Robust integrated actuator control: experimental verification and real‐time hybrid‐simulation implementation

In this paper, we propose a new actuator control algorithm that achieves the design flexibility, robustness, and tracking accuracy to give real‐time hybrid‐simulation users the power to achieve highly accurate and robust actuator control. The robust integrated actuator control (RIAC) strategy integrates three key control components: loop shaping feedback control based on H_∞ optimization, a linear‐quadratic‐estimation block for minimizing noise effect, and a feed‐forward block that reduces small residual delay/lag. The combination of these components provides flexible controller design to accommodate setup limits while preserving the stability of the H_∞ algorithm. The efficacy of the proposed strategy is demonstrated through two illustrative case studies: one using large capacity but relatively slow actuator of 2500 kN and the second using a small‐scale fast actuator. Actuator tracking results in both cases demonstrate that the RIAC algorithm is effective and applicable for different setups. Real‐time hybrid‐simulation validation is implemented using a three‐DOF building frame equipped with a magneto‐rheological damper on both setups. Results using the two very different physical setups illustrate that RIAC is efficient and accurate. Copyright © 2014 John Wiley & Sons, Ltd.     

Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation

In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd.     

Establishing a predictive performance indicator for real‐time hybrid simulation

Real‐time hybrid simulation (RTHS) is increasingly being recognized as a powerful cyber‐physical technique that offers the opportunity for system evaluation of civil structures subject to extreme dynamic loading. Advances in this field are enabling researchers to evaluate new structural components/systems in cost‐effective and efficient ways, under more realistic conditions. For RTHS, performance metric clearly needs to be developed to predict and evaluate the accuracy of various partitioning choices while incorporating the dynamics of the transfer system, and computational/communication delays. In addition, because of the dynamics of the transfer system, communication delays, and computation delays, the RTHS equilibrium force at the interface between numerical and physical substructures is subject to phase discrepancy. Thus, the transfer system dynamics must be accommodated by appropriate actuator controllers. In this paper, a new performance indicator, predictive performance indicator (PPI), is proposed to assess the sensitivity of an RTHS configuration to any phase discrepancy resulting from transfer system dynamics and computational/communication delays. The predictive performance indicator provides a structural engineer with two sets of information as follows: (i) in the absence of a reference response, what is the level of fidelity of the RTHS response? and (ii) if needed, what partitioning adjustments can be made to effectively enhance the fidelity of the response? Moreover, along with the RTHS stability switch criterion, this performance metric may be used as an acceptance criteria for conducting single‐degree‐of‐freedom RTHS. Copyright © 2014 John Wiley & Sons, Ltd.     

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

In this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Smart base isolated buildings with variable friction systems: H∞ controller and SAIVF device

A new control algorithm is developed for reducing the response of smart base isolated buildings with variable friction semiactive control systems in near‐fault earthquakes. The central idea of the control algorithm is to design a H_∞ controller for the structural system and use this controller to determine the optimum control force in the semiactive device. The H_∞ controller is designed using appropriate input and output weighting filters that have been developed for optimal performance in reducing near‐fault earthquake responses. A novel semiactive variable friction device is also developed and with the H_∞ controller shown to be effective in achieving response reductions in smart base isolated buildings in near‐fault earthquakes. The new variable friction device developed consists of four friction elements and four restoring spring elements arranged in a rhombus configuration with each arm consisting of a friction–stiffness pair. The level of friction force can be adjusted by varying the angle of the arms of the device leading to smooth variation of friction force in the device. Experimental results are presented to verify the proposed analytical model of the device. The H_∞ algorithm is implemented analytically on a five storey smart base isolated building with linear elastomeric isolation bearings and variable friction system located at the isolation level. The H_∞ controller along with the weighting filters leads to the smooth variation of friction force, thus eliminating the disadvantages associated with rapid switching. Several recent near‐fault earthquakes are considered in this study. The robustness of the H_∞ controller is shown by considering a stiffness uncertainty of ±10%. Copyright © 2006 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.     

Decentralized static output‐feedback H∞ controller design for buildings under seismic excitation

In this work, we present a new method in designing static output‐feedback H_∞ controllers suitable for vibrational control of buildings under seismic excitation. The method produces a Linear Matrix Inequality (LMI) formulation that allows obtaining static output‐feedback controllers with different information structure constraints by imposing a convenient zero–nonzero structure on the LMI variables. The application of the proposed methodology is illustrated by designing centralized and decentralized velocity‐feedback H_∞ controllers to mitigate the seismic response of a five‐story building. Copyright © 2011 John Wiley & Sons, Ltd.     

Predictive stability indicator: a novel approach to configuring a real‐time hybrid simulation

Real‐time hybrid simulation (RTHS) is an effective and versatile tool for the examination of complex structural systems with rate dependent behaviors. To meet the objectives of such a test, appropriate consideration must be given to the partitioning of the system into physical and computational portions (i.e., the configuration of the RTHS). Predictive stability and performance indicators (PSI and PPI) were initially established for use with only single degree‐of‐freedom systems. These indicators allow researchers to plan a RTHS, to quantitatively examine the impact of partitioning choices on stability and performance, and to assess the sensitivity of an RTHS configuration to de‐synchronization at the interface. In this study, PSI is extended to any linear multi‐degree‐of‐freedom (MDOF) system. The PSI is obtained analytically and it is independent of the transfer system and controller dynamics, providing a relatively easy and extremely useful method to examine many partitioning choices. A novel matrix method is adopted to convert a delay differential equation to a generalized eigenvalue problem using a set of vectorization mappings, and then to analytically solve the delay differential equations in a computationally efficient way. Through two illustrative examples, the PSI is demonstrated and validated. Validation of the MDOF PSI also includes comparisons to a MDOF dynamic model that includes realistic models of the hydraulic actuators and the control‐structure interaction effects. Results demonstrate that the proposed PSI can be used as an effective design tool for conducting successful RTHS. Copyright © 2016 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.     

Passive and active control of three‐dimensional buildings

The majority of the recent research effort on structural control considers two‐dimensional plane structures. However, not all buildings can be modelled as plane structures, thus limiting the capability of the proposed procedures only to regular and symmetrical structures. A new procedure is developed in this paper to analyse three‐dimensional buildings utilizing passive and active control devices. In the building model, the floors are assumed rigid in their own plane resulting in three degrees of freedom at each floor. Two types of active control devices utilizing an active tuned mass damper and an active bracing system are considered. The effect of passive mass dampers and active control force in the equations of motion is incorporated by using the Hamilton's principle. The passive parameters of the dampers as well as the controller gain is then optimized using a genetic based optimizer where the H₂, H_∞ and L₁ norms are taken as the objective functions. Copyright © 2000 John Wiley & Sons, Ltd.     

Discussion of paper ‘Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation’ by Chinmoy Kolay and James M. Ricles,Earthquake Engineering and Structural Dynamics 2014; 43:1361–1380

It seems that the explicit KR‐α method (KRM), which was developed by Kolay and Ricles, is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method [1] for a linear elastic system, and it reduces to CR method (CRM), which was developed by Chen and Ricles [2] if ρ_∞ = 1 is adopted, where ρ_∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd.     

A rational H∞‐norm–based approach for the optimal design of seismically excited reinforced concrete frames

A rational approach is presented for minimizing the dynamic response of reinforced concrete framed structures forced by a seismic base acceleration. Reference is made to EC8 regulations, but the presented approach may in principle be applied to structures ruled by any regulation code. Governing equations are set in the frequency domain (and not in the periods domain as usual) so as to enable the adoption of sound approaches for analysis and design of dynamic structures that are typical of automatics. Among these, a novel usage of the H_∞‐norm concept is proposed that determines a rational design approach capable to minimize the structural response with reference to any quantity of engineering interest, eg, the overall compliance and the displacement of a specific point or the interstorey drift. A numerical investigation on a 6‐storey 3‐bay frame is performed, and relevant analysis and design results are presented in much detail to validate the theoretical framework.     

Retracted: Discussion of paper ‘Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation’ by Chinmoy Kolay and James M. Ricles,Earthquake Engineering and Structural Dynamics 2014; 43:1361–1380

It seems that the explicit KR‐α method (KRM) is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method (GM) for a linear elastic system, and it reduces to CR method (CRM) if ρ_∞ = 1is adopted, where ρ_∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic control of smart base isolated buildings with new semiactive variable damper

A new semiactive independently variable damper, SAIVD, is developed and shown to be effective in achieving response reductions in smart base isolated buildings in near fault earthquakes. The semiactive device consists of four linear visco‐elastic elements, commonly known as Kelvin–Voigt elements, arranged in a rhombus configuration. The magnitude of force in the semiactive device can be adjusted smoothly in real‐time by varying the angle of the visco‐elastic elements of the device or the aspect ratio of the rhombus configuration. Such a device is essentially linear, simple to construct, and does not present the difficulties commonly associated with modelling and analysing nonlinear devices (e.g. friction devices). The smooth semiactive force variation eliminates the disadvantages associated with rapid switching devices. Experimental results are presented to verify the proposed analytical model of the device. A H_∞ control algorithm is implemented in order to reduce the response of base isolated buildings with variable damping semiactive control systems in near fault earthquakes. The central idea of the control algorithm is to design a H_∞ controller for the structural system that serves as an aid in the determination of the optimum control force in the semiactive device. The relative performance of the SAIVD device is compared to a variable friction device, recently developed by the authors in a separate study, and several key aspects of performance are discussed regarding the use of the two devices for reducing the responses of smart base isolated buildings in near fault earthquakes. Copyright © 2006 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.     

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.     

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.     

Optimal design of passive energy dissipation systems based on H∞ and H2 performances

Passive energy dissipation devices (EDDs), such as viscous dampers, viscoelastic dampers, etc., have been used to effectively reduce the dynamic response of civil infrastructures, such as buildings and bridges, subject to earthquakes and strong winds. The design of these passive energy dissipation devices (EDDs) involves the determination of the optimal locations and the corresponding capacities. In this paper, we present two optimal design methodologies for passive EDDs based on active control theories, including H_∞ and H₂ performances, respectively. The optimal design methodologies presented are capable of determining the optimal locations and the corresponding capacities of EDDs. Emphasis is placed on the application of linear matrix inequality (LMI) for the effective design of passive EDDs using the popular MATLAB toolboxes. One important advantage of the proposed approaches is that the computation of the structural response is not needed in the design process. The proposed optimal design methodologies have been applied to: (i) a 10‐storey building and a 24‐storey building both subject to earthquake excitations, and (ii) a 76‐storey wind‐excited benchmark building, to demonstrate the advantages of the proposed design methodologies over the conventional equal capacity design. Copyright © 2002 John Wiley & Sons, Ltd.     

磁流变阻尼器的半主动控制及实时混合模拟试验研究

磁流变阻尼器作为一种比较典型的半主动控制元件,具有构造简单、响应速度快、耐久性好、阻尼力大且连续可调等优点。即使地震中能源中断,磁流变阻尼器仍可以作为被动耗能装置继续工作发挥作用,可靠性高。设计合理有效的磁流变阻尼器半主动控制方法,对于整体结构的减震效果尤其重要。提出一种改进的磁流变阻尼器的半主动控制策略-改进的Bang-Bang控制策略,对装有磁流变阻尼器的减震控制3层框架结构进行了一系列的实时混合模拟试验,对多种半主动控制方法下的振动控制效果进行试验分析。试验结果表明:磁流变阻尼器对框架结构的减震效果显著,并验证了提出的磁流变阻尼器半主动控制策略的有效性。     

Decentralized ℋ︁∞ controller design for large‐scale civil structures

Complexities inherent to large‐scale modern civil structures pose many challenges in the design of feedback structural control systems for dynamic response mitigation. With the emergence of low‐cost sensors and control devices creating technologies from which large‐scale structural control systems can deploy, a future control system may contain hundreds, or even thousands, of such devices. Key issues in such large‐scale structural control systems include reduced system reliability, increasing communication requirements, and longer latencies in the feedback loop. To effectively address these issues, decentralized control strategies provide promising solutions that allow control systems to operate at high nodal counts. This paper examines the feasibility of designing a decentralized controller that minimizes the ??_∞ norm of the closed‐loop system. ??_∞ control is a natural choice for decentralization because imposition of decentralized architectures is easy to achieve when posing the controller design using linear matrix inequalities. Decentralized control solutions are investigated for both continuous‐time and discrete‐time ??_∞ formulations. Numerical simulation results using a 3‐story and a 20‐story structure illustrate the feasibility of the different decentralized control strategies. The results also demonstrate that when realistic semi‐active control devices are used in combination with the decentralized ??_∞ control solution, better performance can be gained over the passive control cases. It is shown that decentralized control strategies may provide equivalent or better control performance, given that their centralized counterparts could suffer from longer sampling periods due to communication and computation constraints. Copyright © 2008 John Wiley & Sons, Ltd.