倒立摆系统的动力学建模与滑模控制  

Dynamical Modeling and Sliding Mode Control of Inverted Pendulum Systems

作　　者：邱德慧[1,2] 王庆林[1] 杨洁[1] 

机构地区：[1]北京理工大学自动化学院,北京100081 [2]首都师范大学信息工程学院,北京100048

出　　处：《控制工程》2012年第S1期8-11,14,共5页Control Engineering of China

摘　　要：针对任意级直线倒立摆系统,基于Lagrange方程,建立其动力学模型,为倒立摆系统建模提供了一个简洁的途径。然后针对存在不确定摆杆长度和外部扰动的一级倒立摆系统的稳定控制,采用坐标变换将一级倒立摆系统动力学模型转换为易于设计的级联规范型,基于此规范型提出了一种新的滑模控制策略。采用柔化符号函数的方法,消除了控制力抖振。并应用Lyapunov理论和摄动理论证明了控制系统的稳定性。仿真结果表明所设计的控制器的有效性和鲁棒性。Based on Lagrange equations,the dynamical model is derived for n order inverted pendulum systems.The proposed method provides a brief way for modeling of inverted pendulum systems.For one order inverted pendulum systems in presence of uncertain length of pendulum and external disturbances,a novel sliding mode control strategy is presented.To simplify the control design,the model of one order inverted pendulum systems is changed into cascade normal forms by coordinate transformation.A continued arithmetic of sign function is used to reduce chattering.The stability of the control system is proved by Lyapunov theory and perturbation theory. The simulation results are included to indicate the effectiveness and robustness of the proposed controller.

关 键 词：滑模控制 任意级倒立摆系统 级联规范型 欠驱动系统 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]