Research on Discrete-time VSS Control

本文对离散VSS控制进行了研究。首先，基于（Furuta, 1990）中提出的滑动扇区概念，分别利用状态空间方程和传递函数设计了两个离散VSS控制器。其次，对离散系统定义了一个新的滑动扇区，其中系统状态范数减小；设计了一种离散VSS控制器，将状态从外部传递到滑动扇区内部。采用最优控制理论对滑动扇形进行设计。最后，将所提出的VSS控制方法应用于旋转倒立摆系统和柔性传动系统等实际系统的控制。作为实验装置，设计了倒立摆系统。给出了仿真结果和实验结果。

In this report, the research on the discrete-time VSS control is presented. Firstly, two discrete-time VSS controllers are designed based on the concept of the sliding sector proposed in (Furuta, 1990) by using state space equation and transfer function, respectively. Secondly, a new sliding sector, inside which a norm of the system state decreases, is defined for discrete-time systems. A discrete-time VSS controller is designed to transfer the state from the outside to the inside of the sliding sector. The optimal control theory is used to design the sliding sector. Finally, the proposed VSS control methods are applied to the control of some practical systems like as the rotational inverted pendulum system and the flexible transmission system. As an experimental divice, an inverted pendulum system is design. The simulation results and experiment results are given.