倒立摆的自适应积分反步控制策略

针对直线单级倒立摆在模型参数不确定和外部扰动情况下的稳定控制问题，提出一种自适应积分反步控制策略。采用拉格朗日方程建立倒立摆系统的运动学模型，为减少稳态误差，将误差积分项引入反步法，设计了倒立摆的控制器；对含有未知参数的系统非线性状态微分方程，设计适当的Lyapunov函数推导出系统未知参数的自适应更新律，削弱了参数不确定性的影响。将自适应积分反步控制与一般的反步法控制、模糊控制及神经网络控制的仿真结果进行了对比，并在LabVIEW开发环境下进行了实物实验。结果表明，自适应积分反步法可以较为迅速且精确地完成稳定控制，较好地克服系统参数不确定及外部扰动的影响，具有较强的鲁棒性。

Adaptive integral backstepping control strategy for inverted pendulum

This paper proposed an adaptive integral backstepping control strategy to solve the stability control problem of inverted pendulum system with uncertain model parameters and external disturbance. It established the kinematics model of inverted pendulum system by using Lagrange equation. In order to reduce the steady state error, it introduced error integral term into backstepping method to design the controller of inverted pendulum. For the nonlinear state differential equations of system with unknown parameters, it designed a proper Lyapunov function to derive an adaptive update law for the unknown parameters of the system, and weakened the influence of parameter uncertainty. This paper compared the simulation results of adaptive integral backstepping control with results of general backstepping control, fuzzy control and neural network control and carried out the physical experiments in the LabVIEW development environment. The results show that the adaptive integral backstepping method which has good robustness can complete the stability control quickly and accurately. It can also overcome the uncertainty of the system parameters and the influence of external disturbance.