结构地震反应性态的物理随机最优控制

本研究发展了结构地震反应性态的随机最优控制理论和方法。这一研究建立在物理随机系统思想的新理论框架下,突破了以I^to随机微分方程描述动力系统的经典随机最优控制的藩篱。提出了基于系统二阶统计量评价、单目标超越概率和多目标能量均衡的控制器参数设计准则,以及基于概率可控指标的控制器位置设计准则,并将它们统一为物理随机最优控制的广义最优控制律。数值算例分析表明,本文发展的物理随机最优控制方法能够实现结构地震反应性态的精细化控制。     

土木工程结构最优控制问题的脉冲干扰法（PDM）

此论文根据土木工程结构主动控制问题的特点提出了研究土木工程结构最优控制问题的一种新方法，即脉冲干扰法，其结果归结为定常线性结构的瞬时最成闭环控制。     

主动变刚度／阻尼控制算法研究

建立了主动变刚度／阻尼控制系统的理论模型;基于瞬时最优控制算法推导了ＡＶＳＤ系统的开关控制律,并从控制结构的层间位移出发提出了一种直接根据结构动力反应符号确定的开关控制律。     

建筑结构的鲁棒H∞最优控制

针对传统线性二次型最优控制(Linear quadratic optimal control,LQR)等主动控制方法存在鲁棒性较差的不足,考虑结构参数和外部激励的不确定性,提出一种控制算法简单、便于工程应用的鲁棒H∞最优控制方法.将工程中常用的二次型最优指标结合于鲁棒H∞控制系统的分析中,使得控制器的性能指标容易衡量;通过引入线性矩阵不等式(Linear Matrix Inequalities,LMI)减小求解的复杂度.以一个多层剪切型建筑结构模型为例进行了仿真,并与LQR方法进行对比,仿真结果初步表明该方法具有较好的控制效果和鲁棒性.     

控制大气污染的一个数学理论框架

讨论了如何利用大气污染的数值预报结果和模式进行大气污染最优控制设计的理论框架问题. 提出了以控制污染源排放量为控制手段的大气污染最优控制问题, 其目的是在事先预报的天气条件下, 通过可行的控制手段使得一个城市的大气污染物浓度在一个选定的地域和时间段内保持在某一可容许的指标之内, 同时又使控制的代价(包括控制导致的工艺提高的耗资或工厂减产的经济损失, 或生活的不便性等)为最小. 基于伴随模式的最优化方法, 推导了求解这一问题的数学方法和相应的计算公式. 由于最优控制方案是根据预报的天气条件计算出来的, 而预报结果都是有误差的, 因此事先计算出的最优控制方案的实施效果会受到天气条件预报误差的影响. 利用伴随算子模式方法, 给出了这一问题的一个近似的却高效的算法, 可以计算不同时刻和地点预报的风场、温度场和污染物初值的不确定性对最优控制效果的影响.     

基于序列最优控制算法的隔震曲线梁桥非线性振动控制研究

强震作用下隔震曲线梁桥会产生较大的弹塑性变形,需要采取一定的控制措施以保证其安全性。采用经典的Bouc-Wen模型,建立考虑上部结构偏心的隔震曲线梁桥的非线性动力方程,求解罕遇地震作用下结构的动力响应。针对隔震曲线梁桥罕遇地震作用下产生的较大弹塑性变形,建立隔震曲线梁桥的非线性振动控制方程,将该方程等效线性化后采用序列最优控制算法(SOC)和经典线性最优控制(COC)对桥梁进行振动控制研究。结果表明：在罕遇地震下,隔震曲线梁桥的下部结构与隔震层都已屈服进入塑性阶段,且有少量的残余位移产生;序列最优控制算法和经典线性最优控制都能有效地减小隔震曲线梁桥弹塑性状态下的平动位移与残余位移,并有效抑制曲线桥的扭转效应,其中序列最优控制算法较经典最优控制更能显著削减隔震曲线梁桥的峰值响应。     

磁流变调谐液柱阻尼器半主动地震反应控制研究

结构的半主动控制装置是国际上研究的一个热点.磁流变式调谐液柱阻尼器(MR-TLCD)是一种新型的减振驱动器.文中提出了抑制结构水平振动的MR-TLCD模型,建立了MR-TLCD与结构相互作用的运动方程.在经典线性最优控制(COC)和瞬时最优控制(IOC)算法的基础上,研究了Clipped-optimal半主动控制策略的减振效果,并与被动控制的减振效果进行了对比.结果表明:磁流变式调谐液柱阻尼器的半主动控制能够有效地减小结构的地震反应,且优于被动控制.     

结构瞬时最优控制参数影响的数值分析

在瞬时最优控制算法理论分析的基础上，分别以单自由度和三自由度结构模型为例，研究了时间间隔和权矩阵对结构控制反应的影响。首先，进行了瞬时最优控制算法的理论分析，提出了控制算法的影响参数；其次，分别对单自由度和三自由度结构在无控、LQR和瞬时最优三种方法控制下，分析了时间间隔和权矩阵对结构反应的影响。结果表明：时间间隔和权矩阵对结构瞬时最优控制效果影响很大。     

结构瞬时开闭环最优控制算法中的迟时研究

本文运用四阶Ｒｕｎｇｅ－Ｋｕｔｔａ法建立了在迟时情况下结构状态方程的离散形式,采用瞬时控制开闭环最优控制算法对开环、闭环和开闭环控制中迟时的影响进行研究,并根据闭环控制的原理提出了迟时补偿算法,以减小迟时的影响。     

地震动作用下的结构瞬时开闭环最优控制算法

本文提出了瞬时开闭环最优控制算法，这是建立在时程分析基础上的最优控制算法，不需要实施结构的模态解耦，适合于地震动作用下非线性结构的控制分析，这种算法不仅可以区分开环，闭环和开闭环控制的不同效果，而且结构的位移，速度和加速度响应都能有效地得到控制。     

Reliability‐based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope

Current reliability‐based control techniques have been successfully applied to linear systems; however, incorporation of stochastic nonlinear behavior of systems in such control designs remains a challenge. This paper presents two reliability‐based control algorithms that minimize failure probabilities of nonlinear hysteretic systems subjected to stochastic excitations. The proposed methods include constrained reliability‐based control (CRC) and unconstrained reliability‐based control (URC) algorithms. Accurate probabilistic estimates of nonlinear system responses to stochastic excitations are derived analytically using enhanced stochastic averaging of energy envelope proposed previously by the authors. Convolving these demand estimates with capacity models yields the reliability of nonlinear systems in the control design process. The CRC design employs the first‐level and second‐level optimizations sequentially where the first‐level optimization solves the Hamilton–Jacobi–Bellman equation and the second‐level optimization searches for optimal objective function parameters to minimize the probability of failure. In the URC design, a single optimization minimizes the probability of failure by directly searching for the optimal control gain. Application of the proposed control algorithms to a building on nonlinear foundation has shown noticeable improvements in system performance under various stochastic excitations. The URC design appears to be the most optimal method as it reduced the probability of slight damage to 8.7%, compared with 11.6% and 19.2% for the case of CRC and a stochastic linear quadratic regulator, respectively. Under the Kobe ground motion, the normalized peak drift displacement with respect to stochastic linear quadratic regulator is reduced to 0.78 and 0.81 for the URC and CRC cases, respectively, at comparable control force levels. Copyright © 2017 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.     

Control of hydrologic systems for multiple uses in a closed-loop framework

The role of linear control theory as an aid to the integral control of hydrologic systems is investigated for the case of a combined lake and aquifer storage system that supplies either a deterministic or stochastic water demand. Only lumped time-invariant systems are considered but both deterministic and stochastic inflows to storage are allowed. The computational example allows for recharge of lake water into the aquifer as well as for the subsequent diversion of pumped groundwater back to the lake. Stability criteria are presented for the closed-loop features of the overall control system. Under a quadratic loss criterion, a calculus of variations problem, subject to constraints imposed by the system equations can be solved for the optimal release policy from the lake and aquifer and optimal feedback policy from aquifer to lake.     

基于二次型性能指标的控制器优化布置方法

本文建立了基于二次型性能指标的结构控制系统控制器最优布置方法。以控制器撤除时的系统最优控制性能指标增量作为控制器对系统最优控制的贡献，并用做确定经济的控制器数量和最优控制器位置的定量分析准则。本文中的控制器位置和控制器设计采用同一个优化性能指标，使得控制系统设计为最优。根据逼近满设置控制器结构控制系统的最优状态求得控制器降阶后等价的反馈控制增益。应用本文的方法对剪切模型框架结构上安装的锚索控制器进行了控制器的总体优化设计。数值分析表明，本文提出的控制器数量、位置和参数优化方法不仅易于实现，而且甚为有效。     

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.     

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.     

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.     

Reliability‐based robust control for uncertain dynamical systems using feedback of incomplete noisy response measurements

A reliability‐based output feedback control methodology is presented for controlling the dynamic response of systems that are represented by linear state‐space models. The design criterion is based on a robust failure probability for the system. This criterion provides robustness for the controlled system by considering a probability distribution over a set of possible system models with a stochastic model of the excitation so that robust performance is expected. The control command signal can be calculated using incomplete response measurements at previous time steps without requiring state estimation. Examples of robust structural control using an active mass driver on a shear building model and on a benchmark structure are presented to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Tuned mass dampers for response control of torsional buildings

This paper presents an approach for optimum design of tuned mass dampers for response control of torsional building systems subjected to bi‐directional seismic inputs. Four dampers with fourteen distinct design parameters, installed in pairs along two orthogonal directions, are optimally designed. A genetic algorithm is used to search for the optimum parameter values for the four dampers. This approach is quite versatile as it can be used with different design criteria and definitions of seismic inputs. It usually provides a globally optimum solution. Several optimal design criteria, expressed in terms of performance functions that depend on the structural response, are used. Several sets of numerical results for a torsional system excited by random and response spectrum models of seismic inputs are presented to show the effectiveness of the optimum designs in reducing the system response. Copyright © 2002 John Wiley & Sons, Ltd.