基于LMI滑模变结构的倒立摆系统稳定控制  

Stability control of inverted pendulum system based on LMI sliding mode variable structure

作　　者：李梦婕 张永立[1,2] 崔世钢 索美霞[1,2] LI Mengjie;ZHANG Yongli;CUI Shigang;SUO Meixia(School of Automation and Electrical Engineering,Tianjin University of Technology and Education,Tianjin 300222,China;Tianjin Key Laboratory of Information Sensing and Intelligent Control,Tianjin University of Technology and Education,Tianjin 300222,China)

机构地区：[1]天津职业技术师范大学自动化与电气工程学院,天津300222 [2]天津市信息传感与智能控制重点实验室,天津300222

出　　处：《天津职业技术师范大学学报》2023年第1期38-43,49,共7页Journal of Tianjin University of Technology and Education

基　　金：国家重点研发计划项目(2017YFB0403904);天津市研究生科研创新项目(2021YJSO2B16).

摘　　要：以一级倒立摆为研究对象,利用牛顿法建立数学模型,针对其不确定性和稳定性问题,采用指数趋近律,利用线性矩阵不等式方法(LMI)辅助滑模控制策略推导设计出滑模变结构控制器,并结合最优控制理论和饱和函数优化系统参数,提高控制性能。通过Matlab对一级倒立摆系统进行性能仿真验证。仿真结果表明:优化改进后的滑模变结构控制方法在克服系统自身参数的不确定性和外界干扰的同时,有效地抑制了系统抖振,且系统响应快、超调小。Taking the first-order inverted pendulum as the research object,a mathematical model is established by Newton′s method. To address the uncertainty and stability problems,the exponential convergence law is used to derive and design a sliding mode variable structure controller using linear matrix inequality(LMI)auxiliary sliding mode con-trol strategy,and the optimal control theory and saturation function are combined to optimize the system parameters and improve the control performance. The performance of the first-order inverted pendulum system is verified by Matlab simulation. The simulation results suggest that the optimized sliding mode variable structure control method overcomes the uncertainty of the system parameters and external disturbances and effectively suppresses the system jitter,and that the system response is fast and the overshoot is small.

关 键 词：倒立摆 滑模控制 线性矩阵不等式 李雅普诺夫 趋近律 稳定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]