457
Advances in Experimental Structural Engineering
Itoh and Aoki (eds.)
ISBN 4-901887-18-1
LARGE SCALE REAL TIME DYNAMIC HYBRID TESTING
TECHNIQUE – SHAKE TABLES SUBSTRUCTURE TESTING
ANDREI M. REINHORN1, METTUPALAYAM V. SIVASELVAN2, ZACH LIANG2 XIAOYUN SHAO3, MARK
PITMAN4 and SCOT WEINREBER4
Professor, 2 Research Associate* , 3 PhD Candidate, 4 Lab Specialist
Department of Civil, Structural, and Environmental Engineering, University at Buffalo (SUNY), Buffalo, New
York, 14260, USA, e-mail: reinhorn@buffalo.edu
1
ABSTRACT
This paper presents the development and implementation of a novel structural testing method involving the combined
use of shake tables, actuators and computational engines for the seismic simulation of structures. The structure to be
simulated is divided into one or more experimental and computational substructures. The interface forces between the
experimental and computational substructures are imposed by actuators and resulting displacements and velocities are
fed back to the computational engine. The earthquake ground motion is applied to the experimental substructures by
shake tables. The unique aspect of the above hybrid system is force-based substructuring. Since the shake tables induce
inertia forces in the experimental substructures, the actuators have to be operated in dynamic force control as well, since
either the force or the displacement, but not both can be controlled at a given point and at a given instant of time. The
resulting testing method is more versatile than existing seismic testing methods. First the substructuring strategy and the
numerical integration algorithms associated with the computational substructures are discussed along with the
implementation of the computational engine. Then a new dynamic force control strategy developed for this purpose
using series elasticity and displacement compensation is briefly reviewed. Issues related to time-delay compensation are
also discussed. Finally, an example of a real-time hybrid test implementation, and results from this experiment are
presented.
INTRODUCTION
Several experimental procedures are used to simulate and test the behavior of structural systems and components under
earthquake loads. These include (1) Quasi-static testing (2) Shake-table testing (Nagarajaiah et al., 1992) (3) Effective
force testing (Shield et al., 2001) and (4) Pseudo-dynamic testing (Shing et al., 1994) (see Fig. 1). Real-time dynamic
hybrid testing extends these methods by allowing for testing substructures under realistic dynamic loads and for
representing rate-dependent and distributed inertia effects accurately. In a recent development, a fast pseudo-dynamic
method was developed to account for rate dependency. While the fast pseudo-dynamic and the real-time dynamic
hybrid testing use sub-structures for physical testing and online computations to simulate the global system in real-time,
the latter technique includes the inertia effects as part of the physical system testing.
Real-time Dynamic Hybrid Testing (RTDHT) shown in Fig. 1(c) is a novel structural testing method involving the
combined use of shake tables, actuators and computational engines for the seismic simulation of structures. The
structure to be simulated is divided into a physical substructure and one or more computational substructures. The
interface forces between the physical and computational substructures are imposed by actuators and resulting
displacements and velocities are fed back to the computational engine. The earthquake ground motion, or motion of
other computational substructures, is applied to the experimental substructure by shake tables. A schematic of the
RTDHT system is shown in Fig. 3. The right side in Fig. 3 shows the physical and computational infrastructure required
for the implementation of the forces and motions at the interface of the physical and computational substructures. The
theoretical basis and the implementation of real time dynamic hybrid testing (RTDHT) is presented in the next sections.
:
m5x5a
:
m4x4a
:
m3x3a
Fi
Fi
:
m2x2a
:
m1x1a
F2
F1
(a) Effective force
method
(b) Pseudodynamic
substructure
(c) Real-time dynamic
substructure
Fig. 1. Modern Methods for “dynamic” testing in earthquake engineering.
*
at time of preparation of manuscript; presently Assistant Professor at University of Colorado at Boulder
458
SUBSTRUCTURING
k3
Substructuring using RTDHT requires first modeling the entire structure
and idealizing the interface conditions between the computational and the
physical substructures. For the sake of simplicity, derivations are
presented here only for a structural configuration shown in Fig. 2. A threestory model is shown with its parameters. If ug is the motion of the ground
with respect to the inertial reference frame. ui and xi are the motions of the
ith story with respect to the fixed reference frame and with respect to the
ground respectively, then ui u g xi . The damping is assumed to be of
x3, u3
m3
c3
m2
k2
x2, u2
c2
m1
k1
x1, u1
the form shown in the figure, in order to preserve a simple formulation for
the computational model Defining the first and third floor as
computational substructures and the second floor as the experimental
substructure as shown also in Fig. 3, the equations of motion in the inertial
reference frame are then given by equation (1). By considering the
influence of the experimental substructure as external disturbance, the
equations of the computational substructures may be written as equation
(2).
c1
ug
Ground
Inertial Reference Frame
Fig. 2. Three story model
m1u1 c1 c2 x1
k1 k2 x1
c2 x2
k2 x2
0 o Computational Substructure 2
m2 u2
c2 x1 c2 c3 x2 c3 x3
k2 x1 k2 k3 x2 k3 x3
m2 u2
c3 x2 c3 x3
k3 x2 k3 x3
0 o Experimental Substructure
(1)
0 o Computational Substructure 1
Optional
Optional
Computationa
l Substructure
MTS Actuator
Controller (STS)
Structural
Actuator
Physical
Substructur
Shake Table
MTS Hydraulic Power
Controller (HPC)
Computationa
l Substructure
Network Simulator
General Purpose
Data Acquisition
System
Real-time Simulator
Data Acquisition
SCRAMNET I
Physical
Substructur
Compensation Controller
xPC Target
SCRAMNET II
Ground/Shake Table
MTS Shake Table
Controller (469D)
CONTROL OF
LOADING SYSTEM
Hybrid Testing
HYBRID CONTROLLER
UB-NEES NODE
Fig. 3. Schematic of real-time dynamic hybrid test system
Similarly the equation governing the experimental substructure may be arranged as shown in equation (3). It is useful to
introduce the relative displacement x21 = x2-x1. Then equation (3) can be rewritten and substituted by equation (4).
m1 x1 c1 x1 k1 x1
m1ug k2 x2 x1 c2 x2 x1 Force measured at the base
of experimental substructure
m3 x3 c3 x3 k3 x3
m3ug k3 x2 c3 x2
(2)
( k3 *displacement +c3 *velocity) of
experimental substructure
§
·
§
·
§
·
m2 ¨ ug x2 ¸ c2 ¨ x2 x1 ¸ k2 ¨ x2 x1 ¸
, ¸
, ¸
¨
¨
¨ ,
¸
Computed ¹
Computed ¹
© External Load
¹
©
©
(3)
§
·
¸
k3 ¨ x3 x
,2
¨ ,
¸
© Computed Measured (Feedback) ¹
m2 u1 x21 c2 x21 k2 x21
k3 x3 x2 (4)
Being able to use both a shake table and an actuator to excite the experimental substructure introduces several
possibilities. A number of alternatives exist for the application of the first floor acceleration u1 and the thirds story
459
force k3 x3 x2 : (a) One possibility is to apply the acceleration using the shake table and the force using the actuator.
(b) Another option is to apply the ground acceleration using the actuator as well (as in the Effective Force method). (c)
Yet another alternative is obtained by rearranging equation (4) as follows:
ª
º
«
»
k3
m2 «u1 x3 x2 x21 » c2 x21 k2 x21
m2
« »
«¬ Equivalent acceleration
»¼
(5)
0
The equivalent acceleration can be applied using the shake table only. However, the first story acceleration and the third
story force can each be divided into two components, one to be applied by the shake table, and the other by the actuator.
The actuator is assumed fixed in the inertial reference frame, while the structure is in a non-inertial frame attached to
the shake table. The actions are shown below:
D1 s u1
Shake table acceleration, ut
D3 s x
3
x2 First story contribution
to shake table acceleration
Actuator Force, Fa
k3
m2
(6)
Third story contribution
to shake table acceleration
>1 D1 s @ m2 u1 >1 D 3 s @ k3 x3 x2 First story contribution
to actuator force
Third story contribution
to actuator force
where D1(s) and D1(s) are frequency dependent splitting
function such as for example band-pass filters. Such a
+
+
splitting has several advantages. For instance, the oil
k
6
6
+
+
column frequency of shake tables is relatively low due to
c
6
1-D (s)
D (s)
their heavy mass and limits their bandwidth. Moreover,
+
+
Disp.
x
6
1-D (s)
Actuator
shake tables that are restrained by bearings do not perform
6
+
Experimental
Substructure Vel.+
well at very low frequencies. These frequency components
+
6
D (s)
Shake Table
6
+
can then be transferred to the actuator. The splitting can
Base
Force
also be based on instantaneous or average power
+
+
minimization for the test. These issues are discussed by
6
+
Kausel (1998). The above substructuring and force
1
1
u
m
x
6
s
s
splitting strategies are shown schematically in Fig. 4. If
D
1(s)  0 and D2(s)  0, then the control requires a shake
Fig. 4. Schematic of hybrid substructuring
table and an actuator to implement the substructure testing.
The actuator therefore has to operate in force control.
If D1(s) = 0 and D2(s) = 0, however, two possibilities exist. Let the force input to the actuator in Fig. 4 be F. Then the
two possibilities are shown in Fig. 5. In dynamic testing, the inertia is part of the experimental system, whereas in
pseudo-dynamic testing, inertia effects are computed. Thus for hybrid testing (D1(s)  0 or D2(s)  0) or dynamic hybrid
testing, the actuator should operate in force control. The force control problem is discussed next.
-
m3
1
s
s
m3 s 2 c3 s k3
6
1/m2
x3
3
3
3
3
m2
2
1
1
g
s2
m1 s 2 c1 s k1
1
1
k2
k2
Displacement
-
F
Actuator
+
6
-
1
m2
Acceleration
³ dt
Velocity
³ dt
F
+
6
-
Computed
1
m2
Acceleration
³ dt
Velocity
Actuator
Displacement
³ dt
c2
c2
(b) Pseudo-dynamic
(a) Dynamic
Fig. 5. Dynamic and pseudo-dynamic testing
Such a unified view of hybrid simultaneous computation and experimentation testing systems provides a better
perspective to develop algorithms and software. The similarities between compensation strategies in force and
displacement control are reviewed for instance by Zhao et al. (2003).
DYNAMIC FORCE CONTROL
The implementation of advanced seismic testing techniques such as the effective force method and real-time dynamic
hybrid testing require the implementation of dynamic force control in the hydraulic actuators. This control is sensitive
to the acceleration and force measurements, to the modeling of the compressibility of fluid, to the nonlinearities of the
servo control system (servovalves) and other stiffness issues as indicated by Dimig et al. (1999) and Shield et al.
(2001).
460
Problems in dynamic force control
By its physical nature, a hydraulic actuator is a rate-type device or velocity source, i.e., a given controlled flow rate into
the actuator results in a certain velocity. Moreover, hydraulic actuators are typically designed for good position control,
i.e., to move heavy loads quickly and accurately. They are therefore by construction high impedance (mechanically
stiff) systems (Nachtigal, 1990). In contrast for force control, a force source is required. Such a system logically would
have to be a low-impedance (mechanically compliant) system. Thus force control using hydraulic actuators is an
inherently difficult problem. It was recognized by (Conrad and Jensen, 1987) that closed-loop control with force
feedback is ineffective without velocity feed-forward or full state feedback. This is further supported by Dimig et al.
(1999) and Shield et al (2001) in their work on the effective force method. Fig. 6 shows the force control with velocity
compensation proposed by Dimig et al (1999). Rearranging terms by multiplying by A and dividing by s, the control
loop in Fig. 7 is obtained. It can be seen that the oil behaves as a spring providing the flexibility required for force
control. Relative deformation occurs across this spring and force is applied through it.
Force
Feedback
Force
Feedback
-
Desired +
Force
6
Valve
Command
+
K
Servovalve
Flow
+
6
Natural Velocity
Feedback
A
C12 s
Desired +
Force
Achieved
Force
6
K
As
Valve
Command
+
Actuator +
Displacement
6
Oil spring
Servovalve
+ Actuator
Actuator
Achieved
Force
A2N
-
A
s
ms 2 cs k
1/K
Velocity
Compensation
As
K
Displacement
Compensation
1
ms 2 cs k
Structure
Displacement
Structure
Structure
Fig. 7. Force control of Dimig et al (1999) rearranged.
Fig. 6. Force control of Dimig et al. (1999).
Actuators designed for position control have stiff oil columns, making force control very sensitive to control parameters
and often leading to instabilities. Moreover friction, stick-slip, breakaway forces on seals, backlash etc. cause force
noise, making force a difficult variable to control. Several strategies have been introduced to work around this problem.
For instance the dual compensation scheme of MTS (2003) uses a primary displacement feedback loop with force as a
secondary tracking variable. It also supports features such as acceleration compensation to compensate for some of the
effects that distort the control force. In robotics, and impedance control strategy has been employed wherein the forcedisplacement relationship is controlled at the actuator interface (Mason, 1982) and (Whitney, 1987). Pratt et al (2002)
have used the idea of series elastic actuators where a flexible mechanism is intentionally introduced between the
actuator and the point of application of force, along with force feedback.
Proposed solution
Motivated by these observations and by the fact that causality requires a flexible component in order to apply a force
(Paynter, 1961), in the force control scheme described here, a spring is introduced between the actuator and the
structure as shown in Fig. 8. Notice that the scheme is similar to that of Fig. 7, except that (1) the intentionally
introduced series spring, KLC, assumes the role of the oil spring and (2) there is no force feedback loop.
Target
Force
Actuator
Displacement
Feedback
Measured
Force
1 / KLC
Command
Signal
Actuator with
Displacement Control
Series
Load
Cell Spring, KLC
Desired
Force
Structure
1/KLC
+
6
+
C|
1
G Actuator
GActuator
Actuator
Displacement
Actuator in
Closed-loop
Displacement Control
Compensation
Structure
Displacement
Compensator
+
6
-
KLC
Achieved
Force
Series Spring
1
ms 2 cs k
Structure
Fig. 8. Proposed force control scheme
Fig. 9. Block diagram of proposed force control
The actuator behaves as a displacement device. The tuning of the hydraulic actuator in displacement control can be
done relatively easily, very precisely and independent of the structure and leads to a well behaved closed-loop transfer
function with good force disturbance rejection. Hence the actuator in the control scheme of Fig. 8 is operated in closedloop displacement control with a PIDF controller. The resulting block diagram is shown in Fig. 9. Although the system
as a whole controls force input, internally the actuator operates in closed-loop displacement control. Hence, there is no
need for an additional force feedback loop to ensure stability. Besides, this would prevent the actuator responding to
spurious force errors caused by the sources listed above. The force transfer function is given by:
Achieved Force
Desired Force
CG
ms 2 cs k
ms 2 cs k K LC 1 CG (7)
In the ideal case where C = 1/G, the transfer function has the value of one. The advantages of using the series spring are
also now apparent: (1) the actuator can be well tuned and operated in displacement control, (2) it provides for one more
parameter than can be altered in the control design (the oil stiffness cannot be) and (3) the term KLC(1-CG) in the
461
transfer function indicates that the smaller the value of KLC the less sensitive is the transfer function to deviations of C
from 1/G. The following paragraphs present results from applying the above control procedure.
Experimental results from pilot tests
Experiments were performed using a small-scale test setup and are described below. The test setup is shown in Fig. 10.
An MTS 252.22 two-stage servo-valve and an MTS actuator were used. The controller used was the MTS FlexTest GT.
The structure was designed to have a resonant frequency of 3 Hz. The force control system consisting of the
compensator C and the displacement feedback was implemented as a cascade controller around the MTS controller
using Simulink and xPC Target (Mathworks, 2003).
Series Spring
Structure Displacement
Transducer
Actuator
Structure
Load Cell
Fig. 10. Small scale force control setup
2.00
0.00
1.80
-0.05
1.60
-0.10
Phase (rad)
Magnitude
1.40
1.20
1.00
0.80
0.60
-0.15
-0.20
-0.25
-0.30
0.40
-0.35
0.20
-0.40
0.00
0.0
2.0
4.0
6.0
8.0
Frequency (Hz)
a) Magnitude response
10.0
0.0
2.0
4.0
6.0
8.0
10.0
Frequency (Hz)
(b) Phase response
Fig. 11. Frequency response function of the actuator in displacement control
2.0
1.8
Experimental
1.6
Numerical
Magnitude
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0
2.0
4.0
6.0
8.0
10.0
Frequency (Hz)
Fig. 12. Magnitude of the input force output force frequency response function
The actuator was tuned first in displacement control and the closed-loop
displacement transfer function was measured. This is shown in Fig. 11.
For the frequency range of interest, it is seen that the actuator can be
modeled as a pure time-delay system with a delay of 5.6 ms.
The resulting force transfer function magnitude of the system is shown
in Fig. 12. There is a significant drop in magnitude at the resonant
frequency, 3 Hz, of the structure. Also shown in the figure is the result
from a numerical simulation performed by modeling the actuator as a
pure time-delay of the measured value. The correspondence between the
results demonstrates that time-delay is indeed the cause for the drop in
the frequency response magnitude. This is because near this frequency,
there is a large gradient in the phase response of the structure and its
response is therefore very sensitive in the phase lag caused by timedelay in the feedback. The existence of time-delay implies that any
control action can be applied only a certain amount of time after it has
been computed.
Predictive Compensation
To correct for this therefore, the control action needs to be predicted. A Smith-type predictor (Marshall, 1979) is used
here for this purpose as shown in Fig. 13. Another approach is to use a lead-lag compensator to produce a phase-lead at
the resonant frequency of the structure (see for example Shield et al. (2001)). The resulting magnitude of the input
force-output force frequency response function is shown in Fig. 14. The deviation from unity is a result of a first order
approximation of the exponential term in the predictor during its digital implementation. A better digital redesign of the
Smith predictor is the subject of current work.
462
2.0
1.8
Without compensation
1.6
Smith Predictive Compensator
+
+
6
+
+
Corrective
Displcement
6
+
6
-
Predictive
Displcement
T0
1
m0 s 2 c0 s k0 K LC 0
Delay
Model
Model of StructureSpring System
With compensation
1.4
T = e-sW
Actuator
+
6
-
Magnitude
1/KLC
KLC
Series Spring
1.2
1.0
0.8
0.6
0.4
0.2
1
ms 2 cs k
0.0
0.0
2.0
Structure
4.0
6.0
8.0
10.0
Frequency (Hz)
Fig. 13. Smith predictive time-delay compensator
Fig. 14. Magnitude of the input force - output force
frequency response function
HYBRID TESTING
A hybrid test was performed at University at Buffalo on a two-story structure with the first story built on the shake table
and the second story simulated. The hybrid test setup is shown in Fig. 15b. Fig. 15a shows the two stories model tested
for reference placed on a 5-dof 50 tons capacity shake table, while Fig 15b shows the hybrid test set-up placed on a 6dof 50 tons capacity shake table. For more details on the shaking systems see the facilities descriptions at
http://nees.buffalo.edu/. The model was a 1:3 scaled model with separated lateral and gravity load resisting systems
consisting of 2m x 3m, 4.5 tons, steel floors (representing the scaled mass) supported by double hinged 1.2m high
“gravity columns” and two portal lateral moment resisting steel frames (Kusumastuti et al., 2005). The force in the
hybrid test set-up was delivered with an MTS 244.51S 100tons capacity, ±0.6m stroke actuator with a high speed MTS
256.80S three stage 3000 lpm servovalve working at its lowest range of capacity. The spring assembly for the elastic
series actuator was a generic design with stiffness of one order of magnitude of the structure. The actuator in the hybrid
system set-up was controlled using an MTS469-STS generic controller and a UB-NEES generic parallel processing
supervisory controller as shown in Fig. 3.
The experimental verification was done using the above set-up defined by the system in Fig. 4, with u1
u g , D1(s) = 1
and D2(s) = 0. The control scheme is shown in Fig. 16. A comparison of the frequency response function measured
from the hybrid test and computed analytically is shown in Fig. 17.
One Story Substructure
Actuator
Shake Table
(a) Two story structure
(b) Hybrid test setup
Fig. 15. Hybrid test setup
463
2
1/KLC
+
6
+
C
GActuator
Compensation
Actuator
+
6
6
Series Spring
+
+
1
m2 s 2 c2 s k2
6
Experimental
Subtructure
³ dt
³ dt
+
-
m3
To computational
Substructure
KLC
-
Hybrid Test
1.8
ug
Shake
Table
Fig. 16. Control scheme for two story hybrid test
Displacement FRF (in/kip)
From
computational
Substructure
Analytical
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.0
2.0
4.0
6.0
8.0
10.0
Frequency (Hz)
Fig. 17. First story frequency response function
DISTRIBUTED REAL-TIME ARCHITECTURE
The real-time hybrid system is implemented using a distributed architecture that uses Shared Random Access Memory
Network (SCRAMNETTM), a very low-latency replicated shared memory fiber optic network implemented in the UBNEES controller. The architecture of hardware-software controller (see right side of Fig. 3) allows for flexibility in the
design of the real-time operating system and in the implementation of the components used. There are three units as
shown in the Hybrid Controller.
1. The Real-time Simulator which simulates the computational substructures. The architecture has been designed so that
this simulator could be seamlessly replaced by one that is at a remote location. With the current state-of-the-art,
however, network speed would become the bottleneck to real-time operation. This is accommodated using an
additional interrupt mechanism.
2. The Data Acquisition System (DAQ) that is used for feedback from the experimental substructure as well as for
archiving information during the test.
3. The Compensation Controller which contains the cascade control loop for force control presented above. This
controller also compensates for time-delays that are inherent in the physical system and those that are introduced by
filtering, computation, network communication, etc.
The controller operates in a synchronous-asynchronous manner using SCRAMNET interrupts.
CONCLUDING REMARKS
The Real Time Dynamic Hybrid Testing System is implementing combined physical testing and computational
simulations to enable dynamic testing of sub-structures including the rate and inertial effects while considering the
whole system. The paper presents a new force control scheme with a predictive compensation procedure which enabled
the real-time implementation. The procedures are implemented in the full / large scale University at Buffalo’ Structural
Engineering and Earthquake Simulation Laboratory (SEESL), an Equipment Site of the US Network for Earthquake
Engineering Simulation (NEES), which includes two six degree of freedom shake tables and three high speed dynamic
actuators and a structural testing system controller (STS) capable to implement the control algorithms presented above
in large three dimensional structures.
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