Multidegrees‐of‐freedom effective force testing: a feasibility study and robust stability assessment

This paper presents a feasibility study of multidegrees‐of‐freedom effective force testing (MDOF‐EFT). The study is intended to facilitate the development of a force feedback controller and investigation of performance as well as robustness of MDOF‐EFT. First, the dynamics of MDOF‐EFT systems are analytically investigated. Analytical transfer functions of the control plant, the valve‐to‐force relations, showed that the plant is dynamically coupled and the natural frequencies of test structures are the transmission zeros of the plant. Using a set of model parameters from a previous study, a case study that includes controller design, numerical simulations and robust stability assessment is performed. A decoupling loop shaping (DLS) controller consisting of a pseudo inverse of the plant and second‐order loop shaping controllers is adopted as the force feedback controller. It is shown that the DLS controller provides a stable control system while successfully decoupling the control loops and compensating the control‐structure interaction. Numerical simulations demonstrate that the DLS controller enables tracking of static and dynamic forces for multiple actuators. Robust stability of MDOF‐EFT with the DLS controller is assessed using Monte Carlo simulation. The stochastic simulation results show that the DLS controller is stable and robust, providing sufficient stability margins for uncertain models with maximum 50% errors in the estimated system parameters. This paper demonstrates that MDOF‐EFT is feasible with the DLS controller and can be implemented in experimental laboratories. Copyright © 2013 John Wiley & Sons, Ltd.     

Effective force testing using a robust loop shaping controller

Effective force testing (EFT) is one of the force‐based experimental methods used for performance evaluation of structures that incorporate dynamic force control using hydraulic actuators. Although previous studies have shown successful implementations of force control, controllable frequency ranges are limited to low frequencies (10 Hz). This study presents the EFT method using a robust loop shaping force feedback controller that can extend the frequency range up to 25 Hz or even higher. Unlike the conventional PID controllers, loop shaping controllers can provide robustness for a high level of force measurement noise. This study investigates the dynamic properties of hydraulic actuators and the design of a loop shaping controller that compensates for control–structure interaction and suppresses the effect of oil‐column resonance. The designed loop shaping controller was successfully implemented into an EFT setup at the Johns Hopkins University. An experimental investigation of the loop shaping controller was performed under step, random, and earthquake force loadings. Experimental results showed that the loop shaping controller provided excellent force tracking performance and robustness for dynamic force loadings. It was also shown that the loop shaping controller had the gain margin of 9.54 dB at the frequency of 28 Hz. Copyright © 2012 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.     

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     

Theory and implementation of switch‐based hybrid simulation technology for earthquake engineering applications

Hybrid simulation (HS) is a novel technique to combine analytical and experimental sub‐assemblies to examine the dynamic responses of a structure during an earthquake shaking. Traditionally, HS uses displacement‐based control where the finite element program calculates trial displacements and applies them to both the analytical and experimental sub‐assemblies. Displacement‐based HS (DHS) has been proven to work well for most structural sub‐assemblies. However, for specimens with high stiffness, traditional DHS does not work because it is difficult to precisely control hydraulic actuators in small displacement. A small control error in displacement will result in large force response fluctuations for stiff specimens. This paper resolves this challenge by proposing a force‐based HS (FHS) algorithm that directly calculates trial forces instead of trial displacements. The proposed FHS is finite element based and applicable to both linear and nonlinear systems. For specimens with drastic changes in stiffness, such as yielding, a switch‐based HS (SHS) algorithm is proposed. A stiffness‐based switching criterion between the DHS and FHS algorithms is presented in this paper. All the developed algorithms are applied to a simple one‐story one‐bay concentrically braced moment frame. The result shows that SHS outperforms DHS and FHS. SHS is then utilized to validate the seismic performance of an innovative earthquake resilient fused structure. The result shows that SHS works in switching between the DHS and FHS modes for a highly nonlinear and highly indeterminate structural system. Copyright © 2017 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.     

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.     

Equivalent force control method for substructure pseudo‐dynamic test of a full‐scale masonry structure

The effectiveness of equivalent force control (EFC) method has been experimentally validated through hybrid tests with simple specimens. In this paper, the EFC method is applied for the MDOF pseudo‐dynamic substructure tests in which a three‐storey frame‐supported reinforced concrete masonry shear wall with full scale is chosen as physical substructure. The effects of equivalent force controller parameters on the response performance are studied. Analytical expressions for the controller parameter ranges are derived to avoid response overshooting or oscillation and are verified by numerical simulation. The controller parameters are determined based on analytical and numerical studies and used in the actual full‐scale pseudo‐dynamic test. The test results show good tracking performance of EFC, which indicates a successful test. Copyright © 2013 John Wiley & Sons, Ltd.     

A buffered impact damper for multi‐degree‐of‐freedom structural control

The results of an experimental investigation into the use of a buffered impact damper for controlling the dynamic response of an MDOF (multi‐degree‐of‐freedom) structure are presented in this paper. Free and forced vibration tests of a three‐DOF test structure equipped with a buffered impact damper are performed to evaluate the resulting damping effect and impact characteristics. The effect of damper parameters, such as clearance, and excitation type on the performance of the impact damper is also investigated. The performance of the buffered impact damper is compared with that of an equivalent conventional rigid impact damper. It is found that the buffered impact damper not only significantly reduces the peak contact force and the associated accelerations and noise generated by collisions but can also substantially enhance the damping effect over a wide range of frequencies, encompassing the natural frequencies of the test structure. Copyright © 2008 John Wiley & Sons, Ltd.     

Shaking table test of the effects of multi‐unit particle dampers attached to an MDOF system under earthquake excitation

This paper presents the results of an experimental and analytical/computational study of the performance of multi‐unit particle dampers with an MDOF system. A series of shaking table tests of a three‐storey steel frame with the particle damper system were carried out to evaluate the performance of the system and to verify the analysis method. An analytical solution based on the discrete element method is also presented. A comparison between the experimental and computational results shows that reasonably accurate estimates of the response of a primary system under earthquake excitations can be obtained. These results also indicate that the excitation characterization influences the performance of the particle damper system, for example, particle dampers have good performance in reducing the seismic response of structures and particle movements of plug flow pattern can yield good vibration attenuation effects. It is shown that by using properly designed multi‐unit particle dampers, a lightly damped primary system can achieve a reasonable reduction in its response, with a small weight penalty. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic Response of Adjacent Buildings Connected with Friction Dampers

The effectiveness of passive energy dissipation systems to improve seismic performance of connected buildings is now well established through extensive analytical and experimental investigations. However, the performance of buildings connected with friction dampers has not been looked into. In this paper, the investigation is carried out to study the structural responses of two adjacent buildings connected with friction dampers under various earthquake excitations. A formulation of the equations of motion for the two adjacent multi degree of freedom (MDOF) buildings connected with friction dampers is presented. The numerical study is carried out in two parts, namely (i) two adjacent MDOF buildings connected with friction dampers having same slip force in all the dampers and (ii) two adjacent MDOF buildings connected with friction dampers having different slip forces in the dampers. The effectiveness of the dampers in terms of the reduction of structural responses, namely, displacement, acceleration and shear forces of connected adjacent buildings is investigated. A parametric study is also conducted to investigate the optimum slip force of the dampers. In addition, the optimal placement of the dampers, rather than providing the dampers at all the floor levels is also studied to minimize the cost of the dampers. Results show that using friction dampers to connect the adjacent buildings of different fundamental frequencies can effectively reduce earthquake-induced responses of either building if slip force of the dampers is appropriately selected. Also, it is not necessary to connect the two adjacent buildings at all floors but lesser dampers at appropriate locations can significantly reduce the earthquake response of the combined system. Further, it is also observed that the reduction in the responses when the two MDOF buildings connected with 50% of the total dampers is almost as much as when they are connected at all the floors, thereby reducing the cost of the dampers significantly.     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 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.     

Dynamic force control with hydraulic actuators using added compliance and displacement compensation

A new approach to dynamic force control of mechanical systems, applicable in particular to frame structures, over frequency ranges spanning their resonant frequencies is presented. This approach is implemented using added compliance and displacement compensation. Hydraulic actuators are inherently velocity sources, that is, an electrical signal regulates their velocity response. Such systems are therefore by nature high‐impedance (mechanically stiff) systems. In contrast, for force control, a force source is required. Such a system logically would have to be a low‐impedance (mechanically compliant) system. This is achieved by intentionally introducing a flexible mechanism between the actuator and the structure to be excited. In addition, in order to obtain force control over frequencies spanning the structure's resonant frequency, a displacement compensation feedback loop is needed. The actuator itself operates in closed‐loop displacement control. The theoretical motivation, as well as the laboratory implementation of the above approach is discussed along with experimental results. Having achieved a means of dynamic force control, it can be applied to various experimental seismic simulation techniques such as the effective force method and the real‐time dynamic hybrid testing method. Copyright © 2008 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.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 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.     

Closed‐form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers

Closed‐form solution for seismic response of adjacent buildings connected by hydraulic actuators with linear quadratic Gaussian (LQG) controllers is presented in this paper. The equations of motion of actively controlled adjacent buildings against earthquake are first established. The complex modal superposition method is then used to determine dynamic characteristics, including modal damping ratio, of actively controlled adjacent buildings. The closed‐form solution for seismic response of the system is finally derived in terms of the complex dynamic characteristics, the pseudo‐excitation method and the residue theorem. By using the closed‐form solution, extensive parametric studies can be carried out for the system of many degrees of freedom. The beneficial parameters of LQG controllers for achieving the maximum response reduction of both buildings using reasonable control forces can be identified. The effectiveness of LQG controllers for this particular application is evaluated in this study. The results show that for the adjacent buildings of different dynamic properties, if the parameters of LQG controllers are selected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced. Copyright © 2001 John Wiley & Sons, Ltd.     

Improved design of sliding mode control for civil structures with saturation problem

A systematic and improved design procedure for sliding mode control (SMC) of seismically excited civil structures with saturation problem is provided in this paper. In order to restrict the control force to a certain level, a procedure for determining the upper limits of the control forces for single or multiple control units is proposed based on the design response spectrum of external loads. Further, an efficient procedure using the LQR method for determining sliding surfaces appropriate for different controller types is provided through the parametric evaluation of the dynamic characteristics of sliding surfaces in terms of SMC controller performance. Finally, a systematic design procedure for SMC required to achieve a given performance level is provided and its effectiveness is verified by applying it to multi‐degree‐of‐freedom (MDOF) systems. Copyright © 2004 John Wiley & Sons, Ltd.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.