Abstract: In order to improve the ability to resist disturbance of inverted pendulum control system, and reduce the sensitivity to the unmodeled dynamics, etc., a design of the uncertain robust adaptive controller for planar double inverted pendulum is studied. The dynamic model of the inverted pendulum is broken down into two parts of the certainty and the uncertainty, using a nonlinear parametric fuzzy logic system to approximate the uncertain dynamic of the planar double inverted pendulum, and then a set of robust controller and adaptive laws are derived based on Lyapunov stability theory which makes the state errors of the planar double inverted pendulum asymptotic convergence. Theoretical analysis and simulation results show that the designed controller is effective. 

Key words: planar double inverted pendulum, fuzzy logic systems, Lyapunov stability theory

摘要： 为提高倒立摆控制系统的抗扰动能力，降低其对未建模动态等的敏感度，研究了不确定平面二级倒立摆的鲁棒自适应控制器的设计方法。把倒立摆动力学模型分解为确定和不确定两部分，用一个非线性参数化模糊逻辑系统逼近平面二级倒立摆的不确定动态，采用李雅普诺夫稳定性理论推导出使平面二级倒立摆的状态误差渐近收敛的鲁棒控制器及自适应律。理论分析和仿真结果表明所提出的控制算法是有效的。

关键词: 平面二级倒立摆, 模糊逻辑系统, 李雅普诺夫稳定性理论