自平衡机器人控制系统的时滞稳定性分析  

Delay Stability Analysis of the Self-balancing Robot Control System

作　　者：陈刚[1] 匡鹏 曾红兵[1] 王炜[1] 王伟民 CHEN Gang;KUANG Peng;ZENG Hongbing;WANG Wei;WANG Weimin(School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou 412007,China)

机构地区：[1]湖南工业大学电气与信息工程学院,湖南株洲412007

出　　处：《控制工程》2025年第4期738-744,共7页Control Engineering of China

基　　金：国家自然科学基金资助项目(62173136);湖南省研究生科研创新项目(CX20220829)。

摘　　要：自平衡机器人是验证各种控制算法的经典装置,研究传输时滞对其控制系统的影响具有重要意义。基于李雅普诺夫-克拉索夫斯基(Lyapunov-Krasovskii,L-K)泛函方法讨论了自平衡机器人的控制问题。首先,建立了直流电机的线性化模型,并应用拉格朗日方程法建立了自平衡机器人的线性数学模型;然后,进一步考虑传输时滞环节,建立基于多闭环比例积分微分(proportional integral differential,PID)控制器的自平衡机器人控制系统的整体状态空间模型;最后,应用广义自由矩阵积分不等式,建立了低保守性的L-K稳定性判据,在此基础上通过MATLAB中的线性矩阵不等式(linear matrix inequality,LMI)工具箱去求解PID控制增益对时滞稳定裕度的影响。仿真结果表明,所提出的系统稳定性判据不仅有效,而且具有较低的保守性。The self-balancing robot is a classical device to verify various control algorithms.It is important to study the effect of transmission delay on its control system.The control problem of the self-balancing robot is discussed based on Lyapunov-Krasovskii(L-K)functional method.Firstly,the linear model of direct-current motor is established,and the linear mathematical model of the self-balancing robot is established by Lagrange equation method.Then,considering the transmission delay,the whole state space model of the self-balancing robot control system based on multi-closed-loop proportional integral differential(PID)controller is established.Finally,a low-conservative L-K stability criterion is proposed by applying the generalized free matrix integral inequality.On this basis,the linear matrix inequality(LMI)toolbox in MATLAB is used to solve the influence of PID control gain on the delay stability margin.The simulation results show that the proposed stability criterion is effective and low-conservative.

关 键 词：自平衡机器人 PID控制 时滞 L-K泛函 

分 类 号：TP16[自动化与计算机技术—控制理论与控制工程]