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.     

Real‐time hybrid experiments with Newmark integration,MCSmd outer‐loop control and multi‐tasking strategies

Real‐time hybrid testing is a promising technique for experimental structural dynamics, in which the structure under consideration is split into a physical test of key components and a numerical model of the remainder. The physical test and numerical analysis proceed in parallel, in real time, enabling testing of critical elements at large scale and at the correct loading rate. To date most real‐time hybrid tests have been restricted to simple configurations and have used approximate delay compensation schemes. This paper describes a real‐time hybrid testing approach in which non‐linearity is permitted in both the physical and numerical models, and in which multiple interfaces between physical and numerical substructures can be accommodated, even when this results in very stiff coupling between actuators. This is achieved using a Newmark explicit numerical solver, an advanced adaptive controller known as MCSmd and a multi‐tasking strategy. The approach is evaluated through a series of experiments on discrete mass–spring systems. Copyright © 2006 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.     

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 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.     

磁流变智能基础隔震系统研究

本文将磁流变(MR)阻尼器与普通橡胶隔震支座相结合,组成智能基础隔震系统应用到结构控制中。在详细介绍了系统的各部分与整体运行情况后,采用LQR经典线性最优控制算法对结构进行了振动台试验研究。试验结果表明,由MR阻尼器提供可调阻尼力的智能隔震控制系统,能有效克服被动隔震最优控制频带窄的缺点,对较宽频域范围地震激励能进行有效的振动控制。其相对一般被动隔震装置,能同时减小上部结构加速度和隔震层位移.     

Real‐time distributed hybrid testing: coupling geographically distributed scientific equipment across the Internet to extend seismic testing capabilities

Large‐scale testing and qualification of structural systems and their components is crucial for the development of earthquake engineering knowledge and practice. However, laboratory capacity is often limited when attempting larger experiments due to the sheer size of the structures involved. To overcome traditional laboratory capacity limitations, we present a new earthquake engineering testing method: real‐time distributed hybrid testing. Extending current approaches, the technique enables geographically distributed scientific equipment including controllers, dynamic actuators and sensors to be coupled across the Internet in real‐time. As a result, hybrid structural emulations consisting of physical and numerical substructures need no longer be limited to a single laboratory. Larger experiments may distribute substructures across laboratories located in different cities whilst maintaining correct dynamic coupling, required to accurately capture physical rate effects. The various aspects of the distributed testing environment have been considered. In particular, to ensure accurate control across an environment not designed for real‐time testing, new higher level control protocols are introduced acting over an optimised communication system. New large time‐step prediction algorithms are used, capable of overcoming both local actuation and distributed system delays. An overview of the architecture and algorithms developed is presented together with results demonstrating a number of current capabilities. Copyright © 2013 John Wiley & Sons, Ltd.     

Semi‐active neuro‐control for base‐isolation system using magnetorheological (MR) dampers

Vibration mitigation using smart, reliable and cost‐effective mechanisms that requires small activation power is the primary objective of this paper. A semi‐active controller‐based neural network for base‐isolation structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (INV‐MR) is constructed to replicate the inverse dynamics of the MR damper. Next, linear quadratic Gaussian (LQG) controller is designed to produce the optimal control force. Thereafter, the LQG controller and the INV‐MR models are linked to control the structure. The coupled LQG and INV‐MR system was used to train a semi‐active neuro‐controller, designated as SA‐NC, which produces the necessary control voltage that actuates the MR damper. To evaluate the proposed method, the SA‐NC is compared to passive lead–rubber bearing isolation systems (LRBs). Results revealed that the SA‐NC was quite effective in seismic response reduction for wide range of motions from moderate to severe seismic events compared to the passive systems. In addition, the semi‐active MR damper enjoys many desirable features, such as its inherent stability, practicality and small power requirements. The effectiveness of the SA‐NC is illustrated and verified using simulated response of a six‐degree‐of‐freedom model of a base‐isolated building excited by several historical earthquake records. Copyright © 2006 John Wiley & Sons, Ltd.     

Stability analysis for real‐time pseudodynamic and hybrid pseudodynamic testing with multiple sources of delay

Real‐time pseudodynamic (PSD) and hybrid PSD test methods are experimental techniques to obtain the response of structures, where restoring force feedback is used by an integration algorithm to generate command displacements. Time delays in the restoring force feedback from the physical test structure and/or the analytical substructure cause inaccuracies and can potentially destabilize the system. In this paper a method for investigating the stability of structural systems involved in real‐time PSD and hybrid PSD tests with multiple sources of delay is presented. The method involves the use of the pseudodelay technique to perform an exact mapping of fixed delay terms to determine the stability boundary. The approach described here is intended to be a practical one that enables the requirements for a real‐time testing system to be established in terms of system parameters when multiple sources of delay exist. Several real‐time testing scenarios with delay that include single degree of freedom (SDOF) and multi‐degree of freedom (MDOF) real‐time PSD/hybrid PSD tests are analyzed to illustrate the method. From the stability analysis of the real‐time hybrid testing of an SDOF test structure, delay‐independent stability with respect to either experimental or analytical substructure delay is shown to exist. The conditions that the structural properties must satisfy in order for delay‐independent stability to exist are derived. Real‐time hybrid PSD testing of an MDOF structure equipped with a passive damper is also investigated, where observations from six different cases related to the stability plane behavior are summarized. Throughout this study, root locus plots are used to provide insight and explanation of the behavior of the stability boundaries. 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.     

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.     

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.     

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.     

LQR control with frequency‐dependent scheduled gain for a semi‐active floor isolation system

Floor isolation is an alternative to base isolation for protecting a specific group of equipment installed on a single floor or room in a fixed‐base structure. The acceleration of the isolated floor should be mitigated to protect the equipment, and the displacement needs to be suppressed, especially under long‐period motions, to save more space for the floor to place equipment. To design floor isolation systems that reduce acceleration and displacement for both short‐period and long‐period motions, semi‐active control with a newly proposed method using the linear quadratic regulator (LQR) control with frequency‐dependent scheduled gain (LQRSG) is adopted. The LQRSG method is developed to account for the frequency characteristics of the input motion. It updates the control gain calculated by the LQR control based on the relationship between the control gain and dominant frequency of the input motion. The dominant frequency is detected in real time using a window method. To verify the effectiveness of the LQRSG method, a series of shake table tests is performed for a semi‐active floor isolation system with rolling pendulum isolators and a magnetic‐rheological damper. The test results show that the LQRSG method is significantly more effective than the LQR control over a range of short‐period and long‐period motions. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive time series compensator for delay compensation of servo‐hydraulic actuator systems for real‐time hybrid simulation

Hydraulic actuators are typically used in a real‐time hybrid simulation to impose displacements to a test structure (also known as the experimental substructure). It is imperative that good actuator control is achieved in the real‐time hybrid simulation to minimize actuator delay that leads to incorrect simulation results. The inherent nonlinearity of an actuator as well as any nonlinear response of the experimental substructure can result in an amplitude‐dependent behavior of the servo‐hydraulic system, making it challenging to accurately control the actuator. To achieve improved control of a servo‐hydraulic system with nonlinearities, an adaptive actuator compensation scheme called the adaptive time series (ATS) compensator is developed. The ATS compensator continuously updates the coefficients of the system transfer function during a real‐time hybrid simulation using online real‐time linear regression analysis. Unlike most existing adaptive methods, the system identification procedure of the ATS compensator does not involve user‐defined adaptive gains. Through the online updating of the coefficients of the system transfer function, the ATS compensator can effectively account for the nonlinearity of the combined system, resulting in improved accuracy in actuator control. A comparison of the performance of the ATS compensator with existing linearized compensation methods shows superior results for the ATS compensator for cases involving actuator motions with predefined actuator displacement histories as well as real‐time hybrid simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

A Rosenbrock‐W method for real‐time dynamic substructuring and pseudo‐dynamic testing

A variant of the Rosenbrock‐W integration method is proposed for real‐time dynamic substructuring and pseudo‐dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Sliding mode control of buildings with base‐isolation hybrid protective system

This paper investigates the application of the sliding mode control (SMC) strategies for reducing the dynamic responses of the building structures with base‐isolation hybrid protective system. It focuses on the use of reaching law method, a most attractive controller design approach of the SMC theory, for the development of control algorithms. By using the constant plus proportional rate reaching law and the power rate reaching law, two kinds of hybrid control methods are presented. The compound equation of motion of the base‐isolation hybrid building structures, which is suitable for numerical analysis, has been constructed. The simulation results are obtained for an eight‐storey shear building equipped with base‐isolation hybrid protective system under seismic excitations. It is observed that both the constant plus proportional rate reaching law and the power rate reaching law hybrid control method presented in this paper are quite effective. Copyright © 2000 John Wiley & Sons, Ltd.     

滚动FPS和MR阻尼器混合基础动力学模型及仿真

本文中作者将新型双磙子FPS系统的动力学方程推广到由滚动FPS和MR阻尼器组成的混合隔震基础系统,得到了更便于应用的水平分量形式的运动微分方程,并将与FPS有关的力和MR阻尼力处理成力源项,构造了可以方便地考虑不同上部结构形式的MATLAB/SIMULINK仿真模型。采用RD-1005型MR阻尼器和模糊逻辑控制器,在两个典型的地震输入情况下对混合系统进行了振动控制仿真。仿真结果表明,本文建立的混合隔震基础系统的动力学模型是正确和精确的,直接利用动力学模型进行前向计算可避免附加的模型误差且计算效率高,而仿真模型中将不同的力源由分开的块组成,使得仿真设计非常方便快捷。     

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.     

Novel coupling Rosenbrock‐based algorithms for real‐time dynamic substructure testing

Real‐time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile method for analysing the general case of linear and non‐linear semi‐discretized equations of motion. In this paper we propose for substructure testing, L‐stable real‐time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real‐time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero‐stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge–Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real‐time substructure tests are used to demonstrate the favourable properties of the proposed algorithms. Copyright © 2007 John Wiley & Sons, Ltd.