Probabilistic approach for active control based on structural energy

This paper presents an active control algorithm using the probability density function of structural energy. It is assumed that structural energy under excitation has a Rayleigh probability distribution. This assumption is based on the fact that the Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of the control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of the control force is determined by the Lyapunov controller design method. The proposed control algorithm shows much reduction of peak responses under seismic excitation compared with the LQR controller, and it can consider the control force limit in the controller design. Also, the chattering problem which sometimes occurs in the Lyapunov controller can be avoided. Copyright © 2003 John Wiley & Sons, Ltd.     

LINEAR QUADRATIC REGULATOR FOR STRUCTURE UNDER ON-LINE PREDICTED FUTURE SEISMIC EXCITATION

A predictive-adaptive (PA) control algorithm has been developed for a structure under a seismic excitation. This algorithm analyses information of an observed seismic excitation, estimates future structural responses and determines the control force for the structure, based on the linear quadratic regulator. That is, at a given moment t_k: (1) seismic excitation information is converted to an autoregressive model, which forms the state equation for the excitation; (2) the identification model is combined with the structural model to build a state equation in an augmented space; (3) the weighted quadratic norm of the state vector and the future control force is formed as a cost function for estimating future responses; (4) the Ricatti equation is solved to find the optimum value of the cost function; and (5) the optimum gain matrix is obtained, and the control force is determined. The PA algorithm is not restricted to one type of control system, but can be applied to both an active driver system and an active tendon system. Its effectiveness is confirmed by numerical experiments for 1DOF and 3DOF structural models under sine and seismic excitations.     

Probabilistic seismic demand analysis of controlled steel moment‐resisting frame structures

This paper describes a proposed methodology, referred to as probabilistic seismic control analysis, for the development of probabilistic seismic demand curves for structures with supplemental control devices. The resulting curves may be used to determine the probability that any response measure, whether for a structure or control device, exceeds a pre‐determined allowable limit. This procedure couples conventional probabilistic seismic hazard analysis with non‐linear dynamic structural analyses to provide system specific information. This method is performed by evaluating the performance of specific controlled systems under seismic excitations using the SAC Phase II structures for the Los Angeles region, and three different control‐systems: (i) base isolation; (ii) linear viscous brace dampers; and (iii) active tendon braces. The use of a probabilistic format allows for consideration of structural response over a range of seismic hazards. The resulting annual hazard curves provide a basis for comparison between the different control strategies. Results for these curves indicate that no single control strategy is the most effective at all hazard levels. For example, at low return periods the viscous system has the lowest drift demands. However, at higher return periods, the isolation system becomes the most effective strategy. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal hybrid control of structures under earthquake excitation

Optimal control of base-isolated and non-base-isolated buildings subjected to earthquake excitation is considered. The control force at any instant is determined on-line through minimizing a quadratic time-dependent performance index based on the total energy imparted to the structure and the control effect. This control algorithm is based upon the use of discrete actuators and sensors that exert the control force and monitor the response of the building. Having constant gain matrices makes this algorithm efficient and easy to implement. The effect of time delay on the efficiency of the algorithm is investigated. Comparisons have been made to demonstrate the effectiveness of the proposed method.     

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.     

一种基于能量的振动主动控制新方法

为了防止控制过程中作动器出现饱和现象,本文提出了一种基于能量的新的振动主动控制策略。该方法是通过比较容许能量与实际能量来确定结构控制力的大小,而其方向是通过对能量求导确定。由于不需要求解线性矩阵不等式,所以计算简单,操作方便。并且当采用同样容量限的多个作动器时,控制输出力一致,从而避免设计多个控制系统,简化了控制器设计。此外,由于采用阶跃控制,控制系统便于实现。最后,以六层建筑物为例来说明本文方法的可行性。     

Unsupervised fuzzy neural network structural active pulse controller

Applying active control systems to civil engineering structures subjected to dynamic loading has received increasing interest. This study proposes an active pulse control model, termed unsupervised fuzzy neural network structural active pulse controller (UFN‐SAP controller), for controlling civil engineering structures under dynamic loading. The proposed controller combines an unsupervised neural network classification (UNC) model, an unsupervised fuzzy neural network (UFN) reasoning model, and an active pulse control strategy. The UFN‐SAP controller minimizes structural cumulative responses during earthquakes by applying active pulse control forces determined via the UFN model based on the clusters, classified through the UNC model, with their corresponding control forces. Herein, we assume that the effect of the pulses on structure is delayed until just before the next sampling time so that the control force can be calculated in time, and applied. The UFN‐SAP controller also averts the difficulty of obtaining system parameters for a real structure for the algorithm to allow active structural control. Illustrative examples reveal significant reductions in cumulative structural responses, proving the feasibility of applying the adaptive unsupervised neural network with the fuzzy classification approach to control civil engineering structures under dynamic loading. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of a tunable friction pendulum system for semi‐active control of building structures under earthquake ground motions

The Friction Pendulum System (FPS) isolator is commonly used as a base isolation system in buildings. In this paper, a new tunable FPS (TFPS) isolator is proposed and developed to act as a semi‐active control system by combining the traditional FPS and semi‐active control concept. Theoretical analysis and physical tests were carried out to investigate the behavior of the proposed TFPS isolator. The experimental and theoretical results were in good agreement, both suggesting that the friction force of the TFPS isolator can be tuned to achieve seismic isolation of the structure. A series of numerical simulations of a base‐isolated structure equipped with the proposed TFPS isolator and subjected to earthquake ground motions were also conducted. In the analyses, the linear quadratic regulator (LQR) method was adopted to control the friction force of the proposed TFPS, and the applicability and effectiveness of the TFPS in controlling the structure's seismic responses were investigated. The simulation results showed that the TFPS can reduce the displacement of the isolation layer without significantly increasing the floor acceleration and inter‐story displacement of the superstructure, confirming that the TFPS can effectively control a base‐isolated structure under earthquake ground motions.     

Predictive control of seismic structures with semi‐active friction dampers

In this paper a predictive control method especially suitable for the control of semi‐active friction dampers is proposed. By keeping the adjustable slip force of a semi‐active friction damper slightly lower than the critical friction force, the method allows the damper to remain in its slip state throughout an earthquake of arbitrary intensity, so the energy dissipation capacity of the damper can be improved. The proposed method is formulated in a discrete‐time domain and cast in the form of direct output feedback for easy control implementation. The control algorithm is able to produce a continuous and smooth slip force for a friction damper and thus avoid exerting the high‐frequency structural response that usually exists in structures with conventional friction dampers. Using a numerical study, the control performance of a multiple degrees of freedom (DOF) structural system equipped with passive friction dampers and semi‐active dampers controlled by the proposed method are compared. The numerical case shows that by merely using a single semi‐active friction damper and a few sensors, the proposed method is able to achieve better acceleration reduction than the case using multiple passive dampers. Copyright © 2004 John Wiley & Sons, Ltd.     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

Feasibility and robustness of predictive control of building structures by active cables

In this paper a theoretical and numerical analysis on the robustness and the practical feasibility of a control system of an experimental model of a building structure is performed. This model has a mechanical actuator employing active cables and the control algorithm is based on a predictive strategy. In order to test the robustness one simulates numerically different control experiments under two kinds of non-ideal conditions: (i) discrepancies between the parameters of the system (mass, natural frequencies and the time delay in the actuator) and those assumed in the formulation of the control algorithm; (ii) operation of the active cables out of the operation range caused by excitations stronger than expected. In order to assess the feasibility, in every control experiment one obtains the values of four performance indices which provide full information about the features of the control action. The numerical results show that predictive control by active cables is robust and feasible.     

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.     

Evaluation of response and energy in actively controlled structures

A computational method of energy evaluation is derived to study the elastic responses and energy distribution of actively controlled single‐degree‐of‐freedom (SDOF) structures during earthquakes. Contrary to the common perception that applying active control force pumps energy into the structure, the applied control force can actually reduce the energy in the structure by reducing the input energy from earthquakes to the structure. In addition, applying control force can dissipate a large amount of energy in the structure when this control force is applied in the direction opposite to the displacement and velocity responses. To demonstrate this energy mechanism in active controlled structures, the two most popular control algorithms, optimal linear control (OLC) and instantaneous optimal control (IOC) algorithms, are used to calculate the control response and energy spectra. One‐step time delay is incorporated into the algorithms to take into consideration the practical aspect of active control. The effects of different earthquakes and damping ratios on control energy and response spectra are studied. These studies show that both OLC and IOC are very effective in reducing the structural displacement and velocity responses by reducing the input earthquake energy as well as dissipating a large amount of energy in the structure. Copyright © 2001 John Wiley & Sons, Ltd.     

Bayesian probabilistic damage detection of a reinforced‐concrete bridge column

A Bayesian probabilistic approach for damage detection has been proposed for the continuous monitoring of civil structures (Sohn H, Law KH. Bayesian probabilistic approach for structure damage detection. Earthquake Engineering and Structural Dynamics 1997; 26 :1259–1281). This paper describes the application of the Bayesian approach to predict the location of plastic hinge deformation using the experimental data obtained from the vibration tests of a reinforced‐concrete bridge column. The column was statically pushed incrementally with lateral displacements until a plastic hinge is fully formed at the bottom portion of the column. Vibration tests were performed at different damage stages. The proposed damage detection method was able to locate the damaged region using a simplified analytical model and the modal parameters estimated from the vibration tests, although (1) only the first bending and first torsional modes were estimated from the experimental test data, (2) the locations where the accelerations were measured did not coincide with the degrees of freedom of the analytical model, and (3) there existed discrepancies between the undamaged test structure and the analytical model. The Bayesian framework was able to systematically update the damage probabilities when new test data became available. Better diagnosis was obtained by employing multiple data sets than just by using each test data set separately. Copyright © 2000 John Wiley & Sons, Ltd.     

Effectiveness of structural control based on control energy perspectives

A computational algorithm for maximizing the control efficiency in actively controlling the elastic structural responses during earthquake is proposed. Study of optimal linear control using a single degree of freedom shows that applying active control is very effective in reducing the structural displacement and velocity responses for long‐period structures, but at the same time it has an adverse effect in increasing the absolute acceleration response. The extent of this adverse effect reduces the effectiveness of the control system, and therefore it poses a limit on the maximum control force in order to provide maximum control efficiency. In view of this shortcoming, maximum control energy dissipation is used to define the most effective optimal linear control law. Less displacement and velocity response are expected as larger control force is applied, but there is always a limit that maximum control energy can be dissipated. This study shows that this limit depends on the structural characteristics as well as the input ground motion, and a general trend is that the maximum control energy decreases as damping increases. Finally, application of the proposed algorithm on a six‐storey hospital building is presented to show the effectiveness of using optimal linear control on a multi‐degree‐of‐freedom system from the control energy perspectives. Copyright © 2001 John Wiley & Sons, Ltd.     

EVALUATION OF SOME IMPLICIT TIME-STEPPING ALGORITHMS FOR PSEUDODYNAMIC TESTS

Two types of implicit time-stepping algorithms have been proposed recently for pseudodynamic tests. The first type consists of an algorithm which relies on Newton iterations to satisfy the equations of motion. The second type consists of an algorithm which is based on the Operator-Splitting technique and does not require any numerical iteration. While one or the other has been preferred by some researchers, these time-stepping algorithms have not been analysed and compared under a uniform setting. In this paper, a concise summary of these schemes is presented, and they are evaluated in a consistent manner in terms of numerical dissipation, frequency distortion and experimental errors. The analytical results are validated by numerical simulations as well as experimental results. It is shown that the algorithm based on Newton iterations can control experimental error effects effectively by means of an error-correction procedure. The algorithm based on the Operator-Splitting technique demonstrates similar performance provided the I-Modification is adopted.     

On the optimality criterion in structural control

The classical performance index optimization control algorithm is considered in order to check the real optimality of the control procedure; the basic steps for the optimal algorithm are reviewed, and the equation for the optimal control force derived. It is shown that the optimality conditions cannot be met with regard to the performance index, unless one is concerned with simple free oscillations. It is proved that in this case on one side the optimal control turns out to be of the linear closed‐loop type, yielding explicit optimal control coefficients, and on the other side that no solution can exist of the optimal problem for a generic forcing function. It is concluded that one is forced to calibrate the control force for free oscillations, and that the reliability of the index procedure mainly rests on some implicit expectation that linear control can be calibrated in the absence of the external disturbance and that it works under forced oscillations as well. Furthermore, the problem of delayed active control, with reference to a s.d.o.f. system controlled by a closed‐loop linear algorithm and under the action of a dynamic forcing function is investigated. In particular, the effects produced on the response of the structure by the introduction in the control law of assessed critical values of time delay are analysed and the comparison is proposed between the numerical results that one gets by adopting two different procedures (on one hand the above‐mentioned optimal linear control law and on the other hand the constrained minimization of the structural response norm) to compensate for time lag occurring in the actuation of the active control servomechanisms. Copyright © 2000 John Wiley & Sons, Ltd.     

Experimental simulation of degrading structures through active control

In experimental studies of structural behaviour, it is often desirable, even necessary, to perform tests on a test structure from its undamaged state, through its damaged states, and finally to failure. The fact that experiments of this type are not often done primarily because of its prohibitive cost. In this paper, a testing procedure is proposed in which a test structure is allowed to undergo its degradation in real time yet it is not physically damaged, thus allowing it to be reused. The underlying concept is that of active structural control. Considerable research and development of active structural control in civil engineering has taken place relative to responsive control of structures against damaging environmental loads. While the use of active control systems to simulate damage in an experimental setting as proposed in this paper appears to be new, much of the existing knowledge base in active structural control is directly applicable. © 1998 John Wiley & Sons, Ltd.     

Semiactive fuzzy control of the seismic response of building frames with MR dampers

A fuzzy‐logic control algorithm, based on the fuzzification of the MR damper characteristics, is presented for the semiactive control of building frames under seismic excitation. The MR damper characteristics are represented by force–velocity and force–displacement curves obtained from the sinusoidal actuation test. The method does not require any analytical model of MR damper characteristics, such as the Bouc‐Wen model, to be incorporated into the control algorithm. The control algorithm has a feedback structure and is implemented by using the fuzzy‐logic and Simulink toolboxes of MATLAB. The performance of the algorithm is studied by using it to control the responses of two example buildings taken from the literature—a three‐storey building frame, in which controlled responses are obtained by clipped‐optimal control and a ten‐storey building frame. The results indicate that the proposed scheme provides nearly the same percentage reduction of responses as that obtained by the clipped‐optimal control with much less control force and much less command voltage. Position of the damper is found to significantly affect the controlled responses of the structure. It is observed that any increase in the damper capacity beyond a saturation level does not improve the performance of the controller. Copyright © 2011 John Wiley & Sons, Ltd.     

H_∞ drift control of time-delayed seismic structures

In this paper,an optimal H∞ control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations.To achieve optimal control performance and to guarantee the stability of the control system,an optimum strategy to select control parameters γ and α was developed.Analytical expressions of the upper and the lower bounds of γ and α were obtained for a single degree-of-freedom system with state fee...