Active Control of Structures Using Energy-Based LQR Method

Abstract:   In this article, a new energy-based technique is proposed to eliminate trial and error in finding appropriate gain matrices in linear quadratic regulator (LQR) controllers used in active control of structures. The gain matrix is obtained by considering the energy of the structure. To compare the efficiency of the proposed method, a three-storey building with two active tendons in the first and third floors is considered. The proposed gain selection and other techniques reported in the literature for LQR controllers are used to compare the response of the structure for three accelograms. A comparison of the displacement and control forces illustrates the superiority of the proposed method.     

State-Derivative Feedback Control of Cable Vibration Using Semiactive Magnetorheological Dampers

Abstract:   This article presents the theoretical and in situ experimental studies on state-derivative feedback control of bridge cable vibration using semiactive magnetorheological (MR) dampers. The semiactive feedback control is accomplished using only one MR damper and one accelerometer collocated near the lower end of the cable. Within the framework of reciprocal state space (RSS), the linear quadratic regulator (LQR) control technique is applied to formulate state-derivative feedback control law and derive the feedback and estimator gains for real-time control of cable vibration using MR dampers. The state-derivative feedback control strategy directly uses acceleration information for feedback and state estimation, which is usually the only measure available in practical cable vibration control implementation. More importantly, the control force commanded by the state-derivative feedback control strategy based on energy weighting is a dissipative force except for low velocity and small force, which is therefore implementable by the semiactive MR dampers without clipping. Numerical simulations of state-derivative feedback control for a stay cable in the cable-stayed Dongting Lake Bridge are conducted under sweeping sine excitation and sinusoidal step relaxation excitation, and then the experimental validation of the prototype cable is carried out in the bridge site with the help of the real-time control system dSPACE. Good agreement between the simulation and experimental results is observed.     

A GBMO-based PIλDμ controller for vibration mitigation of seismic-excited structures

The advantages of fractional-order proportional–integral–derivative (FOPID) controllers in terms of flexibility, robustness against model uncertainties and good disturbance rejection, are good motivations to use them for vibration mitigation of seismic-excited structures. The application of the FOPID controller for adjusting the control force of an active tuned mass damper (ATMD) for seismic control a building is studied in this paper. Gases Brownian motion optimization (GBMO) algorithm is employed for optimal tuning of parameters of the FOPID and PID controllers. Evaluation of the frequency responses of the structure for uncontrolled and controlled cases shows that PID and FOPID controllers are very effective for the seismic control of structures. For further investigation, the performance of the FOPID controller in the reduction of seismic responses of the building in four well-known earthquake excitations is compared with those provided by the PID, linear–quadratic regulator (LQR) and fuzzy logic control (FLC). Simulation results show that the PID and LQR controllers provide the same performance in reducing the maximum top floor displacement of the structure. Moreover, the FLC and FOPID controllers demonstrate a superior performance in seismic control of the structure. The FLC is able to reduce the maximum displacements of all stories for all studied earthquakes. However, the proposed FOPID controller is able to provide a better performance in comparison with the FLC. In average, the FOPID controller mitigates the seismic responses of the structure as much as 29%, 27% and 15% better than the LQR, PID controller and FLC.     

Numerical Investigation of a Variable Damping Semiactive Device for the Mitigation of the Seismic Response of Adjacent Structures

Abstract:   When two structures in close proximity and with different properties (heights, structural systems, materials) are subjected to a strong seismic ground motion there is the possibility that pounding between them may occur. The large impact loads induced by this phenomenon usually lead to catastrophic results. One way to overcome this effect is to couple the structures through elastic or damping elements. This article examines the use of a new variable damping device as a coupling element. The system, which is termed a variable damping semiactive (VDSA) device, consists of two dampers with constant parameters whose lower ends are attached to a common vertical rod whereas the upper ends are attached to the two structures. As the structures vibrate due to the ground motion, the lower end is moved up and down by means of an actuator. By changing the orientation of the dampers, the effective damping in the two structures can be changed in time in an appropriate manner to minimize the response. A new control law is used to calculate the optimal position of the dampers. The algorithm, referred to as Q v , is a variation of the Instantaneous Optimal Control and it is based on the minimization of a performance index J quadratic in the state vector, the control force vector, and a vector of absolute velocities measured at selected points. The algorithm includes a generalized LQR scheme where penalties are imposed on the state vector, on the control vector, and on the absolute velocity vector through three predefined matrices. A numerical simulation is used to verify the performance of the proposed protective system in reducing the seismic response to a series of historic earthquakes. The results show that the proposed device is able not only to eliminate the pounding effects but also to significantly reduce the response of the individual adjacent structures .     

Wavelet PSO‐Based LQR Algorithm for Optimal Structural Control Using Active Tuned Mass Dampers

This study presents a new method to find the optimal control forces for active tuned mass damper. The method uses three algorithms: discrete wavelet transform (DWT), particle swarm optimization (PSO), and linear quadratic regulator (LQR). DWT is used to obtain the local energy distribution of the motivation over the frequency bands. PSO is used to determine the gain matrices through the online update of the weighting matrices used in the LQR controller while eliminating the trial and error. The method is tested on a 10‐story structure subject to several historical pulse‐like near‐fault ground motions. The results indicate that the proposed method is more effective at reducing the displacement response of the structure in real time than conventional LQR controllers.     

层合板壳振动控制LQR方法的理论推导

从层合板壳弹性力学基本方程出发,考虑各种因素影响,导出统一形式的振动方程,利用LQR最优控制理论,根据能量原理确定了Q,R,求出符合条件的最优控制集中力,等效分布荷载的表达式及位移衰减函数。     

Optimal control of structures under earthquake excitation based on the colonial competitive algorithm

The active control of engineering structures is one of the best methods to reduce structural responses under seismic excitation for the best performance of structures. This study presents an effective approach for the optimal control of structures under strong ground motion using the colonial competitive algorithm. The colonial competitive algorithm was developed over the last few years in an attempt to overcome the inherent limitations of traditional optimize method. The colonial competitive algorithm has been applied due to its ideal performance in optimal control problem. The effectiveness and performance of the proposed method have been investigated through two numerical examples for the response control of earthquake‐excited structures. The obtained results have been compared with the Linear Quadratic Regulator (LQR) control algorithm, and the performance of the proposed control approach has been found to be better than the LQR controller. Copyright © 2012 John Wiley & Sons, Ltd.     

Using mesoporous carbon electrodes for brackish water desalination

Electrosorptive deionisation is an alternative process to remove salt ions from the brackish water. The porous carbon materials are used as electrodes. When charged in low voltage electric fields, they possess a highly charged surface that induces adsorption of salt ions on the surface. This process is reversible, so the adsorbed salt ions can be desorbed and the electrode can be reused. In the study, an ordered mesoporous carbon (OMC) electrode was developed for electrosorptive desalination. The effects of pore arrangement pattern (ordered and random) and pore size distribution (mesopores and micropores) on the desalination performance was investigated by comparing OMC and activated carbon (AC). It were revealed from X-ray diffraction and N(2) sorption measurements that AC has both micropores and mesopores, whereas ordered mesopores are dominant in OMC. Their performance as potential electrodes to remove salt was evaluated by cyclic voltammetry (CV) and galvanostatic charge/discharge tests at a range of electrolyte concentrations and sweep rates. It is deduced that under the same electrochemical condition the specific capacitance values of OMC electrode (i.e. 133 F/g obtained from CV at a sweep rate of 1 mV/s in 0.1M NaCl solution) are larger than those of AC electrode (107 F/g), suggesting that the former has a higher desalting capacity than the latter. Furthermore, the OMC electrode shows a better rate capacity than the AC electrode. In addition, the desalination capacities were quantified by the batch-mode experiment at low voltage of 1.2V in 25 ppm NaCl solution (50 micros/cm conductivity). It was found that the adsorbed ion amounts of OMC and AC electrodes were 11.6 and 4.3 micromol/g, respectively. The excellent electrosorptive desalination performance of OMC electrode might be not only due to the suitable pore size (average of 3.3 nm) for the propagation of the salt ions, but also due to the ordered mesoporous structure that facilitates desorption of the salt. Based on the results, it was found that the development of an ordered mesoporous structure and the control of the number of micropores are two important strategies for optimising electrode material properties for electrosorptive deionisation.     

A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD

This paper presents an efficient hybrid control approach through combining the idea of proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) control algorithm. The proposed LQR-PID controller, while having the advantage of the classical PID controller, is easy to implement in seismic-excited structures. Using an optimization procedure based on a cuckoo search (CS) algorithm, the LQR-PID controller is designed for a seismic- excited structure equipped with an active tuned mass damper (ATMD). Considering four earthquakes, the performance of the proposed LQR-PID controller is evaluated. Then, the results are compared with those given by a LQR controller. The simulation results indicate that the LQR-PID performs better than the LQR controller in reduction of seismic responses of the structure in the terms of displacement and acceleration of stories of the structure.     

基于状态微分控制算法的空间结构主动振动控制分析

对于主动振动控制器的设计,传统的控制算法以速度和位移作为系统的输入量,但速度和位移难以观测,给实际应用带来了较大的误差.本文在振动状态空间方程的基础上,对其进行矩阵运算,形成以加速度为系统输入的状态微分反馈控制方程.构造具有约束条件的目标函数,根据Lagrange乘子法和泛函极值运算确定了状态反馈矩阵和状态反馈估计值,从而构造了闭环的状态微分控制算法.根据此算法对一直径为1m的环形空间结构进行了振动控制仿真,利用时域内的模态参数识别方法,对控制效果进行了评价,并以三层剪切型框架结构为对象,对状态微分控制算法和传统的LQR算法进行了控制效果的对比分析.结果表明,利用状态微分控制算法在空间结构上的振动控制是可行的,且减振效果明显,同时优于传统的LQR控制算法.     

Support vector machine based semi‐active control of structures: a new control strategy

The present paper presents the support vector machine (SVM)‐based semi‐active control algorithm used for designing general dampers for multistorey structures under earthquakes. First, the linear quadratic regulator (LQR) controller for the numerical model of a multistorey structure formulated using the dynamic dense method is obtained by using the classic LQR control theory. Then, a SVM model is designed and trained to emulate the performance of the LQR controller. Likewise, this SVM model comprises the observers and controllers of the control system. Finally, in accordance with the features of general semi‐active dampers, a SVM‐based semi‐active control strategy is put forward. More specifically, an online auto‐feedback semi‐active control strategy is developed and then realized by resorting to SVM. In order to numerically verify the control effectiveness of the present control strategy, the time history analysis has been implemented to a structure with general dampers designed by the SVM‐based semi‐active control algorithm. In numerical simulations, four seismic waves including the El Centro, Hachinohe and Kobe waves, as well as the Shanghai artificial wave, whose peak ground accelerations are all scaled to 0.1 g, are taken into consideration. Comparative results demonstrate that general semi‐active dampers designed using the SVM‐based semi‐active control algorithm is capable of providing higher level of response reduction. Copyright © 2009 John Wiley & Sons, Ltd.     

基于加速度趋近律的高层结构的滑模控制及其鲁棒性分析

本文采用加速度趋近律滑模控制算法对多自由度体系的地震响应进行了数字仿真研究。并且将该控制方法与LQR控制方法的控制效果和控制的鲁棒性进行了对比分析。仿真和分析结果表明此控制律的控制效果和鲁棒性均优于LQR控制方法 ,能够有效地减小结构的地震响应 ,同时具有较好的鲁棒性。基于加速度趋近律的滑模控制具有重要的实际应用价值     

柔性悬臂梁振动主动控制研究

采用压电材料作为传感器和致动器,建立了机电耦合的压电智能梁动力学方程,采用基于线性二次型（LQR）最优控制的独立模态控制方法对智能梁振动进行抑制,以有效抑制压电悬臂梁的振动。     

Prediction of maximum dry density and optimum moisture content of stabilised soil using RBF neural networks

This article proposes a novel approach for the prediction of maximum dry density (MDD) and optimum moisture content (OMC) of soil-stabiliser mix by using radial basis function (RBF) neural networks. RBF neural network is utilised to construct comprehensive and accurate models to be able to relate the MDD and OMC of stabilised soil to the properties of natural soil such as particle size distribution, plasticity, linear shrinkage and the type and quantity of stabilising additives. Two separate sets of RBF prediction models, one for the MDD and the other for the OMC, have been developed. A parametric study was also conducted in this study using the results obtained from the proposed models to evaluate the sensitivity of MDD and OMC due to variation of the influencing parameters. A comprehensive set of data including a wide range of soil types obtained from previously published stabilisation test results was used for training, validation and testing the prediction models. The accuracy of the proposed models is satisfactory when compared with that of the experimental results. The results of proposed RBF models were further compared with those of the existing models found in literature and found to be more accurate.     

高柔结构风振AMD控制模糊神经网络预测算法研究

基于Takagi-Sugeno模型的模糊神经网络的基本理论,建立了模糊神经网络预测模型。该模型结合神经网络控制和预测控制的优点,解决了控制中的时滞问题。研究了基于聚类法产生模糊神经网络预测控制的模糊逻辑系统,该方法便捷地解决了模糊逻辑控制中模糊控制规则基于专家控制策略和经验而无自学习能力的困难。以深圳京基金融中心为算例,利用模糊神经网络预测算法控制结构在风荷载作用下的振动,仿真结果表明,模糊神经网络预测算法能够有效地减小高柔结构加速度响应。     

新型橡胶减振驱动链轮性能研究

章针对应用于大型履式推土机驱动链轮橡胶减振新结构，建立了其减振模型并推导出相应的传递率函数，章同时分析了橡胶减振器参数的取值对减振性能产生的影响。     

基于LQR控制算法的输电塔风振控制研究

采用谐波叠加法,模拟了输电塔塔顶脉动风速时程曲线及风荷载时程.介绍了LQR控制算法的原理,利用MATLAB语言编制了LQR控制算法的程序,并对一输电塔模型结构在风荷载作用下的控制效果进行分析,结果表明,LQR控制方法可以有效地减小输电塔的风振响应,说明LQR控制方法是一种比较理想的减震方法.     

A numerical method for choice of weighting matrices in active controlled structures

A feedback control system usually implements active and semi‐active control of seismically excited structures. The objective of the control system is described by a performance index, including weighting matrix norms. The choice of weighting matrices is usually based on engineering experience. A new procedure for weighting matrix components choice based on the parametric optimization method is developed in this study. It represents a two‐step optimization process. In the first step a discrete‐time control system is synthesized according to a quadratic performance index. In the second step the weighting coefficients are obtained using the results of the first step. Numerical simulation of a typical structure subjected to earthquakes is carried out in order to demonstrate the effectiveness of the proposed method. It shows that applying the proposed technique provides a choice of the weighting matrices and results in enhanced structural behaviour under different earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

The Optimization of Signal Settings on a Signalized Roundabout Using the Cross-entropy Method

Abstract:   The cross-entropy method (CEM) is a newly developed approach to the solution of complex combinatorial optimization problems. It is an iterative process that consists of generating solutions from some probability distribution whose parameter values are updated in each iteration using information from the best solutions found in that iteration. The article applies the method to the problem of the optimization of signal settings on a signalized roundabout. The performance of any given set of timings is evaluated using the cell transmission model, a deterministic macroscopic traffic flow model that permits the modeling of the spatial extent of queues and the possibility of "blocking back." The results from the investigations are encouraging, and show that the CEM has the potential to be a useful technique for tackling global optimization problems.     

Integrated wheel loader simulation model for improving performance and energy flow

This paper describes an integrated wheel loader simulation model for improving performance and energy flow. The proposed integrated wheel loader simulation model includes a driver model that is designed to perform the two objectives of working and driving. The driver model for working was designed according to eight conditions considered as events and environment information. The driver model for driving is composed of throttle, brake, and steering inputs which represent an actual driver's input characteristics. By analyzing experimental test data of V-pattern working, human driving characteristics have been derived and applied in the driver model by using linear quadratic regulator (LQR) and model predictive control (MPC). The wheel loader dynamic simulation model with the driver model used in this study consists of four parts: mechanical powertrain, hydraulic powertrain, vehicle dynamic model, and working dynamic model with a simplified load model. All simulation models have been constructed in the Matlab/Simulink environment, and the proposed driver model has been validated from experimental test data. Working performance with the optimized path, energy flow, and loss analysis during V-pattern working was predicted and evaluated with the developed human driver and dynamic simulation model of a wheel loader. The driver model can be utilized in the design stage for prediction and evaluation of a wheel loader's working performance. It is also expected that an investigation of the optimal working pattern and energy flow for various working cycles of wheel loaders will be possible with the driver-model-in-the-loop simulation.