基于输出反馈的建筑结构闭开环次优控制
Closed/Open-loop Sub-optimal Control of Structures Based on Output Feedbacks

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。
Most recent studies have been based on the application of linear quadratic regulator control to earthquake-excited structures. In linear quadratic regulator control problems, the objective function is defined as the integral of a quadratic expression in the control interval with respect to structural states and control vectors, and the optimal regulator can be derived using Pontryagin's maximum principle or Bellman's method of dynamic programming. In traditional linear quadratic regulator control problems, the Riccati equation is obtained without considering the earthquake excitation term. To optimize control and satisfy the optimality condition, in this study, we propose a new closed/open-loop control strategy for structures under earthquake excitation. We derive an analytical solution to a linear regulator problem for structural control without neglecting unknown disturbances. The optimal regulator depends on both the state and disturbances. The solution for this closed/open-loop control requires the knowledge of the earthquake in the control interval, which is approximated based on the real-time prediction of near-future earthquake excitation using the Kalman filtering technique. Earthquake excitation is modeled as an autoregressive process. The prediction algorithm can predict seismic excitation in the near future with high accuracy, although it lacks prediction accuracy for more distant future events. Considering the measurement difficulty of all state variables, especially for some high-order systems, the proposed control strategy only requires the measurement of a partial state. In the calculation of a state transition matrix, which is required to solve a differential equation, large rounding errors may occur when the time-step size is excessively small. To overcome this limitation, we introduce a precise integration algorithm to solve the differential equation. This algorithm is always numerically stable and yields very high precision solutions for numerical integration problems. To demonstrate the effectiveness of the proposed control strategy, we investigated the undamped vibration of a three-story building subjected to horizontal seismic forces. We assumed that the columns of the building are massless and that the mass of the structure is concentrated at floor levels. We implemented control using actuators exerting forces on each story. We also assumed that