Discrete‐time variable structure control method for seismic‐excited building structures with time delay in control

The discrete‐time variable structure control method for seismically excited linear structures with time delay in control is investigated in this paper. The control system with time delay is first discretized and transformed into standard discrete form which contains no time delay in terms of the time delay being integer and non‐integer times of sampling period, respectively. Then the discrete switching surface is determined using ideal quasi‐sliding mode and discrete controller is designed using the discrete approach‐law reaching condition. The deduced controller and switching surface contain not only the current step of state feedback but also linear combination of some former steps of controls. Numerical simulations are illustrated to verify the feasibility and robustness of the proposed control method. Since time‐delay effect is incorporated in the mathematical model for the structural control system throughout the derivation of the proposed algorithm, system performance and dynamic stability are guaranteed. Copyright © 2002 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.     

Semi‐active multi‐step predictive control of structures using MR dampers

A semi‐active multi‐step predictive control (SAMPC) system with magnetorheological (MR) dampers is developed to reduce the seismic responses of structures. This system can predict the next multi‐step responses of structure according to the current state and has a function of self‐compensation for time delay that occurred in real application. To study the performance of the proposed control algorithm for addressing time delay and reducing the seismic responses, a numerical example of an 11‐story structure with MR dampers is presented. Comparison with the uncontrolled structure indicates that both the peak and the norm values of structural responses are all clearly reduced when the predictive length l?10 and the delayed time step d?20 are selected, and the SAMPC strategy can guarantee the stability of the controlled structure and reduce the effects of time delay on controlled responses to a certain extent. A performance comparison is also made between the SAMPC strategy and the passive‐off and passive‐on methods; results indicate that this SAMPC system is more effective than the two passive methods in reducing structural responses subjected to earthquakes. Copyright © 2008 John Wiley & Sons, Ltd.     

Actuator dynamics compensation based on upper bound delay for real‐time hybrid simulation

Real‐time hybrid simulation represents a powerful technique capable of evaluating the structural dynamic performance by combining the physical simulation of a complex and rate‐dependent portion of a structure with the numerical simulation of the remaining portion of the same structure. Initially, this paper shows how the stability of real‐time hybrid simulation with time delay depends both on compensation techniques and on time integration methods. In particular, even when time delay is exactly known, some combinations of numerical integration and displacement prediction schemes may reduce the response stability with conventional compensation methods and lead to unconditional instability in the worst cases. Therefore, to deal with the inaccuracy of prediction and the uncertainty of delay estimation, a nearly exact compensation scheme is proposed, in which the displacement is compensated by means of an upper bound delay and the desired displacement is picked out by an optimal process. Finally, the advantages of the proposed scheme over conventional delay compensation techniques are shown through numerical simulation and actual tests. Copyright © 2013 John Wiley & Sons, Ltd.     

Quadratic jerk regulation and the seismic control of civil structures

Regulation of the total structural jerk is a means of managing the structural energy and enhancing the performance of civil structures undergoing large seismic events. A quadratic regulator is derived for the total structural jerk that produces a single algebraic Riccati equation to define the control gains. The resulting control method is tested using a realistic non‐linear structural control case study where the structural response is statistically quantified for large suites of scaled earthquakes. The control method developed is shown to be more effective than typical displacement‐focused active and semi‐active civil structural control methods. In particular, quadratic jerk regulation provides better performance than typical structural control methods for near‐field seismic events where the response is dominated by a large impulse, and relatively poorer results for far‐field seismic inputs where the response is vibratory. Hence, this type of control approach has strong potential for mitigating the damage for large impulse, near‐field events, where jerk regulation provides much more efficient response and damage management. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Active interaction control of civil structures. Part 1: SDOF systems

This paper presents a family of semi‐active control algorithms termed as active interaction control (AIC) used for seismic response control of civil structures. AIC control algorithms include active interface damping (AID), optimal connection strategy (OCS) and tuned interaction damping (TID). A typical SDOF AIC system consists of a primary structure, an auxiliary structure and an interaction element. The auxiliary structure typically has stiffness comparable to that of the primary structure while its natural frequency is much higher than that of the primary structure. Interactions between the primary and the auxiliary structures are defined by specific AIC control logic such that vibrational energy is extracted from the primary structure into the auxiliary structure during a locking phase and dissipated in the auxiliary structure in the subsequent unlocking phase. The stability of AIC control algorithms is shown using the Lyapunov direct method. The efficacy of AIC control algorithms is demonstrated by the results of numerical simulations of SDOF systems subjected to seismic ground motions. Practical issues such as sampling period and time delay are also investigated in this study. Copyright © 2001 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.     

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.     

结构主动控制系统时间滞后测量与补偿方法

本文研究了结构主动控制系统时间滞后产生的原因,利用作者建立的结构主动控制系统进行了系统时间滞后测量方法的研究,测量得到了该系统时间滞后的具体数值,在此基础上,研究了时间滞后对控制系统的影响,提出了结构主动控制系统时间滞后的三种补偿,即移相法,泰勒级数展开法和预估状态向量法,通过主动控制试验证了时间滞后补偿方法的有效性。     

土木工程智能结构体系的研究与发展

本文概要综述了感知材料、驱动材料和自修复材料等三大类主要的智能材料在土木工程中应用的概况;阐述了土木工程结构智能监测、健康诊断、损伤修复和振动控制的发展趋势和近期研究的主要方向以及对智能材料的发展和改性的要求。     

Predictive optimal control for seismic analysis of non-linear and hysteretic structures

In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd.     

土木工程结构鲁棒控制的发展

评述了结构控制的发展,指出发展结构鲁棒控制策略的重要性。重点评述了结构双重调谐质量阻尼器(DTMD)和多重双重调谐质量阻尼器(MDTMD)的控制策略,提出了需进一步发展主动双重调谐质量阻尼器(ADTMD)和主动多重双重调谐质量阻尼器(AMDTMD)控制策略、此外,评述了结构鲁棒控制的设计准则与高层建筑和大跨桥梁在风与地震作用下的统一自适应主动鲁棒控制策略。     

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.     

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.     

Time‐domain viscoelastic analysis of earth structures

In this paper two causal models that approximate the nearly frequency‐independent cyclic behaviour of soils are analysed in detail. The study was motivated by the need to conduct time‐domain viscoelastic analysis on soil structures without adopting the ad hoc assumption of Rayleigh damping. First, the causal hysteretic model is introduced in which its imaginary part is frequency independent the same way that is the imaginary part of the popular non‐causal constant hysteretic model. The adoption of an imaginary part that is frequency independent even at the zero‐frequency limit, in conjunction with the condition that the proposed model should be causal, yields a real part that is frequency dependent and singular at zero frequency. The paper shows that the causal hysteretic model, although pathological at the static limit, is the mathematical connection between the non‐causal constant hysteretic model and the physically realizable Biot model. The mathematical structure of the two causal models is examined and it is shown that the causal hysteretic model is precisely the high‐frequency limit of the Biot model. Although both models have a closed‐form time‐domain representation, only the Biot model is suitable for a time‐domain viscoelastic analysis with commercially available computer software. The paper demonstrates that the simplest, causal and physically realizable linear hysteretic model that can approximate the cyclic behaviour of soil is the Biot model. The proposed study elucidates how the dynamic analysis of soil structures can be conducted rigorously in terms of the viscoelastic properties of the soil material and not with the ad hoc Rayleigh damping approach which occasionally has been criticized that tends to overdamp the higher vibration modes. The study concludes that under pulse‐type motions the Rayleigh damping approximation tends to overestimate displacements because of the inappropriate viscous type of dissipation that is imposed. Under longer motions that induce several cycles, the concept of equivalent viscous damping is more appropriate and the Rayleigh damping approximation results to a response that is comparable to the response computed with a rigorous time‐domain viscoelastic finite element analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Stability analysis of real‐time dynamic substructuring using delay differential equation models

Real‐time dynamic substructuring is an experimental technique for testing the dynamic behaviour of complex structures. It involves creating a hybrid model of the entire structure by combining an experimental test piece—the substructure—with a numerical model describing the remainder of the system. The technique is useful when it is impractical to experimentally test the entire structure or complete numerical modelling is insufficient. In this paper, we focus on the influence of delay in the system, which is generally due to the inherent dynamics of the transfer systems (actuators) used for structural testing. This naturally gives rise to a delay differential equation (DDE) model of the substructured system. With the case of a substructured system consisting of a single mass–spring oscillator we demonstrate how a DDE model can be used to understand the influence of the response delay of the actuator. Specifically, we describe a number of methods for identifying the critical time delay above which the system becomes unstable. Because of the low damping in many large structures a typical situation is that a substructuring test would operate in an unstable region if additional techniques were not implemented in practice. We demonstrate with an adaptive delay compensation technique that the substructured mass–spring oscillator system can be stabilized successfully in an experiment. The approach of DDE modelling also allows us to determine the dependence of the critical delay on the parameters of the delay compensation scheme. Using this approach we develop an over‐compensation scheme that will help ensure stable experimental testing from initiation to steady state operation. This technique is particularly suited to stiff structures or those with very low natural damping as regularly encountered in structural engineering. Copyright © 2005 John Wiley & Sons, Ltd.