小车倒立摆的自适应动态面控制
Adaptive dynamic surface control of cart-pole inverted pendulum

针对一类含有参数扰动和外部扰动的不确定欠驱动系统提出了一种改进自适应动态面控制方法.首先通过坐标变换,将小车倒立摆模型转换成部分反馈形式,由半严格形式模型设计动态面控制器.利用模糊逻辑处理系统不确定性的能力设计自适应控制器,然后在传统动态面控制器设计中采用跟踪微分器来得到原稳定化函数的精确微分,解决传统反步法的“微分爆炸”,显著提升闭环系统的性能.采用李雅普洛夫方法,设计适当的参数,系统跟踪误差能收敛到原点,仿真结果验证了该方法的有效性.
A modified adaptive dynamic surface control was proposed for a typical underactuated mechanical system. With the help of coordinate transformation, the cart-pole model was transformed to a partially feedback form. Based on semistrict feedback form a dynamic surface controller (DSC) was designed. An adaptive-based controller is constructed using the capability of fuzzy logic to tackle the uncertainties and then, by introducing tracking differentiator (TD), the ‘explosion of complexity’ problem in traditional backstepping technique was eliminated. TD was incorporated into the traditional DSC design procedure to obtain the precise original intermediate control signals and its derivative signals. Accordingly, the closed-loop control performance can be improved significantly. By using Lyapunov theorem, appropriate parameter selection can guarantee that the tracking errors converge to a compact set around zero was proved. Simulation results confirmed the effectiveness of the proposed method