直线二级倒立摆基于线性矩阵不等式算法的滑模鲁棒H_∞控制  

Sliding Mode and Robust H_∞ Control Based on LMI Algorithm for Linear Double Inverted Pendulum

作　　者：刘慧博[1] 蔡蕊[1] 

机构地区：[1]内蒙古科技大学信息工程学院,包头014010

出　　处：《科学技术与工程》2014年第5期270-275,共6页Science Technology and Engineering

摘　　要：倒立摆系统是高阶次、自然不稳定系统,容易受到外界干扰或者自身一些不确定性因素的影响而失去稳定。若用传统的滑模控制难以实现系统具有全程鲁棒抗干扰能力,同时存在控制输入抖振的现象。对此,提出了滑模鲁棒状态反馈H∞控制,即设计了带有滑模面参数和状态反馈增益的复合控制器。将问题转化为通过线性矩阵不等式求解优化值的优化问题,优化了状态反馈增益和滑模面,使得整个闭环控制系统具有全局强鲁棒性的特点;并实现了削弱抖振的目的。仿真结果表明了该控制方法的有效性和可行性,并且具有较强的鲁棒性和响应速度快的优越性,对高阶次不稳定系统具有很好的控制效果。Inverted pendulum system is a high order and naturally unstable system,it is susceptible to outside interference and some uncertain factors so that it loses its stable equilibrium.It is difficult to achieve the system＇s global robust anti-jamming ability using the conventional sliding mode control.At the same time,there is the chattering phenomenon.Therefore,sliding mode robust state feedback H∞control is put forward,that is to say a composite controller is designed with sliding surface parameters and the state feedback gain.The problem is converted into the optimization problem with linear matrix inequalities for solving the optimization value,then the state feedback gain and sliding mode surface are optimized,so that the whole closed-loop control system has the characteristics of fast response of the sliding mode control and robustness of robust control,and gets the global robustness,and getting the realization of the chattering weakened.The simulation results show the effectiveness and feasibility of this method,and it has strong robustness and fast response advantages and has a good control effect for high order unstable system.

关 键 词：滑模控制 鲁棒控 制状态反馈 线形矩阵不等式(linear matrix inequality LMI) 倒立摆 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]