压电智能结构和反馈控制的集成优化设计

针对挠性结构振动控制中智能材料的特性,综合考虑压电敏感器/致动器的位置、尺寸、质量及其对挠性结构刚度特性的影响和控制律,建立系统状态空间模型,提出一种新的优化配置的性能指标和集成优化设计方法。运用李雅普诺夫稳定性定理证明了闭环系统的全局渐近稳定性,性能指标的最小值可取为相应矩阵的迹而不依赖于系统的初始状态。采用遗传算法寻优,数值仿真结果表明,该设计方法能够快速的抑制系统的振动。

Integrated Optimal Design of Piezoelectric Intelligent Structures and Feedback Control

A new approach to the integrated optimal design and the performance criterion of optimal placement based on realistic objective function and constraints was presented.According to the intelligent materials' performance on vibration suppression of flexible structures,the location and sizing of collocated piezoelectric sensor/actuator,including the effect of changes in the mass and the stiffness of the structure by addition of sensor/actuator pairs,and the feedback gains were considered and combined with the quadratic performance criterion used in optimal control to obtain the realistic state-space model of the structure and a composite objective function.By using Lyapunov stability theorem,it was shown that the closed-loop system of flexible structures was global asymptotically stable.In addition,the proposed minimizing performance criterion can be viewed as the trace of the correlative matrix which leads to solutions that are independent of initial conditions of the controlled flexible structure.To solve the optimization problem,the genetic algorithm was utilized.Simulation results not only show that the piezoelectric intelligent structure designed by the proposed approach can fleetly suppress the vibration of the structure,but also demonstrate the validity and feasibility of the proposed approach.