r -t h simulation benchmark tudy with a large -scale …

5th World Conference on Structural Control and Monitoring 5WCSCM-10335

Phillips, Chae, Jiang, Spencer, Ricles, Christenson, Dyke, and Agrawal 1

REAL-TIME HYBRID SIMULATION BENCHMARK STUDY WITH A LARGE-SCALE MR DAMPER

Brian M. Phillips

University of Illinois, Urbana, IL 61801, USA [email protected]

Zhaoshuo Jiang

Univ. of Connecticut, Storrs, CT 06269, USA [email protected]

James M. Ricles

Lehigh University, Bethlehem, PA 18015, USA [email protected]

Shirley J. Dyke

Purdue Univ., West Lafayette, IN 47907, USA [email protected]

Yunbyeong Chae Lehigh University, Bethlehem, PA 18015, USA

[email protected]

B. F. Spencer University of Illinois, Urbana, IL 61801, USA

[email protected]

Richard E. Christenson Univ. of Connecticut, Storrs, CT 06269, USA

[email protected]

Anil Agrawal The City College of New York, NY 10031, USA

[email protected]

Abstract

Real-time hybrid simulation is a powerful and cost effective alternative for testing rate dependent structural components such as advanced energy dissipation devices. Hybrid simulation, of which real-time hybrid simulation is a subset, combines numerical simulation with experimental testing in a closed-loop framework. Real-time hybrid simulation frameworks are not yet standardized. Indeed, most are built using different hardware and software, including different numerical integration and delay compensation techniques, leading to potentially different system behavior for setups designed to test the same structure. A simple three-degree-of-freedom structure with a magnetorheological (MR) damper between the ground and first story is proposed for a real-time hybrid simulation benchmark study. This study is aimed to help corroborate real-time hybrid simulation frameworks, develop MR damper models under semi-active conditions, and develop semi-active control strategies, all in a simple yet realistic environment.

Introduction

Hybrid simulation, a combination of experimental testing and numerical simulation, provides an efficient and cost effective means by which to test large and complex structures. In cases when experimental components exhibit rate dependent behavior, real-time execution of the test is necessary for accurate results. Real-time hybrid testing is a specialized class of hybrid testing in which the time scale is 1:1, or real-time. To maintain this constraint, the loop between analytical and experimental components must typically be executed within 10 to 20 milliseconds. Inherent to this time constraint, each cycle of communication between experimental and analytical components must be performed in a limited amount of time. Failure to do so can lead to errors and even system instabilities (Horiuchi et al., 1996). Because of this closed loop, the input to the physical specimen is not predetermined and any errors experienced during the experiment can accumulate. When conducting real-time hybrid simulation, time delays, including computation delays, communication delays, and actuator lags are a main source of experimental error. Because even the fastest hardware and software cannot eliminate delays, mitigation of their effects is an essential part of real-time hybrid simulation. Real-time hybrid simulation frameworks have been developed at the University of Illinois and Lehigh University using markedly different hardware, software, and the numerical algorithms. In this paper, the frameworks will be referred to by the institute at which they were developed for convenience purposes


only. In fact, the two institutes are working together with mutual goals under a larger project cited in the acknowledgements. A simple linear three-degree-of-freedom structure is chosen as a benchmark structure to provide a straightforward yet realistic means by which to evaluate the system performances. Real-time hybrid simulations were carried out in both passive and semi-active control modes at both institutes. Also, a complete numerical model of the magnetorheological (MR) damper has been developed at the University of Connecticut using parametric damper characterization tests from both Illinois and Lehigh. This benchmark study is used to verify and refine the model by comparing the numerical simulation results with real-time hybrid simulation results for passive and semi-active control modes. Lastly, advanced semi-active control strategies were developed based on observed large-scale MR damper performance. These advanced controllers were tested in both numerical simulation and real-time hybrid simulation using the benchmark study. Thus, the purpose of the benchmark study is presented as threefold: (1) validate independently developed real-time hybrid simulation frameworks, (2) refine developed MR damper models, and (3) test semi-active control strategies. Results of this paper highlight the value in using a simple benchmark study to identify and resolve issues that would also be present in a more complex experiment.

Benchmark Structure

The structure chosen for this benchmark study is similar to a well researched three story, single bay steel frame building tested experimentally at the State University of New York at Buffalo (Chung, 1989). This structure was scaled from a large-scale physical model to a prototype-scale and used in shaking table tests to evaluate multi-degree-of-freedom active control strategies. The prototype-scale structure was later recreated as a small-scale physical model at the University of Notre Dame for further study of active control strategies using a shaking table (Dyke et al., 1996, 1998). Experiments at Notre Dame were then expanded to include semi-active control using an MR damper. To facilitate control development, simplified mass, damping, and stiffness matrices were developed for the small-scale physical model. At the University of Illinois, the simplified small-scale model was again used in conjunction with an MR damper (Carrion and Spencer, 2007). In this case, however, focus was placed on the development of a real-time hybrid simulation framework. Because the substructuring technique was used, the components of the structure that were simulated numerically no longer needed to be at the small-scale. Thus, the full-scale parameters were obtained using the similitude relationships reported in Dyke et al. (1996) based on the simplified small-scale model. However, the physical component of the real-time hybrid simulation, the MR damper, remained at the small-scale. Therefore, scaling factors were applied at the interface between the experimental and numerical components.

Benchmark Structure Parameters

The current state of the benchmark structure, as it is presented in this paper, can be considered a simplified prototype-scale model. The total weight of the structure is 596 kN. The structure is a simple linear three degree-of-freedom model with an MR damper located between the ground and first story. For real-time hybrid simulation, the damper is tested experimentally while the rest of the structure is simulated numerically. The relative displacement between the ground and first story is considered equal to the motion of the MR damper. The restoring force of the MR damper is added as a force opposing the motion of the building at the first story. The second order equation of motion that governs the structural behavior is given as MMMM�� CCCC�� KKKK� � GGGG � MLMLMLML �� (1)


where MMMM, CCCC, and KKKK are the mass, damping, and stiffness matrices of the structure, GGGG and LLLL are the influence vectors of the MR damper force and ground excitation, respectively, � is the displacement vector measured relative to the base, is the MR damper force, and �� is the ground acceleration. The numerical values of the structural parameters are reported below.

MMMM � 10�� 20.25 0 00 20.25 00 0 20.25�� kN · s� mm�� (2)

CCCC � 10�� 7.242 �2.069 0�2.069 4.139 �2.0690 �2.069 2.069 �� kN · s mm�� (3)

KKKK � �� 9.933 �5.662 0�5.662 11.34 �5.6620 �5.662 5.662 �� kN mm�� GGGG � ��100 �� LLLL � ��111�� (4, 5, 6)

Figure 1. Elevation view of benchmark structure and available sensors

A state-space representation of the equations of motion is presented below. Not all real-time hybrid simulation frameworks make use of state-space, however the equations are presented for completeness. $� � AAAA$ � BBBB' (7)

AAAA � (((( 0000)�) *)�)�MMMM�+KKKK �MMMM�+CCCC,,,, BBBB � ((((0000)�+ 0000)�+�LLLL MMMM�+GGGG,,,, (8, 9)

$ � -�+ �. �) �� + �� . �� )/0 ' � -�� 1 /0 (10, 11) where $ is the state variable of the first, second, and third story displacements and velocities relative to the ground, and ' is the input of ground acceleration and damper force.

t

abs,1xɺɺ

abs,2xɺɺ

abs,3xɺɺ

fx ,1

+ -

80V V gxɺɺ

ControllerCurrent Driver

i

cA


The structure is assumed to be equipped with a reasonable array of sensors to compliment the MR damper installation as presented in Figure 1. These include three accelerometers to measure the absolute acceleration each of the three stories, a displacement transducer to measure the stroke of the MR damper (assumed equal to the relative first floor displacement), and a force transducer to measure the restoring force provided by the MR damper. The absolute accelerations and displacement can be extracted during real-time hybrid simulation from the states of the system. The force measurement is extracted from the physical load cell. Thus, these five measurements are available to any semi-active control algorithm. The state space representation output 23456 reflects the available sensors. 23456 � 73456$ � 83456' (12)

73456 � ( �MMMM�9KKKK �MMMM�9CCCC1 0 0 0 0 0, 83456 � (:�;9 MMMM�9GGGG0 0 , (13, 14)

23456 � -�� +,5=6 �� .,5=6 �� ),5=6 �+/0 (15) Because most of the structure is being modeled numerically, a full-scale structure is chosen as there is no increased cost in creating a full-scale numerical model. Constraints exist, however, on the experimental part of the hybrid simulation, such as the cost and time for manufacture and installation, as well as the testing equipment. The damper used in this benchmark structure is a 200 kN MR damper; this is about one third of the total weight of the structure. This size is too large for the structure; therefore, the measured force is scaled down by 1:2 to achieve 100 kN for the maximum nominal damper force. The displacement scaling factor, on the other hand, is governed by the testing equipment. The setup at Illinois has a velocity limitation which necessitates the numerically calculated displacement (and thus velocity) to be scaled down by 1:5 to successfully test the desired input earthquake records. As the benchmark does not aim to test a specific MR damper installation, rather the performance of real-time hybrid simulation frameworks and MR damper models, these scaling factors are acceptable. Large-scale MR Damper

Semi-active control devices such as MR dampers combine the desirable properties of both passive and active control devices. They have the ability to adapt to loading demands on the structure, as for an active control system, while they are unable to introduce energy into the system, as for a passive system, eliminating stability concerns. Also, in the absence of any structural control logic, such as during power loss or controller damage, the devices function passively. With an MR damper, changes in the input current can be used to achieve forces predictably in advanced semi-active control algorithms (Spencer et al., 1997). Illinois and Lehigh collectively house three second-generation large-scale 200 kN MR dampers manufactured by Lord Corporation (see Figure 2). The dampers have a stroke of ± 292 mm (13 in) and can generate forces of about 225 kN. The dampers have an accumulator charged to 5.17 MPa (750 psi) to compensate for the thermal expansion of the MR fluid. The three MR dampers nominally have the same properties, although slight variations in performance have been observed in parametric testing. The current to the MR damper is controlled using a pulse-width modulator, which consists of an Advanced Motion Controls model PS2x300W unregulated power supply providing 80 V DC to an Advanced Motion Controls model 20a8 analog servo-drive. This analog servo-drive switches on and off the input 80 VDC at 22 kHz. By controlling the ratio of on-time to off-time for this fixed frequency pulse signal an average output signal over the range of 0 to 80 VDC can be achieved.

Phillips, Chae, Jiang, Spencer, Ricles, Christenson, Dyke, and Agrawal

Figure 2. MR damper installed in Illinois test frame

Numerical Model of MR Damper

Each individual MR damper was experimentally characterizcomprehensive range of frequencies, amplitudesvelocities, (3) force rise time tests fortime tests for step decreases in currentMR damper behavior is used to develop parameters for a hyperbolic tangent type MR damper model at the University of Connecticut. The hyperbolic tangent model was originally proposed by Gavin (2001) as a simplified version of a model proposed by Gamota and Filisko (1991). Bass and Christenson (2008) applied the hyperbolic tangent model to the 200 kN damper used in this studycontinued at the University of Connecticutcurrent driver and damper inductance were addedtangent model parameters were replaced with monotonically increasing or decreasing fourth order polynomials to make the parameters a function of the input currentimprove prediction of the damper response model of the basic hyperbolic tangent model

Figure 3. Schematic of the MR damper hyperbolic tangent model

In the hyperbolic tangent model, the behavior and the spring-dashpot pair term >? represents the inertia of bothmodeled by the function ?@ �?A.

Phillips, Chae, Jiang, Spencer, Ricles, Christenson, Dyke, and Agrawal

. MR damper installed in Illinois test frame

ach individual MR damper was experimentally characterized using: (1) sine wave tests over a of frequencies, amplitudes, and current levels, (2) triangle wave tests at a variety of

for step increases in current at constant velocities, and (4) force step decreases in current at constant velocities. This comprehensive characterization

MR damper behavior is used to develop parameters for a hyperbolic tangent type MR damper model at The hyperbolic tangent model was originally proposed by Gavin (2001) as

version of a model proposed by Gamota and Filisko (1991). Bass and Christenson (2008) applied the hyperbolic tangent model to the 200 kN damper used in this study; subsequently

Connecticut (Jiang et al., 2010). Additional components modeling the current driver and damper inductance were added. Also, the original 200 kN MR damper

parameters were replaced with monotonically increasing or decreasing fourth order meters a function of the input current. These changes were designed to

response during semi-active control. Figure 3 illustrates a mechanical hyperbolic tangent model, without current driver or damper inductance modeling

. Schematic of the MR damper hyperbolic tangent model

, the spring-dashpot pair B9 and C9 model the pre-dashpot pair B? and C? model the post-yield visco-elastic behavior.

represents the inertia of both the MR fluid and the damper piston. The Coulomb friction is

5

(1) sine wave tests over a , and current levels, (2) triangle wave tests at a variety of

, and (4) force decay characterization of the

MR damper behavior is used to develop parameters for a hyperbolic tangent type MR damper model at The hyperbolic tangent model was originally proposed by Gavin (2001) as

version of a model proposed by Gamota and Filisko (1991). Bass and Christenson (2008) ; subsequently, research has

Additional components modeling the MR damper hyperbolic

parameters were replaced with monotonically increasing or decreasing fourth order . These changes were designed to

illustrates a mechanical uctance modeling.

. Schematic of the MR damper hyperbolic tangent model

-yield visco-elastic elastic behavior. The mass

piston. The Coulomb friction is


Illinois Experimental Setup

Equipment

The real-time hybrid testing framework at the University of Illinois is located in the Newmark Structural Engineering Laboratory (NSEL, http://nsel.cee.illinois.edu) and is a part of the Smart Structures Technology Laboratory (SSTL, http://sstl.cee.illinois.edu). The actuator, manufactured by the Shore Western Corporation, is rated at 556 kN (125 kips) with a stroke of ± 152.4 mm (6 in) and effective piston area of 271 cm2 (42 in2). A three-stage servo-valve is used to control the actuator, built up from a Schenck-Pegasus model 1800 rated at 300 lpm (80 gpm) as the main-spool-valve and a Schenck-Pegasus model 20B two-stage servo-valve rated at 3.26 lpm (0.86 gpm) as the pilot-valve. The model 1800 contains internal circuits to excite and demodulate the main-spool LVDT, making the three-stage servo-valve appear as a two-stage servo-value to the servo-controller. Hydraulic oil is routed through a Schenck-Pegasus model 3170804S hydraulic service manifold rated at rated at 300 lpm (80 gpm) connected a 3000 psi line. The displacement of the actuator is measured using an internal AC LVDT. A 445 kN (100 kip) load cell in line with the actuator measures the restoring force of the attached specimen. The actuator and specimen (MR damper) are both mounted on a 7.62 (3 in) thick steel plate. Steel blocks and wedges are used to prevent lateral translation of the actuator and specimen. The steel plate is tied down to the NSEL strong floor using threaded rods to prevent flexing of the plate and shear keys are used to prevent lateral translation of the plate. The frame is designed to minimize backlash and elastic deformation under the high forces expected during testing. The equipment listed previously has previously proven successful for the dynamic testing of large-scale MR dampers (Yang et al., 2002). In addition, the temperature is monitored continuously during testing by three Omega Engineering model SA1XL-J thermocouples and model SMCJ-J analog converters. This equipment has been adapted into the real-time hybrid simulation framework together with the modern, high speed computational hardware detailed below. A Shore Western model 1104 digital servo-controller is used to control the actuator in displacement feedback mode. The servo-controller accepts externally generated commands from a dSPACE model 1103 digital signal processing (DSP) board. This board is used to perform numerical integration of the equations of motion for the numerical substructure, apply the real-time hybrid simulation delay compensation techniques, and compute the desired current for the MR damper based on semi-active control laws. These three numerical components are programmed on a host computer using Simulink, a block diagram style programming tool within Matlab. The Simulink model is translated to C language using Matlab’s Real-Time Workshop and transferred to the DSP board. Real-time execution of the code is controlled and monitored from the host computer. The host computer also acts as the DAQ, logging data from specified channels within the Simulink model. A fixed-step explicit fourth order Runge-Kutta numerical integration scheme is used to solve the equations of motion.

Model-Based Delay Compensation Technique

Illinois uses a model-based feedforward-feedback delay compensation technique (Carrion and Spencer, 2007). In this technique, the dynamics of the servo-hydraulic testing system are characterized using a transfer function from the input commanded displacement to the output measured displacement. This transfer function inherently includes the dynamics of the actuator, servo-valve, servo-controller, and test specimen. However, a single transfer function is insufficient to characterize the system dynamics under varying conditions. When the properties of a specimen change, the resulting system dynamics change through actuator-specimen interaction (Dyke et al., 1995). In the case of the MR damper, the properties of the damper change drastically with changes to the input current. This can be accommodated by measuring multiple transfer functions to characterize the servo-hydraulic system behavior at different levels of input current.


The model-based delay compensation technique consists of a feedforward component and a feedback component. The feedforward component of the controller is developed based on dynamics of the servo-hydraulic system which are characterized by the measured transfer functions. Models of these transfer functions are inverted and placed in series with a low-pass filter to make the inverse stable. By designing the feedforward component as an inverse of the system dynamics, the controller acts to cancel out the system dynamics, improving system response time. A bumpless transfer is used to smoothly transition between different feedforward controllers designed for different specimen conditions (i.e., input current to the MR damper). A feedback controller is added to reduce the error between the measured displacement and the desired displacement. The model-based delay compensation technique is illustrated in Figure 5, where the compensator sends the command D to make the measured displacement accurately track the desired displacement E.

Figure 4. Block diagram of the model-based delay compensation technique

Lehigh Experimental Setup

Equipment

Figure 5a shows the experimental setup for real-time hybrid simulation at Lehigh University. The MR damper is connected to the hydraulic actuator through a stiff horizontal steel section. This section extends the reach of the actuator to accommodate the spacing of anchor locations that secure the damper and the actuator to the laboratory strong floor. A 534 kN (120 kip) load cell is installed between the horizontal steel section and the damper piston to directly measure the force developed in the damper. Among five large capacity dynamic actuators at Lehigh NEES Real-Time Multi-Directional (RTMD) equipment site (http://www.nees.lehigh.edu/facilities), an actuator with 1700 kN (382 kip) force capacity is used for the real-time hybrid system; this damper can generate up to about 500 kN (112 kip) at a piston velocity of 1.0 m/sec (39.4 in/sec) with 3 servo-valves. Each servo-valve has a maximum flow rate of 2082 lpm (550 gpm) at 20.7MPa (3000 psi). The hydraulic supply system consists of five 450 lpm (118.9 gpm) pumps and 16 accumulators of 190 liters (50.2 gallons) capacity connected to 9 Nitrogen gas bottles of 1325 liters (850.2 gallons) capacity. This configuration enables a typical earthquake to be simulated on a four floor half-scale frame structure in real time for 30 seconds with the supply pressure maintained within 20.7 to 24.1 MPa (3000 to 3500 psi). Within the RTMD IT architecture, the servo-controller (DCS 2000) communicates with all of the servo-valves, actuators, hydraulic service manifold control box and simulation computer (RTMDsim) with a clock speed of 1024 Hz. The servo-controller consists of a digital signal processor (DSP) real-time control card (Module 2201), which is plugged into the computer called RTMDctrl. The real-time hybrid simulation is controlled and implemented by the RTMDxPC module. The Matlab Simulink file from the RTMDsim computer is compiled and downloaded to xPC that runs Mathwork’s real-time Target PC software package. This system provides commands to and receives feedback from RTMDctrl in real time over SCRAMNet which is the underlying communication mechanism between RTMD modules based on a proprietary shared memory bus and fiber optic network technology.

GFF(s)

GFB(s) Gxu(s)e uFB

uFF

xd u

Feedforward Controller

Feedback Controller Experimental Setup

+

-+

+


Delay Compensation Technique

Lehigh uses an inverse compensation procedure to minimize actuator delay in the real-time hybrid simulation (Chen et al., 2008). It is based on the simplified modeling of servo-hydraulic system. By assuming that the actuator achieves the displacement F�9G at time HF�9, and with the linear actuator response shown in Figure 5b, the delayed displacement response of FG at the end of the ith time step can be expressed as

FG � F�9G � 9I @ F � F�9G A (17)

where F is the command displacement issued to the experimental substructure from the integration algorithm for the ith time step. The displacement F�9G is the delayed displacement achieved in the prior time step i−1. Applying the discrete z-transform to (17), the discrete transfer function JG@KA relating the delayed actuator response FG to the command displacement F for a linear elastic experimental substructure is equal to

JG@KA � LM@NAL@NA � N

IN�@I�9A (18)

where OG@KA and O@KA are the discrete z-transforms of FG and F, respectively. The delay constant P for the 1700 kN actuator was identified as 29 (representing an actuator delay of 29/1024 sec.). This value is used in the real-time hybrid simulation.

Figure 5a. Experimental setup at Lehigh University, b. Conceptual actuator response

Example Semi-Active Control Strategies for Large-Scale MR Dampers

Basic Semi-Active Control Strategies

Two passive control cases are considered for reference when designing semi-active control strategies for the MR damper. In the passive control cases, a constant current is maintained in the MR dampers at 0.0 and 2.5 Amps for the passive-off and passive-on cases, respectively. The passive-off case demonstrates the minimum contribution that the damper can provide to the structure. On the other hand, the passive-on case usually performs very well and semi-active controllers can be judged on their ability to improve performance beyond this case. For demonstrative purposes, four semi-active controller designs are presented. These designs are based on variations of the clipped-optimal controller (Dyke et al., 1996) QR � Q35STU@R � 3A3V (19)

MR damper

actuator

MR damperload cell

tie down beam


where QR is the commanded current (input to MR damper), Q35S is the maximum current, R is the commanded (desired) force, 3 is the measured force, and T is the Heaviside function. In short, when the commanded force R is greater in magnitude than the measured force 3 and of the same sign, the maximum current Q35S is sent to the damper. The magnitude of the force 3 will increase in an attempt to reach R. In all other cases, the current is set to 0.0 Amps. The command force R for all controller designs presented is determined using an LQG controller, combining a Kalman filter to estimate the states of the system followed by an LQR controller based on full-state feedback. Inputs to the Kalman filter include the absolute accelerations of the three stories, the displacement of the first story, and the restoring force of the MR damper. An observer to estimate the states of the system and facilitate control using input force is presented below.

$W� � @X � Y73456A$W � ZY , \]G53^ � Y8G53^_` a23456 b (20)

BBBBdamp � ( :)�+MMMM�+GGGG, DDDDdamp � (MMMM�+GGGG0 , (21, 22)

where $W is the estimate of the states, L is the Kalman filter gain, and BBBBdamp and DDDDdamp reflect the fact that only the damper force f is available for control. The estimated states 246g are calculated as below.

246g � 746g$W � 846g a23456 b (23)

CCCCest � -IIIIk;k/ DDDDest � -:k;l/ (24, 25) Once the Kalman filter reconstructs the states of the system, the states are multiplied by an LQR gain to calculate the optimal control force. The LQG gains are determined based on minimizing m � limpq∞ rs tuv -@CCCC$A0QQQQ@CCCC$A � x�/EHp? y (26) where QQQQ and x are the weighting parameters for the outputs and control force, respectively. Note that the CCCC matrix in (26) does not have to be restricted to reflect measurable parameters for LQR design. The design of the Kalman filter and LQR gains, LLLL and KKKK, were performed using the control toolbox in Matlab employing similar weighting parameters as Dyke et al. (1996). In all control cases, the Kalman filter was designed assuming unbiased process and measurement noise with a covariance ratio of z � {;�|;�|/{~�~� � 50. For the bang-bang type control, the LQR weighting was chosen as x � 10�9�

and �\ ��,5=6, ��,5=6_ � 1, i.e., heavily weighing the third floor absolute acceleration relative to the control force. These choices allow the control force to reach very high magnitudes, higher than the 200 kN MR damper can achieve. For the force-tracking-type control, the weight of the control force is increased to x � 1500, which keeps the command force within bounds that are physically achievable.

Advanced Control Strategies

One concept integrated into some of the controller designs is over-driving the MR damper circuit (Yang et al., 2002). Experimental results show that commanding a higher current to the MR damper results in a faster force rise time. If quickly achieving a force of 200 kN were desired, a relatively high current (such as 7.5 Amps) could be applied until 200 kN is achieved, then dropped to a lower current (such as 2.5 Amps) to maintain this force. Leaving a high current on for a long period of time has the potential of both overshooting the desired force and burning out the MR damper coils, so it is important to only use this


high level for overdriving the circuit, not maintaining a force level. Figure 6 shows the experimental results during a constant velocity (50 mm/sec) test for steps in current from 0.0 Amps to a higher current level with the steps beginning at 0.0 seconds. The quick rise time of the higher current steps is the phenomenon being utilized by the over-driven current controller.

Figure 6. Over-driven current during constant 50 mm/sec

Figure 7. Back-driven current during constant 50 mm/sec

A compliment to the concept of over-driving is that of back-driving the MR damper circuit (Yang et al., 2002). If a high level of force exists in the MR damper as a result of an input current, the force can be is reduced by setting the current to zero, as is typically done. This approach is analogous to driving a boat at a high velocity and stopping the engine to reach zero velocity. However, a boat engine can also be set in reverse, and doing so would bring the velocity to zero much more quickly. Likewise, the current in the MR damper could be commanded in the opposite direction rather than set to zero, i.e. back-driving the circuit, which aids in dissipating any residual magnetic field that would cause a slow force decrease time. On the other hand, if the back-driven current were left on for too long, the force would eventually start to rise again as a magnetic field is generated in the opposite direction. Therefore, some intelligence must be

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.40

50

100

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orce

(kN

)

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1 A 2.5 A 3 A 4 A 5 A 6 A 7 A 8 A

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

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added to control the duration of the back-driven current. Figure 7 shows experimental results for applying back-driven current during a constant velocity (50 mm/sec) after a large force is achieved (168 kN) using 2.5 Amps. A back-driven current of -7.5 Amps is applied beginning at 0.0 seconds for various durations, after which the current is set to 0.0 Amps. Results show that using back-driven current decreases the force decay time considerably. However, as noted previously, leaving the back-driven current on for too long causes the force to rise again.

Semi-Active Controllers used in this Study

Four semi-active controllers are designed and tested in numerical simulation using the hyperbolic tangent model and subsequently tested in real-time hybrid simulation. These controllers combine the concepts explored previously, including clipped-optimal control, over-driven control, and back-driven control. Controller (1): Clipped-optimal control (bang-bang). This controller uses the simple clipped-optimal control algorithm with Q35S = 2.5 Amps. The LQR gains are selected to achieve a bang-bang type controller as described previously with x � 10�9�and �\ ��,5=6, ��,5=6_ � 1, i.e. placing virtually no weight on the control force. As a result, the command force will jump between extremely large positive and negative numbers. The damper, limited to a nominal 200 kN, cannot achieve these forces, thus the controller is either driving at 2.5 Amps or turned off if the commanded force is in the wrong direction. Controller (2): Clipped-optimal control (force-tracking). This controller also uses the simple clipped-optimal control algorithm with Q35S = 2.5 Amps. The LQR gains are selected to achieve a force-tracking type controller as described previously with x � 1500 and �\ ��,5=6, ��,5=6_ � 1 . Because the force is achievable by the damper, control becomes an exercise in force-tracking. As the measured force is either above or below the commanded force (and of the same sign), the current will be switched to either 0.0 or 2.5 Amps, respectively, to track the commanded force. If the signs of the forces are different, the force will be set to 0.0 Amps. Controller (3): Over-driven back-driven clipped-optimal control (bang-bang). This controller uses the weight for the LQR control x � 10�9�and �\ ��,5=6, ��,5=6_ � 1, and therefore another bang-bang type controller results. In this case, the maximum current of the clipped-optimal control algorithm is set to 7.5 Amps. The main result of over-driving the current is a faster rise time to the desired force. However, because the controller is a bang-bang type, the desired force can never be achieved. Therefore, the higher current not only decreases the force rise time, but also increases the resulting maximum force. A back-driven current scheme is also implemented in this controller at -7.5 Amps. Three conditions are set where the back-driven current would either not be engaged or would be disengaged: (a) When, after engaged for a minimum amount of time to allow for the force to begin to decrease in magnitude, the force begins to increase in magnitude. This condition indicates that a magnetic field is being generated in the opposite direction, an undesirable outcome. (b) When the preceding commanded current is 0.0 Amps. Because back-driving the current can only reduce MR damper forces caused by current as opposed to velocity, it is important to ensure that such a current-induced force exists. (c) When the measured current is less than 25 kN in magnitude; little benefit is gained by back-driving the current at these low levels of force. This condition would also turn the back-driven current off as the measured force enters this threshold from a higher magnitude, complimenting condition (a) without the time restriction. Controller (4): Over-driven back-driven clipped-optimal control (force-tracking). This controller uses the weight for the LQR control x � 1500 and �\ ��,5=6, ��,5=6_ � 1, resulting in another force-tracking controller. However, in this controller, rather than applying a hard 7.5 Amps when the clipped optimal


controller calls for Q35S, current anywhere between 0.0 and 7.5 Amps is commanded. This current is chosen as proportional to the magnitude of error between the desired and measured force (P control). A back-driven current scheme is also employed at -7.5 Amps similar to controller (3). However, condition (a) on the back-driven controller is removed, because as the commanded force is being tracked by the measured force accurately, the measured force will naturally oscillate above and below the command force. This oscillation can be interpreted as a rise in the force which would erroneously switch off the back-driven current based on condition (a). Condition (c) is found to be sufficient in switching off the back-driven current for this force-tracking type controller.

Real-Time Hybrid Simulation Results

Real-time hybrid simulations of the benchmark structure were performed at both the University of Illinois and at Lehigh University, and in numerical simulation using the hyperbolic tangent model to represent the physical MR damper. Because the behavior of an MR damper is sensitive to changes in temperature (Yang et al., 2002), the temperature was continuously monitored during the real-time hybrid simulations. The Illinois experiments were performed between 25.2 and 28.1 °C while the Lehigh experiments were performed at 20.7 and 21.4 °C, the ambient laboratory conditions in each case. These temperature ranges are relatively close and have little effect on the resulting MR damper behavior.

Table 1. Control results for numerical simulation (entry 1), real-time hybrid simulation at Illinois (entry 2), and real-time hybrid simulation at Lehigh (entry 3)

Uncontrolled

Passive- Off

Passive- On

Clipped-Opt. bang-bang

Clipped-Opt. force-tracking

ODBDCO bang-bang

ODBDCO force-tracking 9

(mm) 138.5 (sim) 104.4 41.8 49.7 (+19.1%)(a) 49.4 (+18.3%) 50.6 (+21.3%) 56.3 (+34.7%) -- (Illinois) 112.9 41.0 50.0 (+21.8%) 51.6 (+25.7%) 51.3 (+25.1%) 57.5 (+40.2%) -- (Lehigh) 108.1 39.9 49.3 (+23.7) 51.1 (+28.0) 52.0 (+30.4) 54.3 (+36.1) � � 9

(mm) 79.4 69.9 36.4 35.5 (−2.5%) 36.2 (-0.7%) 32.4 (−11.1%) 36.0 (−1.2%) -- 73.2 34.2 34.7 (+1.49%) 36.1 (+5.7%) 32.4 (−5.2%) 36.4 (+6.5%) -- 71.4 33.5 33.7 (+0.5%) 35.4 (+5.5%) 31.5 (-6.1%) 35.4 (+5.5%) � � �

(mm) 50.5 43.9 25.5 21.2 (−16.8%) 20.4 (-20.2%) 24.9 (−2.5%) 19.6 (−23.2%) -- 45.9 24.8 21.5 (−13.2%) 19.3 (-22.2%) 25.5 (+2.9%) 19.2 (−22.5%) -- 44.7 24.3 21.3 (-12.4%) 19.0 (-21.7%) 24.8 (+2.2%) 18.9 (-22.1%) �9,��

(g)

0.914 0.638 0.445 0.427 (−4.3%) 0.488 (+9.6%) 0.842 (+89.2%) 0.483 (+8.4%) -- 0.706 0.418 0.525 (+25.6%) 0.472 (+12.9%) 0.757 (+81.2%) 0.478 (+14.4%) -- 0.674 0.403 0.536 (+33.2%) 0.448 (+11.2%) 0.709 (+76.1%) 0.456 (+13.3%) ��,��

(g)

1.110 0.816 0.565 0.472 (−16.4%) 0.539 (-4.6%) 0.643 (+13.9%) 0.592 (+4.7%) -- 0.881 0.530 0.547 (+3.2%) 0.578 (+8.85%) 0.519 (−2.1%) 0.562 (+5.9%) -- 0.838 0.529 0.550 (+4.0%) 0.557 (+5.3%) 0.481 (-9.0%) 0.563 (+6.5%) ��,��

(g)

1.439 1.251 0.727 0.604 (−16.8%) 0.581 (-20.2%) 0.709 (−2.5%) 0.558 (−23.2%) -- 1.307 0.706 0.613 (−13.2%) 0.549 (-22.2%) 0.726 (+2.9%) 0.547 (−22.5%) -- 1.274 0.693 0.606 (-12.4%) 0.542 (-21.7%) 0.708 (+2.2%) 0.538 (-22.1%)

(kN) -- 30.5 177.4 147.5 (−16.8%) 137.2 (-22.7%) 173.2 (−2.3%) 145.4 (−18.0%) -- 20.7 177.5 152.9 (−13.8%) 146.0 (-17.7%) 186.8 (+5.3%) 137.0 (−22.8%) -- 24.7 181.7 158.1 (-13.0%) 145.4 (-20.0%) 188.3 (+3.6%) 139.6 (-23.2%)

(a) percentages are relative to the passive-on case.

Tests were run for the passive-off, passive-on, clipped-optimal (bang-bang), clipped-optimal (force-tracking), over-driven back-driven clipped-optimal (bang-bang), and over-driven back-driven clipped-optimal (force-tracking) control cases. The structure was subjected to the NS component of the 1940 El Centro earthquake at full scale. The maximum absolute values of the first, second, and third story relative displacements (story drifts), first, second, and third story absolute accelerations, and damper forces are presented for each control case in Table 1. In addition, an uncontrolled case was run in numerical simulation without an MR damper. Because semi-active controllers can often be judged based


on their ability to improve upon the passive-on case, each semi-active controller value in Table 1 is followed by the percent increase or decrease relative to the same parameter in the passive-on case.

MR damper time histories of the displacement and force as well as force-displacement and force- velocity hysteresis for the four semi-active controllers are presented in Figures 8 through 11. Because the input current to the MR damper is changing for these controllers, they are seen as the most challenging to achieve a good comparison of results. To highlight the differences more closely, time histories are only presented for the portion of significant response to the earthquake input. On the other hand, hysteresis plots include data for the entire duration of the earthquake.

The clipped-optimal (bang-bang) controller results are presented in Figure 8. Both experimental results compare very well, showing high levels of confidence in both real-time hybrid simulation frameworks. Because of the bang-bang approach, the commanded force will switch between extremely large positive and negative forces. As the measured force tries to track this force, the MR damper undergoes a sudden change in current. This demand tests the limits of the hyperbolic tangent model, which performs well under the dynamic conditions.

The results of the clipped-optimal controller (force-tracking) are shown in Figure 9. Again the two experimental results match very well and the hyperbolic tangent model results only differ slightly as the force is decreasing. In this approach, the force doesn’t increase or decrease as rapidly as the bang-bang approach. This naturally leads to lower story accelerations, as shown in Table 1, because the changes in the MR damper force are smoother. Also, this type of force-tracking control results in a lower MR damper forces while achieving comparable, if not better, control performance to the bang-bang approach. One

0 1 2 3 4 5 6 7 8 9 10

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Figure 8. Clipped-optimal controller (bang-bang)

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Figure 9. Clipped-optimal controller (force-tracking)


shortcoming of this control approach is that the measured force can oscillate around the control force during accurate tracking, causing smaller, higher frequency accelerations. This oscillation is apparent around the peaks of the measured force.

The over-driven back-driven clipped-optimal (bang-bang) controller results are presented in Figure 10. Experimental results compare very well and the hyperbolic tangent model picks up the effect of the back-driven current accurately. In this controller, higher forces are achieved because the current is driven at 7.5 Amps rather than 2.5 Amps. This change does not result in better controller performance; Table 1 shows that the performance is only about as good as the passive-on case. Overall, the over-driven and back-driven components of the controller help to track the commanded force better; however, in the case of the bang-bang

approach, this strategy is not always effective. In the bang-bang approach, the softer force response of not having the over-driven and back-driven components leads to better controller performance.

The results for the over-driven back-driven clipped-optimal (force- tracking) controller are presented in Figure 11. Experimental results and numerical simulation results compare very well in this case. As with the other force-tracking type controller, this controller achieves excellent performance while maintaining relatively low levels of damper force, as seen in Table 1. Because the simple clipped-optimal logic of applying Q35S was replaced with a current command proportional to the magnitude of the error between the commanded and measured forces, the high frequency oscillations of the measured force are reduced significantly when compared to the other force-tracking controller. Also,

because the controller is a force-tracking type, the commanded force does not change rapidly. Thus, the over-driven and back-driven aspects of the controller are less significant for accurate tracking than compare with the bang-bang type controllers. However, they do provide slight improvements.

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Figure 10. Over-driven back-driven clipped-optimal controller (bang-bang)

Figure 11. Over-driven back-driven clipped-optimal controller (force-tracking)

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Conclusions

This paper presented a simple three story benchmark structure for real-time hybrid simulation development and verification experiments. Results show that the independently developed real-time hybrid simulation frameworks at the University of Illinois and Lehigh University achieve very similar performance for the same numerical structure and almost identical MR damper specimens (same make and model). With increasingly more complex structures planned for future real-time hybrid simulations at the two facilities, the benchmark structure provides a confident starting point. The hyperbolic tangent model presented has reached a form where it can accurately predict the semi-active performance of the large-scale MR damper, as seen in comparisons with the experimental results. Also, four semi-active control strategies based on the clipped-optimal controller were evaluated experimentally. Force-tracking type controllers were found to achieve excellent control performance, while maintaining relatively low MR damper forces. In addition, over-driven and back-driven algorithms to overcome delays in force rise time and force decay time, respectively, were explored in the context of control design. These algorithms improved tracking of the commanded forces in all cases; however, they are much more useful if the commanded force changes rapidly. This benchmark structure may be of use to other institutes to verify real-time hybrid simulation frameworks in a simple, well explored environment. For different MR damper specimens, the scaling factors can be chosen appropriately and used for in-house studies, although the results would not exactly match with those presented in this paper.

Acknowledgements

The authors would like to acknowledge the support of the National Science Foundation under award CMMI-1011534.

References

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