Optimal control of linear buildings under seismic excitations

Considerable effort has been devoted to develop optimal control methods for reducing structural response under seismic forces. In this study analytical solution of the linear regulator problem applied widely to the control of earthquake‐excited structures is obtained by using the sufficient conditions of optimality even though almost all of the optimal controls proposed previously for structural control are based on the necessary conditions of optimality. Since the resulting optimal closed–open‐loop control cannot be implemented for civil structures exposed to earthquake forces, the solution of the optimal closed–open‐loop control is carried out approximately based on the prediction of the seismic acceleration values in the near future. Upon obtaining the relation between the exact optimal solution and future values of seismic accelerations, it is shown numerically that the solution of the optimal closed–open‐loop control problem can be performed approximately by using only the first few predicted seismic acceleration values if a given norm criteria is satisfied. Calculated performance measures indicate that the suggested approximate solution is better than the closed‐loop control and as we predict the future values of the excitation more accurately, it will approach the optimal solution. Copyright © 2001 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.     

基于输出反馈的建筑结构闭开环次优控制

对传统的结构抗震闭开环控制算法进行改进。基于地面运动自回归模型,采用Kalman滤波利用可以量测到的地面加速度激励对未来时段即将发生的地面加速度激励进行预估,并在微分方程的求解中引入精确高效的精细积分算法。考虑到实际控制中量测全部状态变量的困难,改进算法仅需量测部分状态变量。数值仿真表明,基于输出反馈的闭开环次优控制策略能大大降低结构的地震响应。     

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.     

Genetic algorithm based LQR vibration wireless control of laminated plate using photostrictive actuators

A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections.This paper addresses the controllability aspect in wireless vibration control of plate structures via photostrictive actuators.A modal force index,which has taken into account the mode number,the spatial distribution,and the dimension of the actuator,is chosen as an objective function to determine the optimal locations of photostrictive actuators.A linear methodology is proposed in this paper and the vibration equation is written in the standard state-space form.A binary-coded GA based combined optimal placement and LQR(linear quadratic regulator) control scheme has been incorporated,which maximizes the modal force index,the closed loop damping and minimizes input light intensity to the actuators.In the present method only three weighting factors have been used to search optimal Q and R matrices using GA,which reduces chromosome length and hence minimizes computational time.Numerical results demonstrate that the use of strategically positioned actuator patches can effectively control the fundamental modes that dominate the structural vibration.     

Development of high‐performance shake tables using the hierarchical control strategy and nonlinear control techniques

Conventional shake tables employ linear controllers such as proportional‐integral‐derivative or loop shaping to regulate the movement. However, it is difficult to tune a linear controller to achieve accurate and robust tracking of different reference signals under payloads. The challenges are mainly due to the nonlinearity in hydraulic actuator dynamics and specimen behavior. Moreover, tracking a high‐frequency reference signal using a linear controller tends to cause actuator saturation and instability. In this paper, a hierarchical control strategy is proposed to develop a high‐performance shake table. A unidirectional shake table is constructed at the University of British Columbia to implement and evaluate the proposed control framework, which consists of a high‐level controller and one or multiple low‐level controller(s). The high‐level controller utilizes the sliding mode control (SMC) technique to provide robustness to compensate for model nonlinearity and uncertainties experienced in experimental tests. The performance of the proposed controller is compared with a state‐of‐the‐art loop‐shaping displacement‐based controller. The experimental results show that the proposed hierarchical shake table control system with SMC can provide superior displacement, velocity and acceleration tracking performance and improved robustness against modeling uncertainty and nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.     

Sub‐optimal control of structures

It is well known that the classical optimal control method requires all the state variables of the controlled system to be measurable and available for control feedback. However, for a high‐order or complex system some state variables are possibly unmeasurable in practice. In addition, the control cost will be higher if more sensors are used, because it is expensive to install sensors. On the other hand, when using the optimal control method with full‐state feedback, some state variables in control feedback have only a small effect on control performance. Neglecting these state variables does not affect the control performance greatly. Good control effectiveness can be obtained by using only the state variables that have a big effect on the control performance. So the questions become how to determine those state variables which have a big effect on the control performance? and how to design the optimal controller using only the determined state variables? The discrete sub‐optimal control method with partial‐state feedback is investigated in this paper. Firstly, the continuous control system and performance index are both transformed into discrete forms. Then the state variables, which have a big effect on the control performance, are determined using the second‐order sensitivity which is the second‐order derivative of the performance index with respect to control gain. The sub‐optimal controller is finally designed using only the determined state variables. Numerical examples are worked out to demonstrate the application of the proposed control algorithm. It is shown that the relative importance of each state variable can be indicated clearly by the second‐order sensitivity. The sub‐optimal control method presented is effective in reducing maximum responses of the structure. Copyright © 2003 John Wiley & Sons, Ltd.     

Active tendon control of cable‐stayed bridges: a large‐scale demonstration

This paper presents a strategy for active damping of cable structures, using active tendons. The first part of the paper summarizes the theoretical background: the control law is briefly presented together with the main results of an approximate linear theory which allows the prediction of closed‐loop poles with a root locus technique. The second part of the paper reports on experimental results obtained with two test structures: the first one is a small size mock‐up representative of a cable‐stayed bridge during the construction phase. The control of the parametric vibration of passive cables due to deck vibration is demonstrated. The second one is a 30 m long mock‐up built on the reaction wall of the ELSA test facility at the JRC Ispra (Italy); this test structure is used to demonstrate the practical implementation of the control strategy with hydraulic actuators. Copyright © 2001 John Wiley & Sons, Ltd.     

An active mass damper designed using ARX models of a building structure

This study proposes a new design method for an active mass damper (AMD) that is based on auto‐regressive exogenous models of a building structure. The proposed method uses the results of system identification in the field of active structural control. The uncontrolled structure is identified as auto‐regressive exogenous models via measurements under earthquake excitation and forced vibration. These models are linked with an equation of motion for the AMD to introduce a state equation and output equation for the AMD–structure interaction system in the discrete‐time space; the equations apply modern control theories to the AMD design. In the numerical applications of a 10‐degree‐of‐freedom building structure, linear quadratic regulator control is used to understand the fundamental characteristics of the proposed design procedure. The feedback control law requires the AMD's acceleration, velocity and stroke; the structure's acceleration; and the ground acceleration as vibration measurements. The numerical examples confirm the high applicability and control effectiveness of the proposed method. One remarkable advantage of the proposed method is that an equation of motion for the structure becomes unnecessary for designing controllers. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal displacement feedback control law for active tuned mass damper

Optimal displacement feedback control law is derived for a vibration control of a single‐degree‐of‐freedom structure with an active tuned mass damper (ATMD). Analytical expressions of the linear quadratic regulator (LQR) feedback gains for the ATMD are derived by solving the Ricatti equation straightforwardly. Based on these solutions, it is found that if the stiffness of the tuned mass damper (TMD) is calibrated to satisfy a certain condition, the control law is simplified to be composed of the feedback gains only for the displacement of the structure and the velocity of the auxiliary mass stroke, which is referred to as ‘optimal displacement feedback control’. The mean‐square responses of the structure as well as the auxiliary mass against Gaussian white noise excitations are evaluated by solving the Lyapunov equation analytically based on the stochastic optimal control theory. Using these analytical solutions, the optimal damping parameter for the auxiliary mass is also derived. Finally, the optimal displacement feedback control law is presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Modified sliding‐mode bang–bang control for seismically excited linear structures

Recently, sliding‐mode control (SMC) methods have been investigated for application to seismically excited civil engineering structures and have proved to be effective control strategic methods. On the other hand, although another class of well‐known optimal control laws, the so‐called ‘bang–bang’ control, has been investigated for several decades, their potential in civil engineering structural control has not been fully exploited. The purpose of this paper is to present a new control law for civil engineering structures, which is the sliding‐mode bang–bang control (SMBBC). The SMBBC method is a combination of the SMC and the bang–bang control. In consideration of actuators not suitable for high‐speed switching of control forces in the SMBBC in practice, modified sliding‐mode bang–bang control (MSMBBC) law is proposed and demonstrated to be able to provide the same control effects as the SMBBC case. Condition modified sliding‐mode bang–bang control (CMSMBBC) law is also investigated in this paper. In the CMSMBBC case, actuators act only when response quantities exceed some designated threshold values. The determination method of maximum control‐forces for actuators is investigated through example computation. The performance and robustness of the proposed control methods are all demonstrated by numerical simulation. Simulation results demonstrate that the presented methods are viable and an attractive control strategy for application to seismically excited linear structures. Copyright © 2000 John Wiley & Sons, Ltd.     

Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust integrated actuator control: experimental verification and real‐time hybrid‐simulation implementation

In this paper, we propose a new actuator control algorithm that achieves the design flexibility, robustness, and tracking accuracy to give real‐time hybrid‐simulation users the power to achieve highly accurate and robust actuator control. The robust integrated actuator control (RIAC) strategy integrates three key control components: loop shaping feedback control based on H_∞ optimization, a linear‐quadratic‐estimation block for minimizing noise effect, and a feed‐forward block that reduces small residual delay/lag. The combination of these components provides flexible controller design to accommodate setup limits while preserving the stability of the H_∞ algorithm. The efficacy of the proposed strategy is demonstrated through two illustrative case studies: one using large capacity but relatively slow actuator of 2500 kN and the second using a small‐scale fast actuator. Actuator tracking results in both cases demonstrate that the RIAC algorithm is effective and applicable for different setups. Real‐time hybrid‐simulation validation is implemented using a three‐DOF building frame equipped with a magneto‐rheological damper on both setups. Results using the two very different physical setups illustrate that RIAC is efficient and accurate. Copyright © 2014 John Wiley & Sons, Ltd.     

CONTROL OF BUILDING VIBRATIONS WITH ACTIVE/PASSIVE DEVICES

Two linear optimal control laws and a non-linear control strategy are critically evaluated. They are implemented in a ten-story frame structure. For the linear control laws, both an active bracing system and a hybrid mass damper are considered as control devices, while the non-linear control law can be implemented with either an active or semi-active bracing system. The active and semi-active systems are compared to a passive bracing system with linear viscous dampers and to a hybrid system consisting of a passive bracing and a hybrid mass damper. Dimensionless indices based on the reduction of the maximum story drift and on the maximum control force required are introduced to compare the efficiencies of different control strategies. While the linear optimal control laws exhibit an excellent performance, the non-linear control law, in addition to its simplicity and robustness, appears to be more efficient when the allowable control force is within a certain limit. Furthermore, one attractive feature of the latter is that it can be implemented with semi-active devices to minimize the power requirement.     

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.     

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.     

Stability analysis of SDOF real‐time hybrid testing systems with explicit integration algorithms and actuator delay

Real‐time hybrid testing is a method that combines experimental substructure(s) representing component(s) of a structure with a numerical model of the remaining part of the structure. These substructures are combined with the integration algorithm for the test and the servo‐hydraulic actuator to form the real‐time hybrid testing system. The inherent dynamics of the servo‐hydraulic actuator used in real‐time hybrid testing will give rise to a time delay, which may result in a degradation of accuracy of the test, and possibly render the system to become unstable. To acquire a better understanding of the stability of a real‐time hybrid test with actuator delay, a stability analysis procedure for single‐degree‐of‐freedom structures is presented that includes both the actuator delay and an explicit integration algorithm. The actuator delay is modeled by a discrete transfer function and combined with a discrete transfer function representing the integration algorithm to form a closed‐loop transfer function for the real‐time hybrid testing system. The stability of the system is investigated by examining the poles of the closed‐loop transfer function. The effect of actuator delay on the stability of a real‐time hybrid test is shown to be dependent on the structural parameters as well as the form of the integration algorithm. The stability analysis results can have a significant difference compared with the solution from the delay differential equation, thereby illustrating the need to include the integration algorithm in the stability analysis of a real‐time hybrid testing system. Copyright © 2007 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.     

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.     

Dynamic force control with hydraulic actuators using added compliance and displacement compensation

A new approach to dynamic force control of mechanical systems, applicable in particular to frame structures, over frequency ranges spanning their resonant frequencies is presented. This approach is implemented using added compliance and displacement compensation. Hydraulic actuators are inherently velocity sources, that is, an electrical signal regulates their velocity response. Such systems are therefore by nature high‐impedance (mechanically stiff) systems. In contrast, for force control, a force source is required. Such a system logically would have to be a low‐impedance (mechanically compliant) system. This is achieved by intentionally introducing a flexible mechanism between the actuator and the structure to be excited. In addition, in order to obtain force control over frequencies spanning the structure's resonant frequency, a displacement compensation feedback loop is needed. The actuator itself operates in closed‐loop displacement control. The theoretical motivation, as well as the laboratory implementation of the above approach is discussed along with experimental results. Having achieved a means of dynamic force control, it can be applied to various experimental seismic simulation techniques such as the effective force method and the real‐time dynamic hybrid testing method. Copyright © 2008 John Wiley & Sons, Ltd.