具有量化输入和边界扰动的柔性臂边界振动滑模控制

Boundary vibration sliding mode control of a flexible arm with quantized input and boundary disturbance

本文针对量化输入和有界扰动下柔性臂系统的振动抑制和边界滑模控制器设计问题开展研究.柔性臂的动态特性由偏微分方程表示的分布参数模型描述.对于具有未知有界干扰的柔性臂系统,其主要控制目标是减小干扰的影响,使柔性臂到达期望角度并同时抑制系统的振动.首先,利用边界输出信号构造滑模函数和滑模面.其次,结合所构造的滑模面,设计一种边界滑模控制器,并利用算子半群理论证明了闭环系统的适定性.所提出的边界滑模控制策略保证了系统状态能够在有限时间内到达滑模面,并且系统状态在滑模面上是指数收敛的.最后,通过物理实验验证了所提出控制策略的有效性.

In this paper,the problems of vibration suppressing and boundary sliding mode control of a flexible arm system with quantized input and bounded disturbance are addressed.The dynamic characteristic of the flexible arm is described by a distributed parameter model in the form of partial differential equations.For a flexible arm system with unknown bounded disturbance,the main control objective is to reduce the influence of the disturbance such that the flexible arm can reach the desired angular position and suppress the vibration of the system,simultaneously.Firstly,the sliding mode function and the sliding surface are constructed by using the boundary signals.Then,a boundary sliding mode controller is proposed and the well-posedness of the closed-loop system is proven through the operator semigroup theory.Under the proposed boundary sliding mode controller,the system state can reach the sliding surface in finite time and the exponential convergence of the system state is guaranteed on the sliding surface.Finally,the effectiveness of the proposed control strategy is verified through physical experiments.