基于Lie理论对两轮不稳定小车的变结构控制

VSC Of Two-Wheel Unstable Vehicle Based On Lie-Theory

为了有效控制两轮不稳定小车,减少在控制过程中产生的抖振,首先利用一种非线性系统微分几何方法—Lie理论对两轮不稳定小车系统进行坐标和输入量的变换,实现了系统的局部反馈线性化,进而通过近似得到系统的线性模型。然后针对常规滑模变结构控制抖振较强的问题,设计了一种新的滑模控制方法,用动态滑模变结构控制。方法通过设计新的切换函数,使切换函数与系统控制输入的一阶或高阶导数有关,可将不连续项转移到控制的一阶或高阶导数中去,得到在时间上本质连续的动态滑模控制律,有效地降低了抖振。仿真和实验结果表明,采用的方法以及设计的控制器对不稳定小车的控制是有效的。

In this paper,to control the two-wheel unstable vehicle effectively and reduce the buffeting caused in the control process,firstly,a kind of differential geometry method for nonlinear system-Lie theory is used to transform the coordinates and input of the unstable vehicle system. From that,we can implement the feedback linearization of the system locally and obtain the linear model by approximate method. Then,thinking of the strong chattering of conventional sliding mode variable structure control （VSC）,we design a new method of dynamic sliding mode VSC to decrease the chattering. By a new switching function,this method can has the switching function related to the first-order or higher-order derivative of the system input,so that,the discontinuity can be transferred to the first-order or higher-order derivative of the system input. And we can obtain a dynamic sliding mode controller that is temporally continuous in nature. As a result,buffeting can be reduced effectively. Simulation and experimental results show that,with the method and controller designed in this paper,it is effective to control the unstable vehicle.