Active and semi-active control of structures

Article

Active and semi-active control of structures – theory and applications: A review of recent advances

Journal of Intelligent Material Systems and Structures 0(0) 1–15 Ó The Author(s) 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1045389X12445029 jim.sagepub.com

Fabio Casciati1, Jose´ Rodellar2 and Umut Yildirim1

Abstract It is internationally recognized that structural control was introduced in civil engineering through a pioneering article by Yao and through the implementations promoted by Kobori. The concepts of active and semi-active structural control in civil and infrastructure engineering date back 40 years and much progress has been recorded during these four decades. Periodically, state-of-the-art manuscripts have been published and technical books were also printed to testify the maturation of the topic. This article only covers the period from the second semester of 2009 to the first semester of 2011, emphasizing the developments in terms of theoretical, numerical and experimental studies, as well as the use of control algorithms and devices in actual implementations. It is observed that there are still several operational limitations to prevent from the expected growth of the applications in standard design. Nevertheless, some innovative concepts help to foresee future developments within special sectors of applications. Keywords active control, control algorithms, intelligent systems, laboratory testing, semi-active control, structural control

Introduction The solutions for mitigating the response of structures under natural hazards, such as earthquakes and strong winds, have been moving from passive control systems to smart and effective active or semi-active systems by exploring recent advances in microprocessor, sensor and actuator technologies. While passive systems are unable to adapt to changes in the structural properties and to the stochastic nature of the external excitations, active control systems can adapt to a wide range of operating conditions and structures. But their input of mechanical energy into the structural system could result in significant increases in hardware costs and reliability issues. Semi-active control systems achieve a compromise between active and passive control systems by combining the inherent reliability of passive systems and the adaptability of active systems without requiring significant sources of external power. In addition they are inherently stable. Over the past four decades, various control algorithms and control devices have been developed, modified and investigated by various groups of researchers since the pioneering work by Yao (1972). Periodic conferences greatly helped to disseminate the scientific and technical developments (Baratta and Rodellar, 1996; Belyaev and Indeitsev, 2008; Casciati, 2003; Casciati

and Magonette, 2001; Flesh et al., 2005; Fujino et al., 2010; Housner et al., 1994; Johnson and Smyth, 2007; Kobori et al., 1999). While many of these structural control strategies have been successfully applied, challenges pertaining to cost, reliance on external power and mechanical intricacy during the life of the structure have delayed their widespread use. An early review article of active structural control in civil engineering was prepared by Soong (1988). The article stated the motivating factors of active control and the benefits of its use under severe conditions. The activities in control system design, algorithm development and some practical considerations were also outlined. The conceptual basic system architecture of actively controlled structures was first proposed by Kobori early in the 1950s. He classified the researches on active control in theoretical research and application

1

Department of Structural Mechanics, University of Pavia, Pavia, Italy Department of Applied Mathematics III, Universitat Polite`cnica de Catalunya (UPC), Barcelona, Spain

2

Corresponding author: Umut Yildirim, Department of Structural Mechanics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy. Email: [email protected]

2 development (Kobori, 1996). Several authors worked together (Housner et al., 1997) to publish a tutorial (or survey) article to provide a starting point for researchers who were wishing to assess the state of the art in the control of civil engineering structures. The article provided a link between structural control and other fields of control theory, pointing out both differences and similarities. The article provided details of passive energy dissipation systems, active control systems, hybrid and semi-active control systems, sensors for structural control, smart material systems as well as structural health monitoring and damage detection as support to structural control. A detailed literature review of semi-active control systems was prepared in Symans and Constantinou (1999). The review specifically focussed on the description of the dynamic behaviour and the distinguishing features of various semi-active systems, which had been experimentally tested both at the component level and within the small-scale structural models. The semiactive systems that were reviewed include stiffness control devices, electrorheological dampers, magnetorheological (MR) dampers, friction control devices, fluid viscous dampers, tuned mass dampers (TMDs) and tuned liquid dampers. The article by Soong and Spencer (2002) presented a brief historical outline of the development and an assessment of the state of the art and state of the practice of evolving structural control technology. Also, their advantages and limitations were included in the context of seismic design and retrofit of civil engineering structures. A review study for the main classes of semi-active control devices and their full-scale implementation to civil infrastructure applications was presented 1 year later (Spencer and Nagarajaiah, 2003). Another review (Datta, 2003), mainly focussed on the application of active control of structures to counteract earthquake excitation, provides theoretical backgrounds of different active control schemes, parametric observations on active structural control, limitations and difficulties of their practical implementation. An overview on some theoretical and practical issues involved in the design and implementation of control algorithms was presented in Rodellar et al. (2008), including selected references. More recently, the article by Soong and Cimellaro (2009) focussed on the integrated design of control/ structural systems. The research opened a gate for new possibilities in structural forms and configurations. The main idea was to separate the control law into two parts: a passive part that was implemented into the physical system by redesigning it and an active part that represents the remaining active control law required after the structure redesign. In other words, the structure can be redesigned for better controllability in terms of a lighter structure for a specified performance in view of minimizing the amount of active control power needed.

Journal of Intelligent Material Systems and Structures 0(0) The developments and advances in semi-active/smart variable stiffness and adaptive passive systems were presented in Naragarajaiah (2010). Semi-active or smart tuned mass dampers (STMDs), adaptive length pendulum (ALP) dampers, adaptive negative stiffness devices (NSD) and also their driving algorithms were proposed. In parallel to the evolution of review papers published in international journals, some books were also prepared (Casciati et al., 2006; Chu et al., 2005; Rodellar et al., 1999), initially in the form of contributed chapters organized by editors. Recent contributions of the new concepts and applications in structural control strategy are disseminated by Rodellar et al. (1999). From mathematical calculations to practical issues at the infrastructure level, several topics are introduced to the readers’ attention. In particular, the book chapters ranged from topics of observability, controllability, model-free approaches, risk adverse control, semi-active control, spillover, decentralized control, HN tools, stability-based control, fuzzy controllers, adaptive structures and so on. Significant issues involved in the integrated implementation of active control systems are introduced in Chu et al. (2005). Basic knowledge of how to handle digital data discretized from analogical measurements, transformation from theoretical values to practical signals and the effects of quantization are introduced. Then, the compatibility between the control hardware and the software of the integrated system is evaluated. Additionally, the issues of discretization in time, output feedback, sensor inaccuracies, time delays, measurement noises and real-time measured signals are considered. The book by Casciati et al. (2006) is organized into two parts: theoretical contributions and experimental evaluations. The first part consists of different kinds of control schemes and strategies. The second part explains the concepts in terms of implementation aspects. This article only covers the developments in the period from the beginning of 2009 to the early 2011. Its general outline moves from a review of the progresses on a theoretical and numerical ground (section ‘Theoretical issues and numerical simulations’). Section ‘Experimental studies’ groups few examples of experimental and hybrid testing studies. Section ‘Full-scale applications’ discusses the full-scale applications together with a foreseeing of the expected developments in structural control. Section ‘Final remarks and conclusions’ outlines some concluding remarks.

Theoretical issues and numerical simulations Control theory is the base for developing active and semi-active strategies. Many issues are involved in designing control laws: model, feedback architecture (centralized/decentralized), performance objective, control methodology, stability, robustness in the presence

Casciati et al. of uncertainties and non-linearities. All of them are crucial and have to be investigated in the design process. Since most of these characteristics are combined in different ways depending on each control problem, there is not a single way of organizing a review on control methods in an area like structural control. This section is divided into subsections where the compiled contributions have significant intersections. Subsection ‘Control laws and feedback architecture’ joins articles where modelling issues and feedback architecture are particularly relevant. Subsection ‘Soft computing and adaptive control laws’ includes mainly soft computing and adaptive approaches. Typical non-linearities arise when using ‘smart’ actuators in semi-active settings, like in the family of MR dampers. This family has attracted intensive research in the last few years and is the subject of subsection ‘Control laws for the MR device family’. Control designs have been sometimes directly motivated by case studies. Results are often based on reduced numerical models without experimental support. They offer the scientists and the designers a common framework for comparing the achieved ability to manage well-defined problems. Among the case studies, a special character must be given to the contributions to the benchmarks launched across the scientific community. Subsections ‘Case studies’ and ‘Benchmark studies’ discuss a number of articles within this framework.

Control laws and feedback architecture This subsection reviews a set of articles whose main focus is on several issues that have an architectural nature within a control loop. Thus, some articles deal with the kind of performance that a system (the structure) is expected to achieve through a control system. Concepts such as desired response and pole assignment are used to design controllers based on performance specifications. The problem of the time delay in the control loop (mainly due to the actuation time lags), which was a subject of big concern for long time in the structural control research community, is still in the focus of some of the reviewed articles. A significant component in a control loop is the architecture linking the sensors and the actuators. Different options can be adopted depending on the number and location of these devices and how the information signals are connected, particularly for systems with large physical dimensions. This may be particularly relevant for large-scale structures like bridges, buildings and others. Some articles in this subsection deal with decentralized strategies where the overall system is first decomposed into subsystems and local controllers are designed and implemented. The final purpose is to reduce the transmission and computation costs within the control loops while increasing the reliability of the control system in case of failures in sensors.

3 A procedure using a two-stage approach was formulated in Cimellaro et al. (2009a) for the integrated design of controlled structural systems. As a first step, an initial structure was chosen and was assumed fixed, while the controller was designed in order to satisfy a given performance requirement (e.g. drift, absolute acceleration, base shear, etc.) of this initial structure. The dynamic response of the initial structure in this step is called ‘Ideal Response’. As a second step, the structure and the controller were redesigned cooperatively to achieve a common goal (the ideal dynamic response of the first step), while a certain objective function was optimized. For example, structural redesign can be accomplished to reduce the amount of active control power needed to achieve the ‘ideal response’. In other words, the structure was redesigned in view of a better controllability. Basically, the integrated redesign procedure was formulated for the case of elastic buildings. The same authors also proposed the integrated design of structural/control systems in the case of inelastic structures (Cimellaro et al., 2009b). The eigenvalues of a linear vibratory system under state-feedback control in the presence of time delay are studied using the method of receptances (Ram et al., 2009). The eigenvalues are separated into two groups, primary and secondary eigenvalues. The primary eigenvalues are the finite eigenvalues of the system without time delay. The secondary eigenvalues are the other eigenvalues emerging from infinity due to the delay. The analysis is based on Taylor series expansion of the control that allows approximation of the primary eigenvalues of the system. This approximation can be improved to desired accuracy by increasing the order of the expansion as shown by examples. The theoretical and practical applications of receptance method for single-input and multi-input state-feedback partial pole placement were developed and demonstrated useful for vibration suppression in structures (Tehrani et al., 2010). One of the advantages of the receptance method, over conventional matrix methods such as state-space control based on a finite element discretization, is that there is no need to know or to evaluate the structural matrices, or of the actuator dynamics, which may be included in the measurement by generalization of the receptance. Poles are assigned sequentially, the force distribution vector in each step being selected from the null space of previously assigned modes to easily excite the next mode, thereby ensuring that the previously assigned poles are uncontrollable and remain unchanged. A good agreement was demonstrated between the simulated and measured poles and also in the natural frequencies and damping of the structures. The problem of noise in measured receptances of robust pole placement in structural vibration is studied in Tehrani et al. (2011). The effects of sequential multiinput state feedback combined with minimization of the eigenvalue sensitivity are investigated. In a

4 sequential multi-input state-feedback approach, the procedure assumes that a different eigenvalue can be assigned at each step without changing those eigenvalues assigned at previous steps. The sequential approach has the advantage of a characteristic equation that is linear in the control gains and is shown to be inherently more robust to measurement noise than the single-input method. A dynamic control strategy, based on pole placement technique, was proposed for application to active or semi-active control systems installed in buildings designed against seismic actions (Pnevmatikos and Gantes, 2010). The general control strategy consists of the following stages: the monitoring of the incoming signal, its fast Fourier transform (FFT) or wavelet analysis for recognition of its dynamic characteristics, the selection of poles of the integrated controlled system, the application of the pole placement algorithm for the calculation of the required actions, and finally, accounting for the limitations of the devices to be used, their action accounting for saturation effects and time delay. The article by Abdel-Rohman et al. (2010) addressed the problem of time delay compensation by two methods. In the first method, the delayed control action was expressed in terms of the current control action and its derivatives using a truncated Taylor’s series. In the second method, the delayed control action was expressed as feedback of the delayed state variables. Both methods were applied on a linear model derived from the actual non-linear model. A technique to verify the stability and accuracy of adaptive control algorithms affected by time delay is proposed in Bursi et al. (2010). The adaptive minimal control synthesis (MCS) algorithm is applied to linear time-invariant plants while the whole controlled system state and control equations, discretized by the zeroorder-hold (ZOH) sampling, are non-linear. The two linearization procedures are obtained by a physical insight scheme and Taylor series expansion. The effectiveness of the methodology is assessed by both simulations and experimental tests. A time-delayed decentralized HN controller was designed and validated using a numerical model of a five-storey structure in Wang (2011). Simulations were conducted to illustrate the effects of different feedback time delays for different decentralized feedback patterns. The performance of the decentralized HN controllers was then compared with the performance of time-delayed decentralized controllers that were based on linear quadratic regulator (LQR) optimization criteria. It was shown that with less feedback latency, decentralized control strategies may achieve similar performance when compared with centralized ones. Therefore, decentralized strategies can be more appealing due to associated lower costs. An algorithm of modified predictive control (MPC), which was derived with the partial-state concept of

Journal of Intelligent Material Systems and Structures 0(0) direct output feedback (DOF) to reduce the number of sensors for real implementation, was given in Yang et al. (2011). According to the algorithm, the online control forces were simply generated from the actual output measurements that were multiplied by a prescribed constant output feedback gain matrix. Decentralized strategies using the concept of overlapping systems have been proposed in control theory and recently focussed on structural control in Bakule et al. (2005) and Palacios-Quin˜onero et al. (2010). Overlapping means to decompose a large-scale system into subsystems that share state and control variables. Using appropriate linear transformations, the overall system can be represented as a set of decoupled subsystems in such a way that ‘virtual’ decentralized controllers can be designed for such subsystems. Then, these controllers are transformed back so that they can be implemented in the real system. The methodology ensures essential structural properties like controllability and observability (Bakule et al., 2001). In the article by Zimmerman and Lynch (2010), an agent-based data processing in the wireless structural health monitoring through the application of marketbased techniques was used in network mode shape estimation. Specifically, following previous wireless sensor work by the authors, in both decentralized frequency domain decomposition (DCFDD) and market-based resource allocation, an algorithm derived from freemarket principles was developed through which an agent-based wireless sensor network can autonomously and optimally shift emphasis between improving the accuracy of its mode shape calculations and reducing its dependency on any of the physical limitations of the wireless network, namely, processing time, storage capacity, wireless bandwidth or power consumption. In summary, most of the articles discussed above deal with eigenvalues, poles, time delay, performance, model decomposition and decentralization. All of them are essential issues in designing and implementing controllers for systems that have a complex architecture, as for the systems encountered in structural control. Some of the above issues are ‘classical’ in the structural control literature. Others, like those related to feedback architecture and decentralization, are more recent in this context and, in our opinion, have potential to grow in the near future, particularly when associated to the new possibilities of wireless sensing and computing.

Soft computing and adaptive control laws Structures are complex systems that include elements and devices with a clear non-linear nature. This issue motivated an increasing interest in the recent years for developing non-linear control methods. In this context, the interaction between modelling and control formulation is very important and the mathematical and computational involvement is a significant problem to

Casciati et al. tackle. Analytical models are, in principle, the ideal framework to describe accurately the dynamic behaviour and to develop appropriate mathematical control laws to ensure stability and performance requirements with robustness capability against discrepancies between the models and the real non-linear behaviour. Since accurate models are not always available and are difficult to validate experimentally, there is a trend to use simplified models based on semi-physical approximations or direct input–output relationships experimentally obtained for control purposes. The articles included in this subsection use tools such as wavelets, neural networks, fuzzy logics and soft computing. They have in common the objective of controlling systems by combining analytically based control methods with model-free tools for uncertain non-linear and time-varying components. A wavelet-based adaptive time-varying controller was investigated by Basu and Nagarajaiah (2008). The modified LQR algorithm of the controller uses the information derived from the wavelet analysis of the response in real time, in order to obtain the local energy distribution over frequency bands. This structural system information is used to adaptively design the controller by updating the weighting matrices to be contributed to the response energy and the control effort. The optimal LQR control problem is solved for each time interval with updated weighting matrices, through the Riccati equation, leading to time-varying gain matrices in real time. A wavelet neuro-controller capable of selfadaptation and self-organization was also proposed in Laflamme et al. (2011) for uncertain systems controlled by semi-active devices, regarded as ideal candidates for large-scale civil structures. The controller was built on neural networks. The adaptive rules of the neurocontroller were derived using Lyapunov stability to ensure robustness. The performance of an adaptive fuzzy sliding mode control (AFSMC) for highway bridges was investigated in Ning et al. (2009). This approach combines the advantages of sliding mode control (SMC), adaptive control and fuzzy control without compromising the stability or robustness. Switching-type control law of the conventional SMC and uncertainty part of the equivalent control was approximated by a fuzzy controller to attenuate the chattering phenomenon of SMC and harmful effects caused by uncertainties. In order to reduce the complexity of the fuzzy rule bases, an adaptive law based on Lyapunov function and Barbalat’s lemma was designed. AFSMC is also integrated with a clipped-optimal (CO) strategy to illustrate its efficiency for semi-active MR dampers. A non-linear robust control approach to address the non-linear control problem of civil structures under strong earthquake excitation was presented in Li et al. (2011). The overall system was decomposed into several

5 subsystems, each adopting a corresponding control algorithm. During the control design process, a direct adaptive fuzzy control design scheme was developed to deal with the non-linear subsystem. The stability of the closed-loop system was proven by Lyapunov’s direct methods. Moreover, HN performance was achieved through a subsystem with the proposed controller. An adaptive control method was proposed in Bitaraf et al. (2010) with the focus on damage mitigation. The purpose was to force the damaged structure to behave like the undamaged structure that has an acceptable performance. The observability of the system shows that the internal states of the system can be inferred by the knowledge of its external outputs. The controllability and observability of the system with the governing equations were checked. An inverse Lyapunov method in a bang-bang type semi-active control for civil structures was used in Hiramoto et al. (2010). In the conventional Lyapunovbased semi-active control, the Lyapunov function is first determined; mostly, it is defined as the sum of the kinetic and potential energies at every instant, and the bang-bang type control is derived so that the dissipation rate of the defined Lyapunov function (the total energy) is maximized. In this specific article, conversely, the bang-bang type control is first introduced, based on an unspecified Lyapunov function. Then, the Lyapunov function was searched over a defined parameter space so that the performance index on vibration control was optimized. The Lyapunov function was parameterized as the weighted sum of the following indices: the sum of the kinetic and the potential energies, the sum of the squared inter-storey drift, the squared modal displacement and velocity of lower modes of vibration. Under the proposed parameterization, the parameters in the Lyapunov function were optimized with genetic algorithms to minimize the quantitative performance indices on vibration suppression. The combination of complementary techniques is, in general, an interesting way of addressing complex problems. The above articles combine analytical methods, like Lyapunov stability, SMC and HN, with ‘soft’ tools trying to exploit benefits from both sides. While the analytical methods provide a solid mathematical background for a class of models within given assumptions and working conditions, model-free tools can help in supplying practical rules for time-varying environments that may be difficult to model. The reviewed articles are some examples in structural control.

Control laws for the MR device family This subsection deals with a class of actuators that contain MR fluids. After application of a magnetic field, the fluid changes from liquid to semi-solid state in few milliseconds. Thus, although they are really dampers that supply dissipative (not active) forces only, they can

6 operate semi-actively under a feedback control that is designed to manipulate either a voltage or an electric current. MR dampers have been received a lot of attention in the last years and can be easily acquired on the market nowadays. A key aspect in designing and implementing a control system through this class of semi-active devices is that, while the structure behaviour is effectively controlled by the force supplied by the device, the final feedback control signal is the voltage (or current) that has to be appropriately derived to generate the desired force. The relation between input voltage and output force at the MR damper is very difficult to model accurately and, if available, a sophisticated model may be impossible to handle in a manageable form for real-time actuation. Then, most of the proposed control strategies modify the voltage through on–off rules without the use of a model. In many cases, these rules consist in adjusting the voltage in such a way that the actual force supplied by the MR damper tracks a desired force in the best possible way under the restriction of the purely dissipative capacity of the device. This desired force is usually calculated by means of an active feedback control law designed to achieve a control objective on the structure. This overall strategy has been popularized as ‘clipped control’ in the literature. Other bang-bang model-free voltage adjustments have been proposed in terms of minimizing Lyapunov energy functions. A recent family of methods considers the tracking of desired active control forces but through the inversion of a simplified model of the voltage–force relation. Altogether, the combination of practical potential and big challenges for control design and implementation has motivated an intensive research on vibration control using MR devices. Perhaps the largest subset of papers in the last 2 years covered by this review is related to MR devices. Du and Zhang (2009) presented a model-based fuzzy control algorithm for non-linear building-MR damper system. First, the MR damper model was obtained as a fuzzy model with Takagi–Sugeno (T-S) fuzzy modelling technique. Identifying the T-S fuzzy model from numerical input–output data includes two steps: the structure identification and the parameter estimation. Gaussian membership functions have been used in identifying the T-S fuzzy model from input–output data. The controller synthesis of the T-S fuzzy system is based on a common quadratic Lyapunov function because the problem can be efficiently solved by linear matrix inequality (LMI) techniques. Then, this fuzzy MR damper model was integrated with the structural system model. Finally, a generalized H2 or energy-topeak control algorithm, which aims to reduce the control output peak value under energy-bounded disturbance, was applied to the fuzzy model. The optimal fuzzy controller theoretically guarantees the closedloop system stability and the closed-loop performance.

Journal of Intelligent Material Systems and Structures 0(0) A different technique, the so-called quantitative feedback theory (QFT), was used in Zapateiro et al. (2009a) in a structure equipped with an MR damper. In this scheme, the controller is designed in the frequency domain and the natural frequencies of the structure can be directly accounted for in the process. Though the QFT methodology was originally conceived for linear time-invariant systems, a new methodology was proposed to characterize the non-linear hysteretic behaviour of the MR damper through the uncertainty template in the Nichols chart. The resulting controller performance was evaluated in a real-time hybrid testing (RTHT) experiment. Always with reference to MR dampers, a semi-active controller based on the backstepping technique was proposed in Zapateiro et al. (2009b). The backstepping control design consists in selecting appropriate functions of the state variables as pseudo control inputs for lower dimension subsystems of the overall system. The reader is referred to Ali and Ramaswamy (2009a) as well as to earlier studies such as Pozo et al. (2006) and Zhou et al. (2006). Each backstepping stage is a new pseudo control design in terms of the preceding stages. The final result is a feedback design for the true control input, which achieves the original design objective by virtue of a final Lyapunov function formed by summing up the Lyapunov functions associated with each individual design stage. A non-clipped semi-active stochastic optimal control strategy for non-linear structural systems with MR dampers was presented in Ying et al. (2009). It was developed and based on the stochastic averaging method and stochastic dynamical programming principle. The control force of an MR damper was separated into its passive and semi-active parts. The passive control force components, coupled in the structural mode space, were incorporated in the drift coefficients by directly using the stochastic averaging method. Then, the stochastic dynamical programming principle was applied to establish a dynamical programming equation, from which a semi-active optimal control law, implementable by the MR damper was determined. An integrated relative displacement sensor (IRDS) technology is implemented to MR dampers based on electromagnetic induction and the principle of an integrated relative displacement self-sensing MR damper (IRDSMRD) based on the IRDS technology were modelled and designed with finite element method (FEM) in Wang and Wang (2009). The IRDSMRD consists of an exciting coil wound on the piston and an induction coil wound on the non-magnetic cylinder. The coil wound on the piston acts as the exciting coil for both the MR damper to adapt the yield stress of the MR fluid and the IRDS simultaneously and the coil evenly wound on the cylinder acts as the induction coil of the IRDS. The exciting coil is fed by the harmonic voltage signal on a direct current (DC). Changing the

Casciati et al. DC current alters the yield stress of the MR fluid in the fluid gap to provide a controllable damping force. The harmonic voltage signal with the same frequency will be induced in the induction coil wound on the cylinder by the harmonic magnetic field along the primary flux path. When the piston moves in and out of the cylinder, the number of the active turns of the induction coil in the primary flux path correspondingly increases or decreases. In this way, demodulating the induced voltage from the induction coil, the relative displacement between the piston and the cylinder of the MR damper can be accessed and used to achieve the self-sensing integrated relative displacement. In Bahar et al. (2010a), a semi-active control was proposed based on a new inverse model of MR dampers (Bahar et al., 2010b). The model relies on an extension of the Bouc–Wen description of the input–output hysteretic behaviour (Ikhouane et al., 2007). The control strategy has a hierarchical structure to allow decentralized control of a set of MR dampers in base-isolated structures. The article by Kim et al. (2010) investigated the behaviour of a seismically excited benchmark building employing MR dampers operated by a model-based fuzzy logic controller (MBFLC) formulated in terms of LMIs. The MBFLC system was developed through integration of a set of Lyapunov controllers, Kalman filters, and semi-active converters with the fuzzy interpolation method. A set of multi-input multi-output (MIMO) autoregressive exogenous (ARX) input models was used for the design of the set of Lyapunov controllers that were formulated in terms of LMIs. Four different semi-active control algorithms (CO, Lyapunov stability theory (LYAP), maximum energy dissipation algorithm (MEDA) and cost function-based semi-active neuro-control (SNC) algorithm) are considered in Lee et al. (2010). CO control strategy is based on the acceleration feedback for controlling an MR damper. As the force generated in the MR damper depends on the local responses of the structural system, the desired optimal control force cannot always be produced by the device. Only the control voltage can be directly controlled to increase or decrease the force produced by the device. According to LYAP, if the rate of change of the Lyapunov function is negative semidefinite, the origin is stable. Therefore, a LYAP determines the control force in order to induce the rate of change of the Lyapunov function to be a negative value (if possible). The MEDA was presented as a variation of the decentralized bang-bang approach. This algorithm considers a Lyapunov function that represents the relative vibratory energy in the structure without including the velocity of the ground in the kinetic energy term. An SNC algorithm, which consists of a clipped algorithm in addition to the neuro-controller, was also proposed. The neuro-controller first calculates the optimal control force. To induce the MR damper to generate the

7 desired optimal control force, a clipped algorithm was then employed to select the command voltage to the MR damper. Since the authors also carried out experimental tests, this article is considered again in section ‘Experimental studies’, where some conclusions on the comparison are also illustrated. More comparative studies of different control laws are available like Shook et al. (2007) and Ali and Ramaswamy (2009c, 2009d). Two voltage control laws were introduced in Purohit and Chandiramani (2011): inverse quadratic voltage law (IQVL) and inverse on–off voltage law (IOOVL), both based on the MR constraint filter. These laws were implemented in addition to the existing clipped voltage law (CVL). The results for controlled response of the building were obtained in terms of peak and root mean square (RMS) values of response quantities (interstorey drift, displacement, acceleration). They were compared with existing results obtained via a linear quadratic Gaussian (LQG) control using CVL and via a passive-on control with constant (saturation) voltage applied. A reduction in the maximum peak inter-storey drift, maximum RMS inter-storey drift and performance index was obtained when using optimal static output feedback (OSOF)–IOOVL/CVL control while comparing with passive-on control. A semi-active control strategy is presented in Aguirre et al. (2011) based on the idea of clipping the voltage signal but using a simpler proportional and integral (PI) control. The two PI parameters are calculated so that the controller guarantees stability, minimization of the closed-loop response and robustness against modelling errors. Simulation results shows that this simple strategy can effectively improve the structural responses and achieve performance index comparable to that of more complex algorithms. By summarizing, a sample of the class of more recent studies on control using MR dampers has been provided. Most significant effort is paid in developing control strategies to be implementable in a semi-active scheme. The mathematical characterization of the semi-active actuators is one of the main components in the control formulation, since they are non-linear devices that cannot apply purely active forces. A variety of methods still rely on the concept of clipped control, where an active control is first designed and then approximated by a damper-like restoring force implementable by a semi-active actuator. Other methods combine semi-physical models, like the Bouc–Wen or related models, with a non-linear control method. A recent review on the use of this model in this context is available in Ismail et al. (2009). In any case, the robustness against the uncertainties in the whole control loop is a matter addressed in most of the articles. Most of the works address the control with a single device. Extensions to strategies to manage sets of several devices are interesting and can motivate further studies (Bahar et al., 2010a).

8

Case studies The contributions summarized below use control methods that could be included in previous subsections, but we have preferred to collect them in a separate subsection since the control designs are driven by specific problems involving specific structures and actuators, like wind turbines, TMD and active mass damper (AMD) and semi-active hydraulic devices. A semi-active control device was considered for decreasing the non-linear vibration of shallow cables in Casciati and Ubertini (2008). The control device was represented by a TMD with a variable out-of-plane inclination. A simple control algorithm was regulated for the out-of-plane inclination of the TMD. The effectiveness of the proposed control strategy was validated by means of numerical simulations, through an FEM formulation and a reduced discrete control-oriented analytical model. The equations of motion derived from the classical updated Lagrangian approach in both the FEM model and the reduced Galerkin model are taken into account in order to get a high numerical accuracy in analytical model. A fuzzy logic-based control algorithm to control a non-linear high-rise structure under earthquake excitation using an AMD device was developed in Li et al. (2011). For the control of a high-rise building under earthquake excitation, due to the complexity of the vibration modes, many inputs were needed for the fuzzy controller, and this may cause the explosion of fuzzy rules. To solve this problem, generalized inputs for fuzzy control were proposed by considering all the states of the structure based on a quadratic performance index. For high-rise buildings, the innovative strategy of using both AMD and inter-storey dampers was developed to control the non-linear vibration of the structure to avoid excessive inter-storey drifts that may be caused by the AMD. A simulation model for the 10-storey shear building structure equipped with displacement-dependent semiactive hydraulic damper (DSHD) was investigated in Go et al. (2010) for the purpose of practical design. Based on the linear analysis approach, the DSHD was assumed with two components: a linear spring and a linear viscous damper. The DSHD was then performing as an equivalent element with linear mechanism. The concept of equivalent stiffness and damping ratio for the simulation were validated by the example of a 10-storey building subject to the El Centro earthquake. The semi-active control system that is developed for wind turbine blades and its tower in the study of Arrigan et al. (2011) employs a frequency-tracking algorithm based on the short-time Fourier transform (STFT) technique. It allows local frequencies of nonstationary signals to be identified in the response of the system that may only exist during a short period of time. The STFT algorithm splits up the signal into

Journal of Intelligent Material Systems and Structures 0(0) shorter time segments and an FFT is performed on each segment to identify the dominant frequencies present in the system during the time period considered and it is used to continually tune the dampers to the dominant frequencies of the system.

Benchmark studies Several benchmarks were launched within the structural control community targeted to aseismic buildings, tall buildings under wind excitation, cable-stayed bridges and eventually base-isolated bridges. The results were usually collected in special issues of journals (Agrawal et al., 2009a, 2009b; Naragarajaiah et al., 2008). Since this review article is limited to the last 2 years only, a short report on base-isolated bridges seems to be adequate, the previous benchmarks being older. A sample control design using passive, active and semi-active control systems for the newly developed benchmark highway bridge model was presented in Tan and Agrawal (2009). An H2/LQG control algorithm was selected for the active case and a CO control algorithm was chosen for the semi-active case by assuming that the system remains linear since the initially elastic model of the benchmark highway bridge was used to derive a reduced-order controller design model. This reduced-order model was obtained by the eigenmode reduction method. It was a modal decoupling approach in which the original state equation was transformed into a diagonal canonical form using the modal coordinates as the states. A control scheme was introduced in Pujol et al. (2009) based on using a passive static hyperbolic damping function. The main feature of the proposed controller was its simplicity in the formulation, design and implementation, depending only on the velocity. This expression can be also seen as an active control law, which can be implemented by an appropriate actuator using only local velocity feedback. The adopted model of the MR damper is based on the Bouc–Wen hysteretic model. It was also proved that the smooth command voltage function was able to produce a force– velocity relationship in a modelled MR damper instead of a clipped control or bang-bang Lyapunov design (Pozo et al., 2010). A two-stage controller to monitor the MR voltage based on the feedback from the system was proposed in Ali and Ramaswamy (2009b). The primary controller should provide an optimal force for the system in the state-feedback form with a control algorithm such as LQR, LQG, pole placement or any other. The goal then was to supply the required voltage to the MR damper so that it produces that force. When the relation between the voltage command signals and the damper forces are linear, it can be explicitly established. However, if it is non-linear (as in the case of MR dampers), a direct monitoring of the MR damper voltage,

Casciati et al. as based on system responses, is required. In this article, a dynamic inversion (DI)–based controller was developed to track the force generated by the primary controller. The tracking error was minimized in an L2 norm sense for a set of controllers, and the voltage supply to each damper, which is required to minimize the tracking error, was optimized. In the process, the DI procedure accounted for the supplied–commanded voltage dynamics and provided a state-dependent explicit form of the voltage supply to each MR damper. The benchmark studies have shown to be useful. The models were built to represent large structures with good fidelity and freely available for the research community. They were an opportunity to test and compare passive, active and semi-active control schemes for large structures. Indeed, computational schemes should not substitute experimental studies, but it is worth to keep and even extend their use in several other problems. They can complement the real implementations and even allow testing, in a feasible, manageable and repetitive way, some issues that would difficult to characterize and measure in reality.

Some prospective remarks When comparing the present trend of development with that of one decade ago, one can say that problems addressed to the system management (as collocated versus non-collocated, centralized versus decentralized, linear versus non-linear, stable versus robust control) are today replaced by problems addressed to the optimal management of a single device. This trend has been mainly motivated by one of the bottle necks of active control: the availability of implementable feasible actuators. The authors guess that besides the actuation issue, the long-term target seems to be the implementation of ‘embedded intelligence’, which is promoted by the availability of distributed microcontrollers able to receive the sensors feedback and to elaborate locally the counteraction(s). It can be foreseen that the main topics (systems oriented) of 10 years ago will be soon back again.

Experimental studies Control theory is the base for developing active and semi-active strategies, but the experimental validation is a must. Indeed, the control strategy relies on having a model of the system and on the assumption that feedback information is available with some degree of precision. The overall feedback control loop is highly sensitive to modelling errors, particularly within semiactive schemes as discussed previously, and to signal noises and other information constraints. Laboratory environments and scaled specimens are the first step towards the promotion of an idea to an exploitable scheme. One expects that any new idea in structural

9 control be first validated on a numerical model and further followed by experimental testing. This is the case of Lee et al. (2010), mentioned in the previous section, where authors investigated experimentally the effectiveness of some semi-active control algorithms based on MR dampers for the seismic protection of a full-scale five-storey steel frame building structure. The frame was excited by the external excitation produced by a linear active mass driver (AMD) and controlled by several semi-active control algorithms, such as the CO control, the LYAP, the MEDA and the SNC algorithm. Under the experimental results of four historical and one filtered artificial earthquakes, the LYAP and SNC algorithms were shown to be appropriate in reducing the accelerations of the structural system. The passive optimal case and MEDA showed excellent performance in reducing the first floor displacement. The CO shows good performance in reducing both displacements and accelerations. As for the case discussed above, most of the experimental studies in the period reported in this article deal with MR dampers in structural applications. The reader can find more details in the book chapter dedicated to a base-isolated building hybrid experiment with MR dampers, which is referred to as Ali and Ramaswamy (2010). In recent years, hybrid testing schemes have been adopted to evaluate structural controllers. They combine, in a closed loop, physical devices and instrumentation with significant structural elements simulated numerically. Two recent works are discussed below, which use such kind of testing to perform experiments with the MR dampers. The seismic performance of a building structure equipped with an MR device was presented in Park et al. (2010) using the real-time hybrid testing method (RT-HYTEM). First, the force required to drive the displacement of the storey, at which the MR damper was located, was measured from the load cell attached to a universal testing machine (UTM). The measured force was then returned to a control computer to calculate the response of the numerically simulated structure. Finally, the experimental structure was excited by the UTM with the calculated response of the numerical structure. The RT-HYTEM implemented in this study was validated by comparing the RTHT results (obtained by application of sinusoidal and earthquake excitations) with the corresponding analytical results obtained using the Bouc–Wen model to compute the control force of the MR damper from input current: they were in good agreement. Also, Zapateiro et al. (2010) carried out experiments in a RTHT configuration. Numerical simulations and experiments on small-scale specimens motivated the feasibility of implementing a backstepping control law in larger systems. The test consisted of the following steps: (a) a computer that simulates the structure to be

10 controlled and generates the commanding signals (displacements and control signals); (b) a small-scale MR damper driven by a hydraulic actuator, which in turn is controlled by a servo-hydraulic controller; (c) a digital signal processor, with its analogue-to-digital (A/D) and digital-to-analogue (D/A) hardware. The available sensors included a linear variable displacement transformer (LVDT) for displacement measurements and a load cell for measuring the MR damper force. The damper was subjected to sinusoidal and random displacements and varying voltages. The MR damper was driven by a hydraulic actuator to impose a displacement from the computer running the simulation. The measured piston displacement during the execution of an experiment showed a good match between the desired and measured displacement. In order to see the performance of the system model, simulations were run to compare with the experimental response. The MR damper piston displacement measured during an experiment was compared with that obtained by the model of the overall system. To make this comparison, the El Centro seismic motion record and the MR damper voltage were taken as inputs to the RTHT system. The results showed the good accuracy of the system model. Two experimental studies are described involving shape memory alloys (SMAs) as actuators. The combination of a control law and a strategy to manage the particular nature of this material is required to produce an effective control system. The effectiveness of a control policy in mitigating the linear and non-linear multimodal cable vibrations was investigated by means of a numerical analysis and a campaign of laboratory tests (Faravelli et al., 2010, 2011b). The proposed control method was a hybrid solution combining wrapped SMA austenitic wires and an open-loop actuation. By operating in this way, a robust and economical control strategy was achieved. It overcomes the damper/actuator localization and the state-tracking difficulties that significantly impair the overall control effectiveness of most of the control solutions already investigated in the literature. A control system actuated by SMA tendons was proposed in Suzuki and Kagawa (2010). The control strategy was designed through a linear approximation of the non-linear relationship between the applied voltage to the SMA actuator and the contraction force resulting from the shape memory effect. An HN control law of the beam–actuator system, which includes the uncertainty of the actuator characteristics, was installed into the control system. The calculated and the experimental results agreed satisfactorily. Interesting experimental studies have been recently reported where passive and semi-active devices were proposed to reduce human-induced vibrations in floors or footbridges. Active vibration control (AVC) via inertial actuators was experimentally tested in Dı´ az and Reynolds (2010a, 2010b). The AVC system was

Journal of Intelligent Material Systems and Structures 0(0) assessed in simulation and implemented in office floor that is already in service. Vibration reductions have achieved in approximately 60% for walking tests and over 90% for daily vibration monitoring. Another efficiency of control system for flexible stress-ribbon footbridge is evaluated in terms of the reduction of the structural response when the footbridge is excited by several types of pedestrian loads in Moutinho et al. (2011). In summary, experimental studies are a necessary step towards the practical use of structural control studies and they will continue. Presumably, hybrid testing experiments should be developed further since they are promising cost-effective schemes somehow between numerical and purely real-time implementations. Particularly they are attractive to test real control devices without having the real structure, which is numerically simulated. Another aspect to expect in future experimental works is the incorporation of any sort of embedded wireless technology as emphasized at the end of the previous section, but mainly in moving from the standard analogue electronics to the current digital format (Casciati and Chen, 2011). It is worth noticing that wireless structural monitoring does not require a real-time data transmission, whereas structural control does it.

Full-scale applications The practical application of AVC and semi-AVC on buildings and bridges around the world is not often explicitly publicized. In several cases, the structure is built without any supplementary control device, which is added later to mask some detected poor performance. The studies associated to the famous Millennium Bridge in London are a key example in this area, where passive TMDs and viscous dampers were installed.

Full-scale implementation in Japan By contrast, in Japan, there was the wish to open a market and the few realized applications (there are approximately 72 active and semi-active control systems in Japan which were installed since 1989) are monitored. A deep discussion of these actual observation records in that country is reported in Ikeda (2009). The largest earthquake that semi-active control systems have experienced, before the terrible event of 2011, was the Niigata-ken Chuetsu-oki Earthquake which occurred on 16 July 2007. In a 31-storey building, the maximum acceleration on the top floor was 99.6 cm/s2, the maximum force of the semi-active damper installed in the fifth storey was 640 kN and the maximum stroke was 5.2 mm. Their limitations are 1500 kN for the control force and 60 mm for the stroke. On 23 October 2004, the same building experienced the Niigata-ken Chuetsu Earthquake. But the

Casciati et al. responses of the semi-active controller–structural system were smaller than those of the 2007 earthquake. Based on an identification process using an ARX model, the equivalent damping ratio in the lowest controlled mode was identified as about 7% under these earthquakes and their aftershocks. The damping ratio without semi-active control was evaluated as 1% by the random decrement (RD) technique applied to wind observation. To confirm the control effectiveness, observed responses of both the structure and the control system have to be analysed appropriately. A harmonically forced vibration test was first applied to a 10-storey office building with an AMD system, the ‘Kyobashi Seiwa Building’. Two AMDs were placed on the 11th floor (roof floor). Two vibrators were placed at opposite locations in the longitudinal direction on the 10th floor. The vibrators excited the structure in the transverse direction with the same phase harmonic loadings and in the rotational direction with the opposite phase harmonic loadings. The controlled displacement was compared with the uncontrolled one on the 10th floor. The same phase harmonic excitation generated the lowest vibration mode in the transverse direction, and the natural frequency was 1.065 Hz. The opposite phase excitation test generated the lowest mode in the torsional direction, and the frequency was 1.85 Hz. The control effectiveness was very high in both vibration modes in terms of structural response. Another parameter for control effectiveness is confirmed by damping ratios in the resonance vibration modes of the structure by free vibration tests. When a typhoon excited the Kyobashi Center Building on August 1990, the controlled and uncontrolled responses were recorded alternately every 30 min. Before verification, the power spectra of the wind velocity, its direction and the acceleration amplitude on the 11th floor were analysed each 10 min to confirm the comparison possibility. The controlled acceleration on the 11th floor was mostly within 2.0 cm/s2, while the uncontrolled acceleration discontinuously exceeded 6.0 cm/s2 with beating. Thus, the AMD system reduced the maximum acceleration on the 11th floor to about one-third of the uncontrolled value. It was also confirmed that the AMD system eliminated the resonance peak at the first natural frequency of 1.07 Hz in the transverse direction.

Full-scale implementations in China The main full-scale implementation of active control outside Japan was realized in China: the Nanjing television tower was equipped by an AMD prototype realized in a joint project with the University of New York at Buffalo. But the device is no longer working at the moment. Nevertheless, several long-span bridges were recently realized and most of them showed some

11 performance limitation which suggested the adoption of semi-active devices. The negative stiffness characteristics realized by semi-active MR damping systems are demonstrated through an in situ field test of a stay cable in the Binzhou Yellow River Highway Bridge in Ou and Li (2010). The stay cable with a length of 219.41 m, tension of 726,000 kN, weight of 18,850 kg, mass per unit length of 95.089 kg/m and damping coefficient per unit length of 0.71 Ns/m2 is employed in this study. An exciter is used to generate a harmonic excitation input to the cable, and then the free vibration of the cable with/ without semi-active control is recorded. An LQG-based control algorithm is used to determine an active control force, which is proposed for the MR damper in the field test. The results indicate that a larger damping can be realized using semi-active control than using passive control. The semi-active damping system can generate the control force with the characteristics of damping and negative stiffness and can replace the active control system. By contrast, any passive linear viscous dampers cannot generate the control force with negative stiffness. The same research team (Li et al., 2011) investigated the seismic behaviour of a cable-stayed bridge incorporating negative stiffness dampers (may be active or semi-active dampers, simulated by pseudo-viscoelastic (P-VE) dampers) between the tower and the deck. The reduction in the seismic response of the cable-stayed bridge was investigated. The results indicate that the seismic performance of the cable-stayed bridge and the damping ratio of the bridge achieve their maximum values when the damper stiffness is optimum.

Operational limitations for viable practical usage As said, most of the full-scale applications outside Japan are in bridges that, designed without any control system, showed some weakness during the first-year monitoring. The main environment hazard comes here from the wind action, but controlled solutions have then to be verified for the other specific actions as traffic and seismic events. A question may come out spontaneously to the reader: why such a massive research effort, as the one in the area of structural control, gave rise to a so modest number of full-scale applications? The answer could span from a drastic ‘because structural control is not viable in civil and infrastructure engineering’ to a more promising ‘because there are operational limitations which have still to be solved’. The authors’ thought is closer to the second proposition. To support it, it is suitable to summarize what actually occurred in the area of passive control (base isolation and energy dissipation). When the designer submits the design of a new structural system to the owner, cost and reliability are the two competitive

12 parameters. Thus, the designer is allowed to introduce extra costs, provided that this reduces other costs of different nature and/or increase the global reliability. This is true provided that the structural code allows the exploitation of passive control solutions, and this is so now in many countries. When extrapolating to non-passive solutions, most of the codes state that the structural system must be able to survive even in the occurrence that the control system fails. Under these conditions, the control devices have just to be accounted as extra costs. The owner could accept these extra costs for promoting innovation, but the solution is out from strict market reasoning.

Journal of Intelligent Material Systems and Structures 0(0)

Final remarks and conclusions In the attempt to send a positive message, the previous sections clearly state that structural control in Civil and Infrastructure Engineering is alive at a theoretical level and that experimental campaigns were carried out or are in progress. The drawback is that the basic principles of structural control do not find easy acceptation in the professional implementations. A research goal, therefore, should be to make the implementation and maintenance easier and easier: this applies to the model of the control loop, the control strategy, the control methodology and the feedback information constraints and its digital implementation. Maintenance and the lack of viable actuation devices remain the main issue towards successful applications.

Future directions It should be noticed that the term extra costs is made of two addenda: initial costs and maintenance costs. The latter item in the passive control case could require a replacement of the devices every 5 or 10 years, and this period is sometimes regarded as too short when compared with the system lifetime. Semi-active and active control may require maintenance plans with shorter schedules, like for instance, biannual maintenance plans. Nevertheless, one cannot conclude that active control is not viable at all: its viability requires a change of mind on the maintenance problem in the economical world associated with civil and infrastructure engineering. Even some sort of ‘continuous’ maintenance can be envisioned where fault detection systems can be implemented along with the feedback control systems. The innovating thought of Professor Takuji Kobori (Casciati and Al-Saleh, 2008; Casciati et al., 2009; Kobori, 2003) in the area of structural control already emphasized the incompatibility of the structural control dynamic issues with the static conception of conventional building due to the different maintenance time scales. A kind of innovative building with a dynamic conception was recently introduced by Fisher (2008, 2010) and Faravelli et al. (2011a). The movement in the rotating towers generates energy but also has an aesthetic character. The maintenance time scale is now consistent with structural control demand and, hence, the building is a good candidate to be equipped with structural control solutions. A further appealing application comes from the current research efforts at National Aeronautics and Space Administration (NASA) (Sherwood et al., 2010). The exploitation of the space is demanded to androids, which are supposed to build residences on the Moon, for instance. These residences will be actually machines hosting machines and the structural control issues are supposed to drive their design, construction and management.

Acknowledgment The authors appreciated the constructive comments of the anonymous reviewers, which have helped to improve the paper.

Funding This work was supported by the Athenaeum Research Funds of the University of Pavia. The Marie-Curie EU project SMARTEN supported the activity of the third author (U.Y.) at the University of Pavia.

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