Gray box identification of flexible structures: application to robust active vibration suppression control

The paper deals with gray box identification of flexible structures and active vibration suppression from a robust control perspective. First, the linearized mathematical model of an N‐storey flexible structure is presented. Next, the generalized mathematical model is particularized for the investigated three‐storey flexible structure. The considered flexible structure is identified based on black box and gray box identification methods and the model's parametric uncertainties are deduced. Furthermore, control constraints are presented for the design problem, in case of velocity as well as acceleration feedback, from a robust control perspective. Finally, the effectiveness of the control system is tested through experiments, when the input disturbance is assumed to be a sinusoidal one as well as a historical earthquake record (1940 El Centro record). Copyright © 2001 John Wiley & Sons, Ltd.     

Optimal design of supplemental viscous dampers for linear framed structures

A methodology for the optimal design of supplemental viscous dampers for framed structures is presented. It addresses the problem of minimizing the added damping subject to a constraint on the maximal interstorey angular drift for an ensemble of realistic ground motion records while assuming linear behaviour of the damped structure. The solution is achieved by actually solving an equivalent optimization problem of minimizing the added damping subject to a constraint on a maximal weighted integral on the squared angular drift. The computational effort is appreciably reduced by first using one ‘active’ ground motion record. If the resulting optimal design fails to satisfy the constraints for other ground motions from the original ensemble, additional ground motions (loading conditions) are added one by one to the ‘active’ set until the optimum is reached. An efficient selecting process which is presented herein will usually require one or two records to attain an optimum design. Examples of optimal designs of supplemental dampers are presented for a 2‐storey shear frame and a 10‐storey industrial frame. The 2‐storey shear frame is required to withstand one given ground motion whereas the 10‐storey frame is required to withstand an ensemble of twenty ground motions. The resulting viscously damped structures have envelope values of interstorey drifts equal or less than the target drifts. Copyright © 2005 John Wiley & Sons, Ltd.     

Predictive active control of MDOF structures

This paper presents a theoretical study of a predictive active control system used to improve the response of multi‐degree‐of‐freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to find a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field. Linear auto‐regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time‐delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure. A numerical analysis of a seven‐storey ER damped structure is presented as an example. It shows a significant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an ‘occurring’ earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a ‘known’ complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control). Copyright © 2000 John Wiley & Sons, Ltd.     

Reliability‐based robust control for uncertain dynamical systems using feedback of incomplete noisy response measurements

A reliability‐based output feedback control methodology is presented for controlling the dynamic response of systems that are represented by linear state‐space models. The design criterion is based on a robust failure probability for the system. This criterion provides robustness for the controlled system by considering a probability distribution over a set of possible system models with a stochastic model of the excitation so that robust performance is expected. The control command signal can be calculated using incomplete response measurements at previous time steps without requiring state estimation. Examples of robust structural control using an active mass driver on a shear building model and on a benchmark structure are presented to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Modeling of an actively braced full‐scale building considering control–structure interaction

Recently, the application of active control to seismic‐excited buildings has attracted international attention. To demonstrate the practical applicability of active control, we have conducted experimental tests using a full‐scale three‐storey building equipped with active bracing systems on the shake table at the National Center for Research on Earthquake Engineering (NCREE), Taiwan. Experimental results indicate that the control–structure interaction (CSI) effect is significant. A state‐space analytical model of this actively controlled building taking into account the CSI effect is established in this paper using a system identification technique based on curve‐fitting of transfer functions. To verify the accuracy of the analytical model for simulating the controlled response, four sets of linear quadratic Gaussian (LQG) controllers using acceleration feedback are designed and further experimental tests are conducted for comparison. It is demonstrated that the correlations between the simulation and experimental results are remarkable. The construction of an accurate analytical model is important for active control, and such an analytical model can be used for future benchmark studies of different control algorithms based on numerical simulations. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimization of structural control via a smart NEURO‐FBG control system

This study improves a NEURO‐FBG active control system to mature the concept of a smart structure. Originally, a system similar to the human brain is created from FBG sensors and neural networks. The system comprises three parts, namely, a structural condition surveillance system, a NEURO‐FBG converter, and a NEURO‐FBG controller. To solve the inherent time‐consuming and reliability problem of the NEURO‐FBG converter, a new technology is first proposed, and the relationship between inter‐story drift and strain data is established. Global indices such as displacement and velocity of the structure are then reconstructed for searching the optimal control force of the actuator. Meanwhile, the soundness of a building with hydraulic actuators is also an important issue to be solved. To make the building sound, the characteristics of earthquakes are considered for enhancing the performance of the NEURO‐FBG controller. Theoretical analysis shows satisfactory improvement to the control efficiency of both displacement and acceleration. To verify the enhanced system, a series of shaking table tests was conducted. Experimental results demonstrated that the new NEURO‐FBG system can effectively manage the structure; and the controller, taking into consideration the ground acceleration effect, is more reliable and robust for practical application than a conventional controller. Copyright © 2007 John Wiley & Sons, Ltd.     

Market‐based control of linear structural systems

To limit the response of structures during external disturbances such as strong winds or large seismic events, structural control systems can be used. In the structural engineering field, attention has been shifted from active control to semi‐active control systems. Unlike active control system devices, semi‐active devices are compact, have efficient power consumption characteristics and are less expensive. As a result, an environment of a large number of actuators and sensors will result, rendering a complex large‐scale dynamic system. Such a system is best controlled by a decentralized approach such as market‐based control (MBC). In MBC, the system is modelled as a market place of buyers and sellers that leads to an efficient allocation of control power. The resulting MBC solution is shown to be locally Pareto optimal. This novel control approach is applied to three linear structural systems ranging from a one‐storey structure to a 20‐storey structure, all controlled by semi‐active hydraulic dampers. It is shown that MBC is competitive in the reduction of structural responses during large seismic loadings as compared to the centralized control approach of the linear quadratic regulation controller. Copyright © 2002 John Wiley & Sons, Ltd.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Active interaction control of civil structures. Part 2: MDOF systems

In this paper, the performance of active interaction control (AIC) algorithms is assessed within the context of two realistic building models. The AIC control approach is proposed as a semi‐active means of mitigating the structural response during large earthquakes. To implement the AIC control algorithms into MDOF systems, the modal control (MC) approach that directs the control effort to certain dominant response modes is formulated and utilized herein. Two structures, a 3‐storey building and a 9‐storey steel‐framed benchmark building controlled by the AIC algorithms are analysed for two historical earthquake records. The results of numerical simulation verify the efficacy of the AIC control algorithms in controlling vibration of building structures during large earthquakes. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental validation of semi‐active resetable actuators in a ⅕th scale test structure

The seismic performance of a test structure fitted with semi‐active resetable devices is experimentally investigated. Shaking table tests are conducted on a ?th scale four‐storey building using 27 earthquake records at different intensity scalings. Different resetable device control laws result in unique hysteretic responses from the devices and thus the structure. This device adaptability enables manipulation or sculpting of the overall hysteresis response of the structure to address specific structural cases and types. The response metrics are presented as maximum 3rd floor acceleration and displacement, and the total base shear. The devices reduce all the response metrics compared with the uncontrolled case and a fail‐safe surrogate. Cumulative probability functions allow comparison between different control laws and additionally allow tradeoffs in design to be rapidly assessed. Ease of changing the control law in real‐time during an earthquake record further improves the adaptability of the system to obtain the optimum device response for the input motion and structural type. The findings are an important step to realizing full‐scale structural control with customized semi‐active hysteretic behaviour using these novel resetable device designs. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic structural control using a novel high‐performance active mass driver system

To resolve difficulties encountered by current technology in structural control against earthquakes, this study proposes a novel high‐performance active mass driver (HP‐AMD) system. Based on an active mass driver system, the device is integrated with a mechanical pulley system for stroke amplification to enhance simultaneously efficiency and save power. Meanwhile, an instantaneous optimal direct output feedback control algorithm is derived alongside the hardware development. Numerical simulation is performed using a five‐storey steel frame as the object structure under the 1940 El Centro earthquake. To gain further insight into the HP‐AMD system, the effects of stroke amplification as well as damper weight on system performance are explored. Analysis results demonstrate that the proposed HP‐AMD system is a promising means to improving current active structural control techniques. Copyright © 2000 John Wiley & Sons, Ltd.     

Influence of construction deficiencies on the seismic response of structures

The quality of construction is one of the main factors that affect the seismic vulnerability of structures. The damage observations of modern buildings after almost all recent earthquakes report cases of poor quality of materials, inadequate detailing of reinforcement and absence of capacity design principles. Looking at the modern codes for seismic design, which rely on high behaviour factor supplies, the assessment of the effects of poor quality of execution in otherwise well‐conceived and well‐designed structures becomes an important problem. This paper presents an experiment‐based estimation of the seismic response of a cast‐in‐situ one‐storey industrial reinforced concrete frame designed according to Eurocodes. The influence of the quality of construction is estimated by consideration of two models of the experimental prototype: a structure erected under strict measures for control of the quality of execution, and a structure erected with normal measures for control of the quality of execution which resulted in significant deficiencies in the practical arrangement of the reinforcement. On the basis of the experimental data the ductility and behaviour factor supplies of the two structures are estimated. Quantitative expressions for the influence of the quality of construction on the first yield displacement, ultimate storey displacement, maximum base‐shear force and behaviour factor supply are provided. Recommendations for the refinement of modern seismic design codes, particularly Eurocode 8, to take into account the quality of construction are given. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal placement of sensors on buildings subjected to intermediate‐storey excitation according to QN control method

An algorithm to calculate direct velocity feedback gain with limited number of sensors is developed in a simple way such that a certain performance index is minimized according to QN control method. If a limited number of velocity outputs can be measured, full velocity responses of the whole structure can be interpolated based on the mode shapes. By defining the performance index function as a combination of the structure's velocity responses and control forces only, feedback gain can be determined according to QN control method with the external excitation being taken into account throughout the entire algorithm. Control forces are then regulated by the time‐invariant feedback gain matrix. The effective location of the active control devices for a building structure subjected to intermediate‐storey excitation has been determined to be in the three floors adjacent to the vibration source. Hence for the purpose of this paper, only the optimal placement of sensors is verified. It is shown in this paper that if the dynamic behaviour of the structure is well described by a mathematical model, sufficient response reduction effect can be achieved according to the new DVFC algorithm, and the degradation of control performance due to time delay can also be verified. Copyright © 2001 John Wiley & Sons, Ltd.     

Neuro‐control of seismically excited steel structure through sensitivity evaluation scheme

The neuro‐controller training algorithm based on cost function is applied to a multi‐degree‐of‐freedom system; and a sensitivity evaluation algorithm replacing the emulator neural network is proposed. In conventional methods, the emulator neural network is used to evaluate the sensitivity of structural response to the control signal. To use the emulator, it should be trained to predict the dynamic response of the structure. Much of the time is usually spent on training of the emulator. In the proposed algorithm, however, it takes only one sampling time to obtain the sensitivity. Therefore, training time for the emulator is eliminated. As a result, only one neural network is used for the neuro‐control system. In the numerical example, the three‐storey building structure with linear and non‐linear stiffness is controlled by the trained neural network. The actuator dynamics and control time delay are considered in the simulation. Numerical examples show that the proposed control algorithm is valid in structural control. Copyright © 2001 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.     

Probabilistic approach for active control of structures: experimental verification

In our previous study (Earthquake Engineering and Structural Dynamics 2003; 32 :2301), we have developed a probabilistic algorithm for active control of structures. In the probabilistic control algorithm, the control force is determined by the probability that the structural energy exceeds a specified target critical energy, and the direction of a control force is determined by the Lyapunov controller design method. In this paper, an experimental verification of the proposed probabilistic control algorithm is presented. A three‐story test structure equipped with an active mass driver (AMD) has been used. The effectiveness of the control algorithm has been examined by exciting the test structure using a sinusoidal signal, a scaled El Centro earthquake and a broadband Gaussian white noise; and, especially, experiments on control have been performed under different conditions to that of system identification in order to prove the stability and robustness of the proposed control algorithm. The experimental results indicate that the probabilistic control algorithm can achieve a significant response reduction under various types of ground excitations even when the modeling error exists. Copyright © 2004 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.     

Effective location of active control devices for building vibrations caused by periodic excitation acting on intermediate storey

In order to investigate ways of reducing vibrations of building structures subjected to excitation acting on intermediate storey, active vibration controls are conducted with active control devices installed on different floors of the structure, and the effective location of control devices is also investigated. In this paper, we propose a new ‘Discrete‐Optimizing Control Method’ for vibration control. The control forces are determined analytically which makes the ‘discrete‐index function’ minimum. Through numerical simulation, the Discrete‐Optimizing Control Method is proved to be an effective control method. The response reduction effects are best when the control devices are concentrated on the adjacent three floors of the vibration source. Copyright © 2000 John Wiley & Sons, Ltd.     

Sliding mode fuzzy control: Theory and verification on a benchmark structure

A sliding mode fuzzy control (SMFC) algorithm is presented for vibration reduction of large structures. The rule base of the fuzzy inference engine is constructed based on the sliding mode control, which is one of the non‐linear control algorithms. In general, fuzziness of the controller makes the control system robust against the uncertainties in the system parameters and the input excitation, and the non‐linearity of the control rule makes the controller more effective than linear controllers. For verification of the present algorithm, a numerical study is carried out on the benchmark problem initiated by the ASCE Committee on Structural Control. To achieve a high level of realism, various aspects are considered such as actuator–structure interaction, sensor noise, actuator time delay, precision of the A/D and D/A converters, magnitude of control force, and order of control model. Performance of the SMFC is examined in comparison with those of other control algorithms such as H_{mixed 2/∞}, optimal polynomial control, neural networks control, and SMC, which were reported by other researchers. The results indicate that the present SMFC is efficient and attractive, since the vibration responses of the structure can be reduced very effectively and the design procedure is simple and convenient. Copyright © 2000 John Wiley & Sons, Ltd.     

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

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