µ= · = m(γ yx )n−1
γ yx
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 13 / 40

22. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Dependent Fluids Behavior
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 14 / 40

23. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Dependent Fluids Behavior
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 14 / 40

24. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Dependent Fluids
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 15 / 40

25. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Time Dependent Fluids
Thixotropy
Houska Model
· n
τyx = (τy 0 + τy 1 ) + (m0 + ξm1 ) γ yx ,
· ε
dξ
dt = a(1 − ξ) − bξ γ yx .
Rheopexy or Negative Thixotropy
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 15 / 40

26. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Non Newtonian Fluid Models
Viscoelastic
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 16 / 40

27. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Non Newtonian
Non Newtonian Fluid Models
Viscoelastic
Maxwell Model
· ·
τ + λτ = µγ
Voigt Model
·
τ = Gγ + µ γ
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 16 / 40

28. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Structural Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 17 / 40

29. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Structural Control
I Base Isolation
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 17 / 40

30. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Structural Control
I Base Isolation
II Structural Control
(i) Passive Control,
(ii) Active Control,
(iii) Hybrid Control,
(iv) Semi Active Control.
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 17 / 40

31. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Passive Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 18 / 40

32. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Passive Control
a Metallic yield Damping Control,
b Friction Damping Control,
c Viscoelastic Damping Control,
d Viscous Fluid Damping Control,
e Tuned mass dampers (TMD) Control.
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 18 / 40

33. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Active Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 19 / 40

34. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Active Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 19 / 40

35. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Hybrid Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 20 / 40

36. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Hybrid Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 20 / 40

37. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Semi Active Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 21 / 40

38. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Semi Active Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 21 / 40

39. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Structural Control
Semi Active Control
a Variable orifice viscous damper,
b Variable friction damper,
c Variable stiffness damper,
d Controllable fluid damper.
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 21 / 40

40. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 22 / 40

41. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bingham Model
Bouc Wen Model
Hyperbolic Tangent Model
Dahl Friction Model
Others
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 22 / 40

42. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models Non Parametric Models
Bingham Model Neural Network
Bouc Wen Model Fuzzy Logic
Hyperbolic Tangent Model Others
Dahl Friction Model
Others
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 22 / 40

43. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bingham Model
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 23 / 40

44. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bingham Model
Basic Bingham Model
· ·
fmr = fc sgn x + c0 x + f0
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 23 / 40

45. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bingham Model
Basic Bingham Model
· ·
fmr = fc sgn x + c0 x + f0
Extended Bingham Model
· ·
c0 x 1 + fc sgn x1 + f0 = k2 (x3 − x2 ) + f0 |F | > fc ,
fmr = ·
k1 (x2 − x1 ) + c1 x 2 + f0 = k2 (x3 − x2 ) + f0 |F | ≤ fc .
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 23 / 40

46. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bouc-Wen Model
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 24 / 40

47. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bouc-Wen Model
Basic Bouc-Wen Model
·
fmr = c0 x +k0 (x − x0 ) + αz,
· · · ·
z = −ϕ x z|z|n−1 − β x |z|n + κ x .
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 24 / 40

48. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Bouc-Wen Model
Basic Bouc-Wen Model
·
fmr = c0 x +k0 (x − x0 ) + αz,
· · · ·
z = −ϕ x z|z|n−1 − β x |z|n + κ x .
Modified Bouc-Wen Model
·
fmr = c1 y +k1 (x − x0 )
· ·
1
y = c +c αz + c0 x +k0 (x − y )
0 1
· · · · ·
z = −ϕ x − y z|z|n−1 − β|z|n + κ x − y
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 24 / 40

49. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Hyperbolic Tangent Model
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 25 / 40

50. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Hyperbolic Tangent Model
Hyperbolic Tangent Model by Ghao
· ·
x
x 0 = Ξ1 x0 + Ξ2 x + Ξ3 f0 tanh V0r
T T
∧ −k1 k1
f mr = x0 + x,
−c1 c1
0 1
Ξ1 = ,
− k0m0 1 − c0m0 1
+k +c
0 0
Ξ2 = k c ,
− m10 − m10
0
Ξ3 = 1 .
− m0
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 25 / 40

51. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Hyperbolic Tangent Model
Hyperbolic Tangent Model by Ghao
· ·
x
x 0 = Ξ1 x0 + Ξ2 x + Ξ3 f0 tanh V0r
T T
∧ −k1 k1
f mr = x0 + x,
−c1 c1
0 1
Ξ1 = ,
− k0m0 1 − c0m0 1
+k +c
0 0
Ξ2 = k c ,
− m10 − m10
0
Ξ3 = 1 .
− m0
Hyperbolic Tangent Model by Ghao
· V0 · V0
fmr = A1 tanh A3 x + x + A2 x + x
X0 X0
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 25 / 40

52. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Dahl Friction Model
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 26 / 40

53. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Dahl Friction Model
Dahl Friction Model
·
F = kx (v ) x(t) + kw (v )z(t)
· · ·
z =ρ x− x z .
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 26 / 40

54. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
MR Damper Models
Parametric Models
Dahl Friction Model
Dahl Friction Model
·
F = kx (v ) x(t) + kw (v )z(t)
· · ·
z =ρ x− x z .
Others
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 26 / 40

55. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
Semi Active Control Techniques for MR Dampers
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 27 / 40

56. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
Semi Active Control Techniques for MR Dampers
Model Based Control
Clipped Optimal Control
Control Based on Lyapunov’s
Stability Theory
Bang Bang Control
Sliding Mode Control
Backstepping Control
Quantitative Feedback Theory
H2 and H∞ Control
Bilinear Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 27 / 40

57. Outline Introduction State of the Art My Present Status Future Goals/Milestones
MR Damper Models and Control Techniques
Semi Active Control Techniques for MR Dampers
Model Based Control Soft Computing Based Control
Clipped Optimal Control Neural Networks
Control Based on Lyapunov’s
Stability Theory Fuzzy Logic
Bang Bang Control Genetic Algorithms
Sliding Mode Control
Backstepping Control
Quantitative Feedback Theory
H2 and H∞ Control
Bilinear Control
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 27 / 40

58. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Outline
1 Introduction
2 State of the Art
3 My Present Status
Bilinear System
Damped Linear Oscillator
Biliear Control
L2 Gain and Passivity
Basic System Modified to Control Earthquake Excitation
H∞ Control
4 Future Goals/Milestones
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 28 / 40

59. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Outline
1 Introduction
2 State of the Art
3 My Present Status
4 Future Goals/Milestones
Goals
Timeline
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 37 / 40

60. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Goals
Milestones/Goals
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 38 / 40

61. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Goals
Milestones/Goals
Detailed Modelling Simulations
More Accurate Models
More Complex Models of
System Evaluation
More Complex Models of
Damper
Publications
Controller Design
L2 Gain and Passivity
Other Nonlinear Documentation
Techniques
Stability Proofs
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 38 / 40

62. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Goals
Milestones/Goals
Detailed Modelling Simulations
More Accurate Models
More Complex Models of
System Evaluation
More Complex Models of
Damper
Publications
Controller Design
L2 Gain and Passivity
Other Nonlinear Documentation
Techniques
Stability Proofs
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 38 / 40

63. Outline Introduction State of the Art My Present Status Future Goals/Milestones
Timeline
Time Line
Mughal, U.N. (IOC, UPC) S.A.C. of MRD for Structures July 2011 39 / 40

64. I Appreciate Your Attention :)