Improved design of sliding mode control for civil structures with saturation problem

A systematic and improved design procedure for sliding mode control (SMC) of seismically excited civil structures with saturation problem is provided in this paper. In order to restrict the control force to a certain level, a procedure for determining the upper limits of the control forces for single or multiple control units is proposed based on the design response spectrum of external loads. Further, an efficient procedure using the LQR method for determining sliding surfaces appropriate for different controller types is provided through the parametric evaluation of the dynamic characteristics of sliding surfaces in terms of SMC controller performance. Finally, a systematic design procedure for SMC required to achieve a given performance level is provided and its effectiveness is verified by applying it to multi‐degree‐of‐freedom (MDOF) systems. Copyright © 2004 John Wiley & Sons, Ltd.     

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

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

Discrete‐time variable structure control method for seismic‐excited building structures with time delay in control

The discrete‐time variable structure control method for seismically excited linear structures with time delay in control is investigated in this paper. The control system with time delay is first discretized and transformed into standard discrete form which contains no time delay in terms of the time delay being integer and non‐integer times of sampling period, respectively. Then the discrete switching surface is determined using ideal quasi‐sliding mode and discrete controller is designed using the discrete approach‐law reaching condition. The deduced controller and switching surface contain not only the current step of state feedback but also linear combination of some former steps of controls. Numerical simulations are illustrated to verify the feasibility and robustness of the proposed control method. Since time‐delay effect is incorporated in the mathematical model for the structural control system throughout the derivation of the proposed algorithm, system performance and dynamic stability are guaranteed. Copyright © 2002 John Wiley & Sons, Ltd.     

结构可变阻尼半主动控制

本文阐述了结构半主动控制的概念，并介绍了国内外有关结构半主动控制的研究状态，阐述了几种有关结构半主动控制的算法，包括基于经典最优控制的控制律及算法，基于变结构系统理论的滑动模太控制算法和非线性奇次系统的ｂａｎｇ－ｂａｎｇ控制算法。重点阐述了变结构系统理论和滑移面的确定及控制律的设计。     

Reaching law based sliding mode control for a frame structure under seismic load

Implementation of efficient vibration control schemes for seismically excited structures is becoming more and more important in recent years. In this study, the influence of different control schemes on the dynamic performance of a frame structure excited by El Centro wave, with an emphasis on reaching law based control strategies, is examined. Reaching law refers to the reachable problem and criteria for the sliding state of a control system. Three reaching laws are designed to present different sliding mode control strategies by incorporating a state space model that describes structural dynamic characteristics of a frame structure. Both intact and damaged structures are studied by using the aforementioned control strategies. The influence of different structural damage extents, control locations and reaching law based control methods are further investigated. The results show that the structure can be well controlled using the sliding mode strategy when the induced structural damage extent does not exceed the standard percentage for considering the structure was damaged, which is 20% reduction in structure stiffness, as reported in the literature. The control effectiveness is more satisfactory if the control location is the same as the direction of external excitation. Furthermore, to study the chattering phenomenon of the sliding mode control method, approximation and detail components extracted from the phase plots of the sliding mode control system are compared via wavelet transform at different scales. The results show that for the same type of control law, the system behaves with similar chattering phenomenon.     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 John Wiley & Sons, Ltd.     

Multi‐objective optimal design of FLC driven hybrid mass damper for seismically excited structures

Structural vibration control using active or passive control strategy is a viable technology for enhancing structural functionality and safety against natural hazards such as strong earthquakes and high wind gusts. Both the active and passive control systems have their limitations. The passive control system has limited capability to control the structural response whereas the active control system depends on external power. The power requirement for active control of civil engineering structures is usually quite high. Thus, a hybrid control system is a viable solution to alleviate some of the limitations. In this paper a multi‐objective optimal design of a hybrid control system for seismically excited building structures has been proposed. A tuned mass damper (TMD) and an active mass driver (AMD) have been used as the passive and active control components of the hybrid control system, respectively. A fuzzy logic controller (FLC) has been used to drive the AMD as the FLC has inherent robustness and ability to handle the non‐linearities and uncertainties. The genetic algorithm has been used for the optimization of the control system. Peak acceleration and displacement responses non‐dimensionalized with respect to the uncontrolled peak acceleration and displacement responses, respectively, have been used as the two objectives of the multi‐objective optimization problem. The proposed design approach for an optimum hybrid mass damper (HMD) system, driven by FLC has been demonstrated with the help of a numerical example. It is shown that the optimum values of the design parameters of the hybrid control system can be determined without specifying the modes to be controlled. The proposed FLC driven HMD has been found to be very effective for vibration control of seismically excited buildings in comparison with the available results for the same example structure but with a different optimal absorber. Copyright © 2002 John Wiley & Sons, Ltd.     

Real‐time force control for servo‐hydraulic actuator systems using adaptive time series compensator and compliance springs

Servo‐hydraulic actuators have been widely used for experimental studies in engineering. They can be controlled in either displacement or force control mode depending on the purpose of a test. It is necessary to control the actuators in real time when the rate‐dependency effect of a test specimen needs to be accounted for under dynamic loads. Real‐time hybrid simulation (RTHS) and effective force testing (EFT) method, which can consider the rate‐dependency effect, have been known as viable alternatives to the shake table testing method. Due to the lack of knowledge in real‐time force control, however, the structures that can be tested with RTHS and EFT are fairly limited. For instance, satisfying the force boundary condition for axially stiff members is a challenging task in RTHS, while EFT has a difficulty to be implemented for nonlinear structures. In order to resolve these issues, this paper introduces new real‐time force control methods utilizing the adaptive time series (ATS) compensator and compliance springs. Unlike existing methods, the proposed force control methods do not require the structural modeling of a test structure, making it easy to be implemented especially for nonlinear structures. The force tracking performance of the proposed methods is evaluated for a small‐scale steel mass block system with a magneto‐rheological damper subjected to various target forces. Accuracy, time delay, and resonance response of these methods are discussed along with their force control performance for an axially stiff member. Overall, a satisfactory force tracking performance was observed by using the proposed force control methods.     

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

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

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.     

Hybrid control of seismic-excited bridge structures

Recently, several hybrid protective systems have been explored for applications to seismic-excited bridge structures. In particular, two types of aseismic hybrid protective systems have been shown to be quite effective: (i) rubber bearings and variable dampers (or actuators), and (ii) sliding bearings and actuators. In this paper, control methods are presented for these hybrid protective systems. The control methods are based on the theory of variable structure system (VSS) or sliding mode control (SMC). Emphasis is placed on the static (direct) output feedback controllers using only the information measured from a few sensors without an observer. Simulation results demonstrate that the control methods presented are robust with respect to system parametric uncertainties and the performance is quite remarkable. Sensitivity studies are conducted to evaluate the effectiveness of hybrid protective systems and passive sliding isolators for reducing the response of seismic-excited bridge structures. The advantages of each protective system are demonstrated by simulation results for a wide range of earthquake intensities.     

Compensation of time‐delay for control of civil engineering structures

Time‐delay is an important issue in structural control. Applications of unsynchronized control forces due to time‐delay may result in a degradation of the control performance and it may even render the controlled structures to be unstable. In this paper, a state‐of‐the‐art review for available methods of time‐delay compensation is presented. Then, five methods for the compensation of fixed time‐delay are presented and investigated for active control of civil engineering structures. These include the recursive response method, state‐augmented compensation method, controllability based stabilization method, the Smith predictor method and the Pade approximation method, all are applicable to any control algorithm to be used for controlled design. Numerical simulations have been conducted for MDOF building models equipped with an active control system to demonstrate the stability and control performance of these time‐delay compensation methods. Finally, the stability and performance of the phase shift method, that is well‐known in civil engineering applications, have also been critically evaluated through numerical simulations. Copyright © 2000 John Wiley & Sons, Ltd.     

Multiple active–passive tuned mass dampers for structures under the ground acceleration

An Erratum has been published for this article in Earthquake Engineering and Structural Dynamics 2003; 32(15):2451. Multiple active–passive tuned mass dampers (MAPTMD) consisting of many active–passive tuned mass dampers (APTMDs) with a uniform distribution of natural frequencies have been, for the first time here, proposed for attenuating undesirable oscillations of structures under the ground acceleration. The MAPTMD is manufactured by keeping the stiffness and damping coefficient constant and varying the mass. The control forces in the MAPTMD are generated through keeping the identical displacement and velocity feedback gain and varying the acceleration feedback gain. The structure is represented by the mode‐generalized system corresponding to the specific vibration mode that needs to be controlled. Through minimization of the minimum values of the maximum dynamic magnification factors (DMF) of the structure with the MAPTMD (i.e. through implementation of Min.Min.Max.DMF), the optimum parameters of the MAPTMD are investigated to delineate the influence of the important parameters such as mass ratio, total number, normalized acceleration feedback gain coefficient and system parameter ratio on the effectiveness (i.e. Min.Min.Max.DMF) and robustness of the MAPTMD. The optimum parameters of the MAPTMD include the optimum frequency spacing, average damping ratio and tuning frequency ratio. Additionally, for the sake of comparison, the results for a single APTMD are also taken into account in the present paper. It is demonstrated that the proposed MAPTMD can be employed to significantly reduce the oscillations of structures under the ground acceleration. Also, it is shown that the MAPTMD can render high robustness and has better effectiveness than a single APTMD. In particularly, if and when requiring a large active control force, MAPTMD is more promising for practical implementations on seismically excited structures with respect to a single APTMD. Copyright © 2003 John Wiley & Sons, Ltd.     

Adaptive bang–bang control for the vibration control of structures under earthquakes

An adaptive method based on the modified bang–bang control algorithm is proposed for the vibration control of structures subjected to unexpected severe seismic loads greater than the design loads. A hydraulic‐type active mass damper was made and experiments were carried out in the laboratory using a one‐story test structure and a five‐story test structure with the active mass damper. Through numerical simulations and experiments it was confirmed that the proposed method works well to suppress the vibration of structures subjected to unexpected severe seismic loads greater than the design loads without causing any unstable situations. Copyright © 2003 John Wiley & Sons, Ltd.     

Unsupervised fuzzy neural network structural active pulse controller

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

Placement of sensors/actuators on civil structures using genetic algorithms

The optimal design and placement of controllers at discrete locations is an important problem that will have impact on the control of civil engineering structures. Though algorithms exist for the placement of sensor/actuator systems on continuous structures, the placement of controllers on discrete civil structures is a very difficult problem. Because of the nature of civil structures, it is not possible to place sensors and actuators at any location in the structure. This usually creates a non‐linear constrained mixed integer problem that can be very difficult to solve. Using genetic algorithms in conjunction with gradient‐based optimization techniques will allow for the simultaneous placement and design of an effective structural control system. The introduction of algorithms based on genetic search procedures should increase the rate of convergence and thus reduce the computational time for solving the difficult control problem. The newly proposed method of simultaneously placing sensors/actuators will be compared to a commonly used method of sensors/actuators placement where sensors/actuators are placed sequentially. The savings in terms of energy requirements and cost will be discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

地震作用下参数不确定系统的变结构控制

本文对结构参数具有有确定性的变结构控制系统设计方法进行了研究。首先采用摄动方法给出了结构参数具有确定性的控制系统的运动方程,证明了基于层间剪切模型的参数不确定受控系统与其标称系统具有相同的滑动模态,从而解决了系统切换函数的确定问题,并利用到达条件推导了控制律的表示式。算例分析结果表明,本文的控制方法能有效地减小结构的地震响应,对于结构系统建模存在误差或系统本身存在学确定性的情况,控制效果仍十分显著     

Multi‐level design model and genetic algorithm for structural control system optimization

The integrated optimum problem of structures subjected to strong earthquakes and wind excitations, optimizing the number of actuators, the configuration of actuators and the control algorithms simultaneously, is studied. Two control algorithms, optimal control and acceleration feedback control, are used as the control algorithms. A multi‐level optimization model is proposed with respect to the solution procedure of the optimum problem. The characteristics of the model are analysed, and the formulation of each suboptimization problem at each level is presented. To solve the multi‐level optimization problem, a multi‐level genetic algorithm (MLGA) is proposed. The proposed model and MLGA are used to solve two multi‐level optimization problems in which the optimization of the number of actuators, the positions of actuators and the control algorithm are considered in different levels. In problem 1, an example structure is excited by strong wind, and in problem 2, an example structure is subjected to strong earthquake excitation. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing

This paper presents an experimental implementation and verification of multi‐degrees‐of‐freedom effective force testing (MDOF‐EFT). An experimental setup that consists of a two‐degrees‐of‐freedom structural system and two hydraulic actuators at the Johns Hopkins University was utilized in this study. First, experimental system identification was performed to develop compatible analytical models for the multi‐input and multi‐output systems. Dynamics of the control plant, that is, the valve‐to‐force relations, were modeled with a rational polynomial transfer function matrix and delay components. By using the analytical model, a centralized decoupling loop‐shaping force feedback controller was designed such that the forces are uncoupled and the loop transfer functions have desirable dynamic characteristics in the frequency domain. Then, a series of harmonic force and earthquake simulation tests were performed to assess capabilities and limitations of MDOF‐EFT. Experimental results showed that the dynamic forces in the two actuators were accurately controlled to provide tracking while the system was stable and robust for the entire period of the experiment. Furthermore, earthquake simulation tests with increased levels of the reference forces demonstrated the feasibility of MDOF‐EFT with highly nonlinear test structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic retrofit of low‐rise steel buildings in Canada using rocking steel braced frames

This article examines the use of rocking steel braced frames for the retrofit of existing seismically deficient steel building structures. Rocking is also used to achieve superior seismic performance to reduce repair costs and disruption time after earthquakes. The study focuses on low‐rise buildings for which re‐centring is solely provided by gravity loads rather than added post‐tensioning elements. Friction energy dissipative (ED) devices are used to control drifts. The system is applied to 2‐storey and 3‐storey structures located in 2 seismically active regions of Canada. Firm ground and soft soil conditions are considered. The seismic performance of the retrofit scheme is evaluated using nonlinear dynamic analysis and ASCE 41‐13. For all structures, rocking permits to achieve immediate occupancy performance under 2% in 50 years seismic hazard if the braces and their connections at the building's top storeys are strengthened to resist amplified forces due to higher mode response. Base shears are also increased due to higher modes. Impact at column bases upon rocking induces magnified column forces and vertical response in the gravity system. Friction ED is found more effective for drift control than systems with ring springs or bars yielding in tension. Drifts are sufficiently small to achieve position retention performance for most nonstructural components. Horizontal accelerations are generally lower than predicted from ASCE 41 for regular nonrocking structures. Vertical accelerations in the gravity framing directly connected to the rocking frame are however higher than those predicted for ordinary structures. Vertical ground motions have limited effect on frame response.