基于SDRE方法的一级旋转倒立摆控制  

SDRE based control of one-level rotary inverted pendulum

作　　者：杨帆[1] 赵党军[1] 李国平[1] 胡为兵[1] 

机构地区：[1]武汉工程大学电气信息学院,湖北武汉430073

出　　处：《华中科技大学学报（自然科学版）》2008年第10期25-28,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：湖北省教育厅基金资助项目(20060271)

摘　　要：基于拉格朗日方程建立了一级旋转倒立摆的非线性微分方程模型,提出了一种参数化方法以获得伪线性化系统模型.研究了系统的逐点可控性,表明系统除了在摆杆垂直向下位置外都为可控.设计了基于状态相关黎卡提方程(SDRE)方法的控制器,控制增益与系统状态相关,计算复杂程度较高,但控制效果好.与线性最优二次型调节器(LQR)进行了仿真对比,结果表明:SDRE在摆杆远离平衡位置时的控制效果要优于LQR,具有超调小,调节时间短的特点,且能同时完成摆起及平衡控制而不需要另外设计控制器.A parameterization method was introduced to obtain a pseudo-linearizing model after estab lishing nonlinear differential equations of one-level-rotary pendulum. The point-wise controllability of system was studied, showing that the system is controllable except the points in which the pendulum is down vertical. A state dependent Riccati equation （SDRE） based controller was designed, and the controller＇s gain relates to the state, which results in complexity in computing but good effects of con trol. Comparative simulations between SDRE and least quadratic regulation （LQR） reflect that advan- tages of the SDRE technique such as small over shooting, short settling time, are over the LQR design while a larger deflection from balancing point; and only a single controller is needed for both swing-up and balancing control of the pendulum.

关 键 词：旋转倒立摆 状态相关黎卡提方程 最优控制 逐点可控性 最优二次型调节器 

分 类 号：TP202[自动化与计算机技术—检测技术与自动化装置]