三级倒立摆建模与H_∞鲁棒优化保性能控制  

Modeling of triple inverted pendulum and H_∞ robust optimal guaranteed cost control

作　　者：薛安克[1] 官伯林[1] 尚群立[1] 王建中[1] 

机构地区：[1]杭州电子科技大学智能信息与控制技术实验室,浙江杭州310018

出　　处：《浙江大学学报（工学版）》2004年第12期1637-1641,共5页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(60174029).

摘　　要：针对倒立摆系统当中存在的自然不稳定性和大量不确定性,提出了一种H∞鲁棒优化保性能控制方法.利用分析力学中的Lagrange方程建立三级倒立摆的不确定数学模型,把系统的不确定性和外界扰动分别转化为模型状态矩阵的不确定性和模型的扰动输入,从而将系统稳定问题转化为H∞范数求解问题.仿真实验结果证明,应用这种方法可以保证系统指数稳定,二次代价泛函满足性能指标,同时使系统具有相同H∞范数界γ.与传统方法相比,该方法对三级倒立摆的控制具有较强的鲁棒性,能够在系统存在外界干扰和不确定性时,仍能保持系统的稳定性.The H_∞ robust optimal guaranteed cost control method was proposed to control the triple inverted pendulum system, especially for the natural instability and the large uncertainties of the system. After setting up the model of the triple inverted pendulum by the Lagrange equation, this method reformulated the stability problem of the system as H_∞ norm problem by reformulating the uncertainties and the disturbance of the system as the uncertainties of the state and the disturbing input of the model respectively. The result of the simulation shows that this robust method can ensure the exponential stability of the system and the target of the performance, and make the same H_∞ norm boundary γ for the system. Compared with traditional methods, the method for the triple inverted pendulum system is robust, and can maintain the stability of the system that has large uncertainties and disturbance.

关 键 词：鲁棒控制 倒立摆 不确定性 鲁棒H∞控制 保性能控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]