滑动变量受限情况下的二阶滑模控制设计

在实际系统中状态受限普遍存在,因此考虑状态受限下的控制设计问题具有重要的理论意义和工程价值.本文考虑了滑动变量受限情况下的二阶滑模控制设计问题.首先,在不考虑滑动变量受限的情况下,基于Lyapunov方法,给出了一种新的二阶滑模控制器构造方法,并严格证明了在该控制器的作用下滑动变量将在有限时间内稳定到平衡点.其次,考虑滑动变量受限情况,证明了在受限区域内存在一个与控制参数相关的吸引域,使得当初始状态在该吸引域内时其相轨迹不会逃离它.最后,状态受限情况下倒立摆系统的控制设计验证了该算法的有效性.

Second-order sliding mode control design subject to sliding variable constraints

In real system, the state constraints are ubiquitous. Thus it is of great theoretical and engineering significance to consider the control design problem under state constraints. In this paper, the problem of second-order sliding mode (SOSM) controller design under sliding variable constraints is considered. Firstly, by using the Lyapunov method, a kind of new SOSM controller is presented without considering the sliding variable constraints. It is proved that the sliding variable will be stabilized to the equilibrium point in a finite time under the designed SOSM controller. Secondly, considering the case that the sliding variable is restricted to be in a preset region, it is also proved that there is a domain of attraction associated with the control parameters in the restricted region so that its phase trajectory will not escape from the attractive domain when the initial states are within it. Finally, the control of the inverted pendulum under state constraints is given to demonstrate the effectiveness of the proposed algorithm.