Transcript Effective Force Testing

Outline of the Presentation
•
•
•
•
•
Introduction To Effective Force Test (EFT)
Dynamic Characteristics of Hydraulic Actuators
Experimental Setups
Loop Shaping Force Feedback Controller
Experimental Verification
– Linear Elastic Structures
– Nonlinear Inelastic Structures
• Expansions of Force-Based Experimental
Methods
• Conclusions
Introduction to Effective Force Testing
Concept:
Shake Table Test
(
m x + xg
)
Effective Force Test
mx
xg x
( )
( )
R x, x
R x, x
xg
Eq. of Motion:
(
x
) ( )
m x + xg + R x, x = 0
Input:
Ground Acceleration
•
f r = -mxg
xg
( )
mx + R x, x = -mxg = f r
Dynamic Force
f r = -mxg
EFT requires dynamic force control using hydraulic actuators.
Past Studies in EFT
Development of Initial Concept
Mahin and Shing (1985), Thewalt and Mahin (1987)
Past Studies in EFT
Development of Initial Concept
Mahin and Shing (1985), Thewalt and Mahin (1987)
Experimental Implementation of Force Feedback Control
• Dimig, Shield, French et al (1999): EFT of a Linear SDOF with PID and
Velocity Feedback Compensation
• Zhao, Shield, French et al (2005): Nonlinear Valve Dynamics for Velocity
Feedback Compensation
• Zhao, French, Shield et al (2006): SDOF EFT with Fluid Dampers
Past Studies in EFT
Development of Initial Concept
Mahin and Shing (1985), Thewalt and Mahin (1987)
Experimental Implementation of Force Feedback Control
• Dimig, Shield, French et al (1999): EFT of a Linear SDOF with PID and
Velocity Feedback Compensation
• Zhao, Shield, French et al (2005): Nonlinear Valve Dynamics for Velocity
Feedback Compensation
• Zhao, French, Shield et al (2006): SDOF EFT with Fluid Dampers
Research Needs
Existing studies are limited to SDOF systems and controllable frequency ranges are
up to only 10 Hz.
Past Studies in EFT
Development of Initial Concept
Mahin and Shing (1985), Thewalt and Mahin (1987)
Experimental Implementation of Force Feedback Control
• Dimig, Shield, French et al (1999): EFT of a Linear SDOF with PID and
Velocity Feedback Compensation
• Zhao, Shield, French et al (2005): Nonlinear Valve Dynamics for Velocity
Feedback Compensation
• Zhao, French, Shield et al (2006): SDOF EFT with Fluid Dampers
Research Needs
Existing studies are limited to SDOF systems and controllable frequency ranges are
up to only 10 Hz.
Robust Force Feedback Controllers to Expand the Capabilities of EFT
Hydraulic Actuation System
Actuators and Servo Valves
Actuators at JHU
Servo Valve
Actuators at E-Defense
Dynamics of Hydraulic Actuators
i : Valve current
A : Piston area
From DesignAerospace LLC
Transfer Functions:
Dynamics of Hydraulic Actuators
i : Valve current
Transfer Functions:
( )= 1
( ) i s 1+ t s
()
H di s =
tv
d : Spool opening
A : Piston area
From DesignAerospace LLC
d s
v
: Time Delay of the Valve
Dynamics of Hydraulic Actuators
i : Valve current
Transfer Functions:
( )= 1
( ) i s 1+ t s
()
H di s =
tv
v
: Time Delay of the Valve
( ) =k
() ds
()
H qd s =
d : Spool opening
A : Piston area
From DesignAerospace LLC
q s
q
1-
k d : Flow gain
ps : Supply pressure
p
q : Oil flow
d s
: Pressure drop
d p
» kq
d ps
Dynamics of Hydraulic Actuators
i : Valve current
Transfer Functions:
( )= 1
( ) i s 1+ t s
()
d s
H di s =
tv
v
: Time Delay of the Valve
( ) =k
() ds
()
H qd s =
d : Spool opening
q
d p
» kq
d ps
: Pressure drop
Flow continuity equation
q = Av + ke f +
A : Piston area
v : Piston velocity
H fq
f : Force
x : Piston displacement
V
f
4b A
( )=
s
=
( ) q s AsH
()
f s
=
From DesignAerospace LLC
1-
k d : Flow gain
ps : Supply pressure
p
q : Oil flow
q s
d xf
(
xf
Transfer function of
the test structure
1
,
+ ke + k l s
)
Asnxf + ke + kl s d xf
æ
nxf ö
ç H xf =
÷
ç
d xf ÷ø
è
Dynamics of Hydraulic Actuators
i : Valve current
Transfer Functions:
From valve current to actuator force
()
()
() ()
H fi s = H fq s H qd s H di s
=
d : Spool opening
A : Piston area
(
)
1+ t v s Asnxf + ke + kl s d xf
at the natural frequencies of the test structure
Actuator cannot apply forces at the natural frequencies
of the test structure.
v : Piston velocity
f : Force
From DesignAerospace LLC
d xf
Denominator of the transfer function of the test
structure
d xf = 0
q : Oil flow
kq
x : Piston displacement
Control-Structure Interaction
Experimental Setup at JHU
Test Setup
u
v
a
f
i x
m = 52.7 kg
k = 210.0 kN/m
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Actuator: Shore Western 911D
o Stroke: +-3.0 inch, Load: 5.5 Kip
Servovalve: MTS 252
LVDT: DC Operated LVDT
Load Cell: Interface 1010 Series, 5Kip
HPS: 30 GPM and 3000 psi
Mass: 122.3 lb (55.45 kg)
Low Friction Bearings and Guides
u : Valve voltage
System Identification of Actuator Dynamics
Frequency Response Functions
Valve to Force
Control-Structure Interaction: 10 Hz
Force to Displacement
Valve to Velocity
Oil-Column Resonance: 90 Hz
Force Feedback Control
Block Diagram
fr
Reference
Force
+-
Input
Noise
wu
ef
uf
Cf (s)
++
Controller
wf
Hfu (s)
++
Actuator Dynamics
Measurement
Noise
fm
Measured
Force
Closed-Loop Transfer Function
C f n f nqd ndi niu d xf
Fm
Hf =
=
Fr d f dqd d di diu Asnxf + ke + kl s d xf + C f n f nqd ndi niu d xy
{
) }
(
A controller has to cancel out
d xf
in the numerator.
Loop Shaping Controller (Robust Control)
Design Criteria (Astrom and Murray 2006)
Design the controller
Cf
so that the loop transfer function
L = C f H fu
has a desired shape.
Application to Dynamic Force Control
g
Cf s =
d xf
()
where
g
: Loop Shaping Gain
Controller and Loop Transfer Functions
Cf
CfHfi
Nyquist Plot
Loop Shaping Controller
Closed-Loop Transfer Function
Hf =
()
( s)
Fm s
Ff
•
•
Compensation of the
control-structure interaction
by the loop shaping
controller
Robustness for the oilcolumn resonance by the
loop shaping controller
Experimental Validation: (1) Linear Structure
Kobe Earthquake
Maximum Reference Force: 1500 N
Force Time Histories
Fourier Spectrum
6
10
Reference
Measured
5
Fourier Amplitude
10
4
10
3
10
2
10
1
10
0
10
0
(b)
10
20
30
Frequency (Hz)
40
50
Experimental Validation: (2) Linear Structure
Loma Prieta Earthquake
Maximum Reference Force: 1500 N
Force Time Histories
Fourier Spectrum
5
10
Reference
Measured
4
Fourier Amplitude
10
3
10
2
10
1
10
0
10
(b)
0
10
20
30
Frequency (Hz)
40
N. Nakata. “Effective Force Testing with a Robust Loop Shaping Controller”, Earthquake
Engineering and Structural Dynamics, DOI:10.1002/eqe.2207.
50
Nonlinear Test Structures
u
Nonlinear Test Setup for EFT Tests
x i
f a
Accelerometer
LVDT
Servo Valve
Replaceable
Steal Rods
Load Cell
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Wheels
•
Loading Beam:
• Type: W6 x 20
• Length: 42 in
Steal Rods:
• Fy=53.0 ksi
• Length: 9.0 in
Characteristics of the Nonlinear Test Structure
Displacement Controlled Test
Increasing Cyclic Loading
Peak strength of the nonlinear test structure is about 5000 N.
Experimental Validation: (3) Nonlinear Structure
EFT (Northridge Earthquake Canoga Record)
Maximum Reference Force: 8007 N
Experimental Validation: (4) Nonlinear Structure
EFT (Kobe Earthquake Takatori Record)
Maximum Reference Force: 7562 N
Experimental Validation: Nonlinear Structure
Nonlinear Test Specimens after the Tests
Maximum Reference Force: 8007 N
Maximum Reference Force: 6672 N
N. Nakata and E. Krug. “Validation of the Effective Force Test Method with Nonlinear Test
Structures”, ASCE Journal of Engineering Mechanics (Under review).
Expansion of Force-Based Test Methods (1):
Substructure Effective Force Testing
Concept of Substructure EFT
Effective Force Testing (EFT)
Substructure EFT with Acceleration Feedback
Accelerometer
fr
am
Actuator
fr
m
m
c
)
f r = - 1+ a mxg
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•
(
)
f r = - 1+ a mxg - a mx
k
Governing Equation
Input: Predefined force
am
Computational
Substructure
Experimental
Substructure
Governing Equation
k
(1+ a ) mx + cx + kx = f
fr
c
Load Cell
(
x
r
mx + cx + kx = f r
Input: Dynamically updated force
(
)
f r = - 1+ a mxg - a mx
Preliminary experimental validation
Model-based prediction for actuator delay compensation
N. Nakata and S. Combs. “Substructure Effective Force Testing Incorporating Acceleration
Feedback for Simulated Mass”, Engineering Structures (Under review).
Expansion of Force-Based Test Methods (2):
MDOF Effective Force Testing
Nonlinear Test Setup for MDOF EFT
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System Identification
Hu1f1
Hu1f2
Hu2f1
Hu2f2
Multi-Input Multi-Output System
Control Structure Interaction
Coupled System
Controller design and experimental validation of MDOF EFT are currently underway at the
Johns Hopkins University.
Expansion of Force-Based Test Methods (3):
Substructure Shake Table Testing with Force Control
Concept of SSTT
Experimental Implementation
F
Substructuring
Interaction
Shake
Table
Actuator
Shake Table
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Application of Dynamic Force Control
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Force-based real-time hybrid simulation
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Controller Design with Stability and Robustness
A three-story test structure for validation of the substructure shake table testing with force
control is currently in progress.
Expansion of Force-Based Test Methods (4):
Acc. Feedback Control of Shake Tables with Force
Stabilization
Experimental Setup
Control Block Diagram
M. Stehman and N. Nakata. “A new approach for
acceleration tracking of shake tables: combined
acceleration and force feedback control” (In
preparation).
Conclusions
• A loop shaping force feedback controller that compensates
for the control-structure interaction is presented.
• Experimental validation of the loop shaping force feedback
controller in the EFT method was performed with linear and
nonlinear test structures at the Johns Hopkins University.
• Experimental results showed that the loop shaping controller
provided an excellent force tracking performance as well as
robustness for the force disturbances including the oilcolumn resonance.
• Expansions of force-based experimental methods such as
substructure EFT and MDOF EFT are also presented.
Acknowledgements
National Science Foundation
Faculty Early Career Development (CAREER) Program:
CAREER: Advanced Acceleration Control Methods and Substructure
Techniques for Shaking Table Tests (CMMI-0954958).
Thank you!