Large‐scale real‐time hybrid simulation involving multiple experimental substructures and adaptive actuator delay compensation

Real‐time hybrid simulation provides a viable method to experimentally evaluate the performance of structural systems subjected to earthquakes. The structural system is divided into substructures, where part of the system is modeled by experimental substructures, whereas the remaining part is modeled analytically. The displacements in a real‐time hybrid simulation are imposed by servo‐hydraulic actuators to the experimental substructures. Actuator delay compensation has been shown by numerous researchers to vitally achieve reliable real‐time hybrid simulation results. Several studies have been performed on servo‐hydraulic actuator delay compensation involving single experimental substructure with single actuator. Research on real‐time hybrid simulation involving multiple experimental substructures, however, is limited. The effect of actuator delay during a real‐time hybrid simulation with multiple experimental substructures presents challenges. The restoring forces from experimental substructures may be coupled to two or more degrees of freedom (DOF) of the structural system, and the delay in each actuator must be adequately compensated. This paper first presents a stability analysis of actuator delay for real‐time hybrid simulation of a multiple‐DOF linear elastic structure to illustrate the effect of coupled DOFs on the stability of the simulation. An adaptive compensation method then proposed for the stable and accurate control of multiple actuators for a real‐time hybrid simulation. Real‐time hybrid simulation of a two‐story four‐bay steel moment‐resisting frame with large‐scale magneto‐rheological dampers in passive‐on mode subjected to the design basis earthquake is used to experimentally demonstrate the effectiveness of the compensation method in minimizing actuator delay in multiple experimental substructures. Copyright © 2011 John Wiley & Sons, Ltd.     

Improving the inverse compensation method for real‐time hybrid simulation through a dual compensation scheme

Real‐time hybrid simulation combines experimental testing of physical substructure(s) and numerical simulation of analytical substructure(s), and thus enables the complete structural system to be considered during an experiment. Servo‐hydraulic actuators are typically used to apply the command displacements to the physical substructure(s). Inaccuracy and instability can occur during a real‐time hybrid simulation if the actuator delay due to servo‐hydraulic dynamics is not properly compensated. Inverse compensation is a means to negate actuator delay due to inherent servo‐hydraulic actuator dynamics during a real‐time hybrid simulation. The success of inverse compensation requires the use of a known accurate value for the actuator delay. The actual actuator delay however may not be known before the simulation. An estimation based on previous experience has to be used, possibly leading to inaccurate experimental results. This paper presents a dual compensation scheme to improve the performance of the inverse compensation method when an inaccurately estimated actuator delay is used in the method. The dual compensation scheme modifies the predicted displacement from the inverse compensation procedure using the actuator tracking error. Frequency response analysis shows that the dual compensation scheme enables the inverse compensation method to compensate for actuator delay over a range of frequencies when an inaccurately estimated actuator delay is utilized. Real‐time hybrid simulations of a single‐degree‐of‐freedom system with an elastomeric damper are conducted to experimentally demonstrate the effectiveness of the dual compensation scheme. Exceptional experimental results are shown to be achieved using the dual compensation scheme without the knowledge of the actual actuator delay a priori. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability analysis of SDOF real‐time hybrid testing systems with explicit integration algorithms and actuator delay

Real‐time hybrid testing is a method that combines experimental substructure(s) representing component(s) of a structure with a numerical model of the remaining part of the structure. These substructures are combined with the integration algorithm for the test and the servo‐hydraulic actuator to form the real‐time hybrid testing system. The inherent dynamics of the servo‐hydraulic actuator used in real‐time hybrid testing will give rise to a time delay, which may result in a degradation of accuracy of the test, and possibly render the system to become unstable. To acquire a better understanding of the stability of a real‐time hybrid test with actuator delay, a stability analysis procedure for single‐degree‐of‐freedom structures is presented that includes both the actuator delay and an explicit integration algorithm. The actuator delay is modeled by a discrete transfer function and combined with a discrete transfer function representing the integration algorithm to form a closed‐loop transfer function for the real‐time hybrid testing system. The stability of the system is investigated by examining the poles of the closed‐loop transfer function. The effect of actuator delay on the stability of a real‐time hybrid test is shown to be dependent on the structural parameters as well as the form of the integration algorithm. The stability analysis results can have a significant difference compared with the solution from the delay differential equation, thereby illustrating the need to include the integration algorithm in the stability analysis of a real‐time hybrid testing system. Copyright © 2007 John Wiley & Sons, Ltd.     

Real‐time hybrid testing of a smart base isolation system

Real‐time hybrid testing is a very effective technique for evaluating the dynamic responses of rate‐dependent structural systems subjected to earthquake excitation. A smart base isolation system has been proposed by others using conventional low‐damping isolators and controllable damping devices such as magnetorheological (MR) dampers to achieve specified control target performance. In this paper, real‐time hybrid tests of a smart base isolation system are conducted. The simulation is for a base‐isolated two‐degrees‐of‐freedom building model where the superstructure and the low‐damping base isolator are numerically simulated, and the MR damper is physically tested. The target displacement obtained from the step‐by‐step integration of the numerical substructure is imposed on the MR damper, which is driven by three different control algorithms in real‐time. To compensate the actuator delay and improve the accuracy of the test, an adaptive phase‐lead compensator is implemented. The accuracy of each test is investigated by using the root mean square error and the tracking indicator. Experimental results demonstrate that the hybrid testing procedure using the proposed actuator compensation techniques is effective for investigating the control performance of the MR damper in a smart base isolation system. Copyright © 2013 John Wiley & Sons, Ltd.     

Real‐time force control for servo‐hydraulic actuator systems using adaptive time series compensator and compliance springs

Servo‐hydraulic actuators have been widely used for experimental studies in engineering. They can be controlled in either displacement or force control mode depending on the purpose of a test. It is necessary to control the actuators in real time when the rate‐dependency effect of a test specimen needs to be accounted for under dynamic loads. Real‐time hybrid simulation (RTHS) and effective force testing (EFT) method, which can consider the rate‐dependency effect, have been known as viable alternatives to the shake table testing method. Due to the lack of knowledge in real‐time force control, however, the structures that can be tested with RTHS and EFT are fairly limited. For instance, satisfying the force boundary condition for axially stiff members is a challenging task in RTHS, while EFT has a difficulty to be implemented for nonlinear structures. In order to resolve these issues, this paper introduces new real‐time force control methods utilizing the adaptive time series (ATS) compensator and compliance springs. Unlike existing methods, the proposed force control methods do not require the structural modeling of a test structure, making it easy to be implemented especially for nonlinear structures. The force tracking performance of the proposed methods is evaluated for a small‐scale steel mass block system with a magneto‐rheological damper subjected to various target forces. Accuracy, time delay, and resonance response of these methods are discussed along with their force control performance for an axially stiff member. Overall, a satisfactory force tracking performance was observed by using the proposed force control methods.     

Compensation of actuator delay and dynamics for real‐time hybrid structural simulation

Compensation of delay and dynamic response of servo‐hydraulic actuators is critical for stability and accuracy of hybrid experimental and numerical simulations of seismic response of structures. In this study, current procedures for compensation of actuator delay are examined and improved procedures are proposed to minimize experimental errors. The new procedures require little or no a priori information about the behavior of the test specimen or the input excitation. First, a simple approach is introduced for rapid online estimation of system delay and actuator command gain, thus capturing the variability of system response through a simulation. Second, an extrapolation procedure for delay compensation, based on the same kinematics equations used in numerical integration procedures is examined. Simulations using the proposed procedures indicate a reduction in high‐frequency noise in force measurements that can minimize the excitation of high‐frequency modes. To further verify the effectiveness of the compensation procedures, the artificial energy added to a hybrid simulation as a result of actuator tracking errors is measured and used for demonstrating the improved accuracy in the simulations. Copyright © 2007 John Wiley & Sons, Ltd.     

Accurate real‐time hybrid earthquake simulations on large‐scale MDOF steel structure with nonlinear viscous dampers

This paper presents real‐time hybrid earthquake simulation (RTHS) on a large‐scale steel structure with nonlinear viscous dampers. The test structure includes a three‐story, single‐bay moment‐resisting frame (MRF), a three‐story, single‐bay frame with a nonlinear viscous damper and associated bracing in each story (called damped braced frame (DBF)), and gravity load system with associated seismic mass and gravity loads. To achieve the accurate RTHS results presented in this paper, several factors were considered comprehensively: (1) different arrangements of substructures for the RTHS; (2) dynamic characteristics of the test setup; (3) accurate integration of the equations of motion; (4) continuous movement of the servo‐controlled hydraulic actuators; (5) appropriate feedback signals to control the RTHS; and (6) adaptive compensation for potential control errors. Unlike most previous RTHS studies, where the actuator stroke was used as the feedback to control the RTHS, the present study uses the measured displacements of the experimental substructure as the feedback for the RTHS, to enable accurate displacements to be imposed on the experimental substructure. This improvement in approach was needed because of compliance and other dynamic characteristics of the test setup, which will be present in most large‐scale RTHS. RTHS with ground motions at the design basis earthquake and maximum considered earthquake levels were successfully performed, resulting in significant nonlinear response of the test structure, which makes accurate RTHS more challenging. Two phases of RTHS were conducted: in the first phase, the DBF is the experimental substructure, and in the second phase, the DBF together with the MRF is the experimental substructure. The results from the two phases of RTHS are presented and compared with numerical simulation results. An evaluation of the results shows that the RTHS approach used in this study provides a realistic and accurate simulation of the seismic response of a large‐scale structure with rate‐dependent energy dissipating devices. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance of a real‐time pseudodynamic test system considering nonlinear structural response

This paper presents the implementation details of a real‐time pseudodynamic test system that adopts an implicit time integration scheme. The basic configuration of the system is presented. Physical tests were conducted to evaluate the performance of the system and validate a theoretical system model that incorporates the dynamics and nonlinearity of a test structure and servo‐hydraulic actuators, control algorithm, actuator delay compensation methods, and the flexibility of an actuator reaction system. The robustness and accuracy of the computational scheme under displacement control errors and severe structural softening are examined with numerical simulations using the model. Different delay compensation schemes have been implemented and compared. One of the schemes also compensates for the deformation of an actuator reaction system. It has been shown that the test method is able to attain a good performance in terms of numerical stability and accuracy. However, it has been shown that test results obtained with this method can underestimate the inelastic displacement drift when severe strain softening develops in a test structure. This can be attributed to the fact that the numerical damping effect introduced by convergence errors becomes more significant as a structure softens. In a real‐time test, a significant portion of the convergence errors is caused by the time delay in actuator response. Hence, a softening structure demands higher precision in displacement control. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive multi‐rate interface: development and experimental verification for real‐time hybrid simulation

Real‐time hybrid simulation (RTHS) is a powerful cyber‐physical technique that is a relatively cost‐effective method to perform global/local system evaluation of structural systems. A major factor that determines the ability of an RTHS to represent true system‐level behavior is the fidelity of the numerical substructure. While the use of higher‐order models increases fidelity of the simulation, it also increases the demand for computational resources. Because RTHS is executed at real‐time, in a conventional RTHS configuration, this increase in computational resources may limit the achievable sampling frequencies and/or introduce delays that can degrade its stability and performance. In this study, the Adaptive Multi‐rate Interface rate‐transitioning and compensation technique is developed to enable the use of more complex numerical models. Such a multi‐rate RTHS is strictly executed at real‐time, although it employs different time steps in the numerical and the physical substructures while including rate‐transitioning to link the components appropriately. Typically, a higher‐order numerical substructure model is solved at larger time intervals, and is coupled with a physical substructure that is driven at smaller time intervals for actuator control purposes. Through a series of simulations, the performance of the AMRI and several existing approaches for multi‐rate RTHS is compared. It is noted that compared with existing methods, AMRI leads to a smaller error, especially at higher ratios of sampling frequency between the numerical and physical substructures and for input signals with high‐frequency content. Further, it does not induce signal chattering at the coupling frequency. The effectiveness of AMRI is also verified experimentally. Copyright © 2016 John Wiley & Sons, Ltd.     

Considerations for the development of real‐time dynamic testing using servo‐hydraulic actuation

This paper presents a study of the use of servo‐hydraulic systems in the implementation of real‐time large‐scale structural testing methods in force control such as effective force testing (EFT) and in displacement control such as real‐time pseudodynamic testing (RPsD). Mathematical models for both types of control systems are presented and used to investigate the influences of servo‐systems on the overall system performance. Parameters investigated include the overall system dynamics, nonlinearities of servo‐systems, actuator damping, system mass including piston mass, and system response delay. Results of both numerical simulations and experiments showed that many of the influences of the servo‐hydraulic system that significantly affect the real‐time dynamic tests can be properly compensated through control schemes identified in this paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Dual compensation strategy for real‐time hybrid testing

Real‐time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo‐hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simulations of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer‐loop feed‐forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of numerical time‐integration schemes for real‐time hybrid testing

We present a comparison of methods for the analysis of the numerical substructure in a real‐time hybrid test. A multi‐tasking strategy is described, which satisfies the various control and numerical requirements. Within this strategy a variety of explicit and implicit time‐integration algorithms have been evaluated. Fully implicit schemes can be used in fast hybrid testing via a digital sub‐step feedback technique, but it is shown that this approach requires a large amount of computation at each sub‐step, making real‐time execution difficult for all but the simplest models. In cases where the numerical substructure poses no harsh stability condition, it is shown that the Newmark explicit method offers advantages of speed and accuracy. Where the stability limit of an explicit method cannot be met, one of the several alternatives may be used, such as Chang's modified Newmark scheme or the α‐operator splitting method. Appropriate methods of actuator delay compensation are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Real‐time hybrid simulation for an RC bridge pier subjected to both horizontal and vertical ground motions

It is well known that real‐time hybrid simulation (RTHS) is an effective and viable dynamic testing method. Numerous studies have been conducted for RTHS during the last 2 decades; however, the application of RTHS toward practical civil infrastructure is fairly limited. One of the major technical barriers preventing RTHS from being widely accepted in the testing community is the difficulty of accurate displacement control for axially stiff members. For such structures, a servo‐hydraulic actuator can generate a large force error due to the stiff oil column in the actuator even if there is a small axial displacement error. This difficulty significantly restricts the implementation of RTHS for structures such as columns, walls, bridge piers, and base isolators. Recently, a flexible loading frame system was developed, enabling a large‐capacity real‐time axial force application to axially stiff members. With the aid of the flexible loading frame system, this paper demonstrates an RTHS for a bridge structure with an experimental reinforced concrete pier, which is subjected to both horizontal and vertical ground motions. This type of RTHS has been a challenging task due to the lack of knowledge for satisfying the time‐varying axial force boundary condition, but the newly developed technology for real‐time force control and its incorporation into RTHS enabled a successful implementation of the RTHS for the reinforced concrete pier of this study.     

Stability analysis of MDOF real‐time dynamic hybrid testing systems using the discrete‐time root locus technique

The time delay resulting from the servo hydraulic systems can potentially destabilize the real‐time dynamic hybrid testing (RTDHT) systems. In this paper, the discrete‐time root locus technique is adopted to investigate the delay‐dependent stability performance of MDOF RTDHT systems. Stability analysis of an idealized two‐story shear frame with two DOFs is first performed to illustrate the proposed method. The delay‐dependent stability condition is presented for various structural properties, time delay, and integration time steps. Effects of delay compensation methods on stability are also investigated. Then, the proposed method is applied to analyze the delay‐dependent stability of a single shaking table RTDHT system with an 18‐DOF finite element numerical substructure, and corresponding RTDHTs are carried out to verify the theoretical results. Furthermore, the stability behavior of a finite element RTDHT system with two physical substructures, loaded by twin shaking tables, is theoretically and experimentally investigated. All experimental results convincingly demonstrate that the delay‐dependent stability analysis on the basis of the discrete‐time root locus technique is feasible. Copyright © 2014 John Wiley & Sons, Ltd.     

Real‐time hybrid testing using the unconditionally stable explicit CR integration algorithm

Real‐time hybrid testing combines experimental testing and numerical simulation, and provides a viable alternative for the dynamic testing of structural systems. An integration algorithm is used in real‐time hybrid testing to compute the structural response based on feedback restoring forces from experimental and analytical substructures. Explicit integration algorithms are usually preferred over implicit algorithms as they do not require iteration and are therefore computationally efficient. The time step size for explicit integration algorithms, which are typically conditionally stable, can be extremely small in order to avoid numerical stability when the number of degree‐of‐freedom of the structure becomes large. This paper presents the implementation and application of a newly developed unconditionally stable explicit integration algorithm for real‐time hybrid testing. The development of the integration algorithm is briefly reviewed. An extrapolation procedure is introduced in the implementation of the algorithm for real‐time testing to ensure the continuous movement of the servo‐hydraulic actuator. The stability of the implemented integration algorithm is investigated using control theory. Real‐time hybrid test results of single‐degree‐of‐freedom and multi‐degree‐of‐freedom structures with a passive elastomeric damper subjected to earthquake ground motion are presented. The explicit integration algorithm is shown to enable the exceptional real‐time hybrid test results to be achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

Large‐scale real‐time hybrid simulation of a three‐story steel frame building with magneto‐rheological dampers

A series of large‐scale real‐time hybrid simulations (RTHSs) are conducted on a 0.6‐scale 3‐story steel frame building with magneto‐rheological (MR) dampers. The lateral force resisting system of the prototype building for the study consists of moment resisting frames and damped brace frames (DBFs). The experimental substructure for the RTHS is the DBF with the MR dampers, whereas the remaining structural components of the building including the moment resisting frame and gravity frames are modeled via a nonlinear analytical substructure. Performing RTHS with an experimental substructure that consists of the complete DBF enables the effects of member and connection component deformations on system and damper performance to be accurately accounted for. Data from these tests enable numerical simulation models to be calibrated, provide an understanding and validation of the in‐situ performance of MR dampers, and a means of experimentally validating performance‐based seismic design procedures for real structures. The details of the RTHS procedure are given, including the test setup, the integration algorithm, and actuator control. The results from a series of RTHS are presented that includes actuator control, damper behavior, and the structural response for different MR control laws. The use of the MR dampers is experimentally demonstrated to reduce the response of the structure to strong ground motions. Comparisons of the RTHS results are made with numerical simulations. Based on the results of the study, it is concluded that RTHS can be conducted on realistic structural systems with dampers to enable advancements in resilient earthquake resistant design to be achieved. Copyright © 2014 John Wiley & Sons, Ltd.     

Control issues relating to real‐time substructuring experiments using a shaking table

Real‐time substructuring is a method of dynamically testing a structure without experimentally testing a physical model of the entire system. Instead the structure can be split into two linked parts, the region of particular interest, which is tested experimentally, and the remainder which is tested numerically. A transfer system, such as a hydraulic actuator or a shaking table, is used to impose the displacements at the interface between the two parts on the experimental substructure. The corresponding force imposed by the substructure on the transfer system is fed back to the numerical model. Control of the transfer system is critical to the accuracy of the substructuring process. A study of two controllers used in conjunction with the University of Bristol shaking table is presented here. A proof‐of‐concept one degree‐of‐freedom mass–spring–damper system is substructured such that a portion of the mass forms the experimental substructure and the remainder of the mass plus the spring and the damper is modelled numerically. Firstly a linear controller is designed and tested. Following this an adaptive substructuring strategy is considered, based on the minimal control synthesis algorithm. The deleterious effect of oil‐column resonance common to shaking tables is examined and reduced through the use of filters. The controlled response of the experimental specimen is compared for the two control strategies. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance evaluation of a real‐time pseudodynamic test system

This paper presents a detailed analysis of a real‐time pseudodynamic test system using a system transfer function. The analysis considers the actuator control scheme, the dynamics of the actuator, test structure, and actuator reaction frame, the influence of actuator time delay on response computation, and methods to compensate for the time‐lag errors. It has been observed that the system can achieve an excellent performance with optimum control gains. The two error‐compensation methods presented here are also proven to be effective. Further, it has been demonstrated that the adverse effect of the inertia force developed by the test structure can be corrected for during a real‐time test, and that the influence of the reaction frame flexibility is small when the frame is reasonably massive and stiff as compared to the test structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Operator‐splitting method for real‐time substructure testing

It has been shown that the operator‐splitting method (OSM) provides explicit and unconditionally stable solutions for quasi‐static pseudo‐dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real‐time substructure testing (RST) when the velocity‐dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM‐RST algorithm are investigated. It is shown that the OSM‐RST is unconditionally stable so long as the non‐linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM‐RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non‐classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM‐RST is preserved when the experimental substructure generates velocity‐dependent reaction forces, whereas the stability of real‐time substructure tests based on the central difference method is worsened by the damping of the specimen. Copyright © 2005 John Wiley & Sons, Ltd.     

Linear dynamic modeling of a uni‐axial servo‐hydraulic shaking table system

This paper focuses on the development of a linear analytical model (even though servo‐hydraulic actuation systems are inherently non‐linear, especially for large amplitude simulations — near the performance capacity of the system — linearized models proved experimentally to be quite effective overall in capturing the salient features of shaking table dynamics) of a uni‐axial, servo‐hydraulic, stroke controlled shaking table system by using jointly structural dynamics and linear control theory. This model incorporates the proportional, integral, derivative, feed‐forward, and differential pressure gains of the control system. Furthermore, it accounts for the following physical characteristics of the system: time delay in the servovalve response, compressibility of the actuator fluid, oil leakage through the actuator seals and the dynamic properties of both the actuator reaction mass and test structure or payload. The proposed model, in the form of the total shaking table transfer function (i.e. between commanded and actual table motions), is developed to account for the specific characteristics of the Rice University shaking table. An in‐depth sensitivity study is then performed to determine the effects of the table control parameters, payload characteristics, and servovalve time delay upon the total shaking table transfer function. The sensitivity results reveal: (a) a potential strong dynamic interaction between the oil column in the actuator and the payload, and (b) the very important effect of the servovalve time delay upon the total shaking table transfer function. Copyright © 2000 John Wiley & Sons, Ltd.