基于LMI的不确定结构自适应保性能PID鲁棒控制  

Adaptive guaranteed performance PID robust control for uncertain structures based on LMI

作　　者：潘兆东[1] 谭平[2] 周福霖[1,2] 

机构地区：[1]湖南大学土木工程学院,湖南长沙410082 [2]广州大学工程抗震研究中心,广东广州510405

出　　处：《地震工程与工程振动》2017年第4期15-21,共7页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(97315301-07;51408142);国家"973"项目(2012BAJ07B02);教育部创新团队项目(IRT13057)~~

摘　　要：针对模型参数不确定的结构振动控制问题提出一种自适应保性能PID鲁棒控制(LMIAGCPID)算法。首先,结合传统PID控制理论建立了考虑模型参数不确定性的受控结构扩阶状态方程,同时利用线性矩阵不等式方法,推导了保证系统渐进稳定和性能上界最小的保性能PID控制律,并引入约束条件,将其转化为凸优化求解问题;在此基础上,通过设置能够时变调节比例增益、微分增益和积分增益的自适应函数,进而得到自适应保性能PID鲁棒控制律。最后,对一个3层结构进行仿真分析。结果表明,不同地震激励下,无论结构参数是否存在不确定,LMI-AGCPID控制较LQG控制而言均能更好地抑制结构的振动响应。in this paper, an adaptive guaranteed performance PID robust control （LMI-AGCPID） algorithm is proposed for the vibration control problem of building structure with uncertain parameters. Firstly, the extended order state equation of the control system is established based on the traditional PID control theory. A guaranteed performance PID control law is derived through linear matrix inequality method to guarantee the asymptotic stability of the system and the upper bound of the performance simultaneously. And it is transformed into a convex optimization problem by introducing the constraint conditions. Secondly, the adaptive functions are set up to adjust the proportional gain, differential gain and integral gain, and then the adaptive guaranteed cost PID control law is obtained. Results of vibration control analysis for a 3-story structure show that under different seismic excitations, no matter whether the model parameter uncertainties exist or not, the LMI-AGCPID control can suppress the vibration response of the structure better than the LQG control.

关 键 词：主动控制 自适应控制 保性能控制 PID控制 鲁棒控制 线性矩阵不等式 

分 类 号：P315.31[天文地球—地震学]