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.     

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.     

A new method of reduced order feedback control using Genetic Algorithms

Genetic Algorithms (GAs) have been applied as an effective optimization search technique in various fields, including the field of control design. In this paper, a new control method using GAs is proposed to attenuate the responses of a structure under seismic excitation. The proposed controller uses the state space reconstruction technique based on the embedding theorem to obtain full state performance from the available reduced order feedback. The parameters of the new controller are optimized using GAs. The proposed GA-based control method is verified on a benchmark problem—active mass driver system—and the results are compared with other control methods. The robustness of the proposed control method is also examined. Copyright © 1999 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.     

Experimental verification of a wireless sensing and control system for structural control using MR dampers

The performance aspects of a wireless ‘active’ sensor, including the reliability of the wireless communication channel for real‐time data delivery and its application to feedback structural control, are explored in this study. First, the control of magnetorheological (MR) dampers using wireless sensors is examined. Second, the application of the MR‐damper to actively control a half‐scale three‐storey steel building excited at its base by shaking table is studied using a wireless control system assembled from wireless active sensors. With an MR damper installed on each floor (three dampers total), structural responses during seismic excitation are measured by the system's wireless active sensors and wirelessly communicated to each other; upon receipt of response data, the wireless sensor interfaced to each MR damper calculates a desired control action using an LQG controller implemented in the wireless sensor's computational core. In this system, the wireless active sensor is responsible for the reception of response data, determination of optimal control forces, and the issuing of command signals to the MR damper. Various control solutions are formulated in this study and embedded in the wireless control system including centralized and decentralized control algorithms. Copyright © 2007 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.     

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.     

Damper placement optimization in a shear building model with discrete design variables: a mixed‐integer second‐order cone programming approach

Supplemental damping is known as an efficient and practical means to improve seismic response of building structures. Presented in this paper is a mixed‐integer programming approach to find the optimal placement of supplemental dampers in a given shear building model. The damping coefficients of dampers are treated as discrete design variables. It is shown that a minimization problem of the sum of the transfer function amplitudes of the interstory drifts can be formulated as a mixed‐integer second‐order cone programming problem. The global optimal solution of the optimization problem is then found by using a solver based on a branch‐and‐cut algorithm. Two numerical examples in literature are solved with discrete design variables. In one of these examples, the proposed method finds a better solution than an existing method in literature developed for the continuous optimal damper placement problem. Copyright © 2013 John Wiley & Sons, Ltd.     

A reduced‐order modeling technique for tall buildings with active tuned mass damper

It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reduced‐order control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reduced‐order system is updated repeatedly until a desired one is obtained, the accuracy of the reduced‐order system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. Another advantage of the method is that the reduced‐order system is defined in the subspace of the original physical space, which makes the state vectors have physical meaning. An eigenvalue shifting technique is applied to accelerate the convergence of iteration and to make the reduced system retain all the dynamic characteristics of the full system within a given frequency range. Two schemes to establish the reduced‐order system by using the proposed method are also presented and discussed in this paper. The results for a tall building with active tuned mass damper show that the proposed method is efficient for the reduced‐order modelling and the accuracy is very close to exact only after two iterations. Copyright © 2001 John Wiley & Sons, Ltd.     

Modal control of seismic structures using augmented state matrix

In conventional methods of modal control, the number of controllable structural modes is usually restrained by the number of sensors that feedback the structural signals. In this paper a modal control scheme where the feedback gain is formulated in an augmented state space is proposed. The advantage of the proposed method is that it increases the number of the controllable modes without adding extra sensors. The method is verified experimentally by an earthquake simulation test with a full‐scale building model. The proposed modal control was also compared with the conventional ones in the test. For the building model tested, the performance of the proposed control with only one feedback signal can be as efficient as that of modal control with full state feedback. Copyright © 2001 John Wiley & Sons, Ltd.     

QN control method for building vibration caused by periodic excitation acting on intermediate story

It has been proved in the authors' latest paper that the effective location of active control devices for building vibration caused by periodic excitation acting on intermediate story is the adjacent three floors to the vibration source. However, in terms of the Discrete‐Optimizing control method, the control forces are on‐line calculated step‐by‐step and time‐delay must exist. The degradation of control effect caused by time‐delay can not be avoided. In this paper, QN control method is proposed in order to resolve this practical problem. Since the external excitations which the building structure would experience are supposed to be periodic to some degree, Quasi‐Newton method is applied into the close‐loop Linear–Quadratic optimal control method and the new control method is called the ‘QN control method’. In this new control method, instead of solving the Riccati equation, the feedback gain matrix is determined by optimizing the quadratic performance index of the structure with the Quasi‐Newton method, one of the most commonly used minimization of functions. The new control law can easily be implemented for time‐delay problems, the degradation can be greatly improved with compensated feedback gain matrix. As a result, the QN control method is proved to be an efficient method to determine the feedback gain matrix. Copyright © 2000 John Wiley & Sons, Ltd.     

A first-order approximation to stochastic optimal control of reservoirs

A new approximate method of solution for stochastic optimal control problems with many state and control variables is introduced. The method is based on the expansion of the optimal control into the deterministic feedback control plus a caution term. The analytic, small-perturbation calculation of the caution term is at the heart of the new method. The developed approximation depends only on the first two statistical moments of the random inputs and up to the third derivatives of the cost functions. Its computational requirements do not exhibit the exponential growth exhibited by discrete stochastic DP and can be used as a suboptimal solution to problems for which application of stochastic DP is not feasible. The method is accurate when the cost-to-go functions are approximately cubic in a neighbourhood around the deterministic trajectory whose size depends on forecasting uncertainty. Furthermore, the method elucidates the stochastic optimization problem yielding insights which cannot be easily obtained from the numerical application of discrete DP.     

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.     

Seismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method

The uncertainty in the seismic demand of a structure (referred to as the engineering demand parameter, EDP) needs to be properly characterized in performance‐based earthquake engineering. Uncertainties in the ground motion and in structural properties are responsible for EDP uncertainty. In this study, sensitivity of EDPs to major uncertain variables is investigated using the first‐order second‐moment method for a case study building. This method is shown to be simple and efficient for estimating the sensitivity of seismic demand. The EDP uncertainty induced by each uncertain variable is used to determine which variables are most significant. Results show that the uncertainties in ground motion are more significant for global EDPs, namely peak roof acceleration and displacement, and maximum inter‐storey drift ratio, than those in structural properties. Uncertainty in the intensity measure (IM) of ground motion is the dominant variable for uncertainties in local EDPs such as the curvature demand at critical cross‐sections. Conditional sensitivity of global and local EDPs given IM is also estimated. It is observed that the combined effect of uncertainties in structural properties is more significant than uncertainty in ground motion profile at lower IM levels, while the opposite is true at higher IM levels. Copyright © 2005 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.     

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.     

Time‐delay effect and compensation on direct output feedback controlled mass damper systems

In active control, the control force execution time delay cannot be avoided or eliminated even with present technology, which can be critical to the performance of the control system. This paper investigates the influence of time delay on the stability of an SDOF system with an optimal direct output feedback controlled mass damper. An active mass damper system can take the form of a hybrid mass damper (HMD) or a fully active mass damper (AMD) depending upon imposed design constraints resulting from space, strength and power limitations. Explicit formulas and numerical solutions to determine the maximum delay time which causes onset of system instability are obtained. The control effect of the two‐DOF HMD/AMD benchmark system with and without time delay is illustrated quantitatively in a continuous‐time approach. In order to fit the digital implementation of the computer‐controlled system in practice, the control gains will be compensated by using their discrete‐time version to overcome the degradation of control effect due to time delay. Copyright © 2001 John Wiley & Sons, Ltd.     

A new method of reduced-order feedback control using Genetic Algorithms

Genetic Algorithms (GAs) have been applied as an effective optimization search technique in various fields, including the field of control design. In this paper, a new control method using GAs is proposed to attenuate the responses of a structure under seismic excitation. The proposed controller uses the state-space reconstruction technique based on the embedding theorem to obtain full-state performance from the available reduced order feedback. The parameters of the new controller are optimized using GAs. The proposed GA-based control method is verified on a benchmark problem—active mass driver system, and the results are compared with other control methods. The robustness of the proposed control method is also examined. Copyright © 1999 John Wiley & Sons, Ltd.     

OPTIMAL POLYNOMIAL CONTROL FOR SEISMICALLY EXCITED NON-LINEAR AND HYSTERETIC STRUCTURES

In this paper, we present an optimal polynomial controller for reducing the peak response quantities of seismically excited non-linear or hysteretic building systems. A performance index, that is quadratic in control and polynomial of any order in non-linear states, is considered. The performance index is minimized based on the Hamilton–Jacobi–Bellman equation using a polynomial function of non-linear states, which satisfies all the properties of a Lyapunov function. The resulting optimal controller is a summation of polynomials in non-linear states, i.e. linear, cubic, quintic, etc. Gain matrices for different parts of the controller are determined from Riccati and Lyapunov matrix equations. Numerical simulation results indicate that the percentage of reduction for the selected peak response quantity increases with the increase of the earthquake intensity. Such load adaptive properties are very desirable, since the intensity of the earthquake ground acceleration is stochastic in nature. The proposed optimal polynomial controller is an effective and viable control method for non-linear or hysteretic civil engineering structures. It is an addition to available control methods in the literature.     

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.