基于观测器的一类连续非线性系统的采样控制

Observer-based Sampled-data Control for a Class of Continuous Nonlinear Systems

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器.接下来利用零阶保持法对连续时间状态反馈控制器进行离散化,获得了状态反馈采样控制器;利用零阶保持法对基于连续时间观测器的连续时间控制器离散化,获得了基于连续时间观测器的采样控制器;利用Euler法对连续时间观测器离散化,同时利用零阶保持法对控制器离散化,从而获得了采样观测器和基于采样观测器的采样控制器.本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定,而基于采样观测器的采样控制器可以保证被控对象的状态是有界的,其最终边界依赖于设计参数与采样周期.最后,通过选择适当的采样周期,完成了闭环采样控制系统的设计.一个船舶航向控制的例子表明应用本文所提方法设计出的三种采样控制器具有良好的控制效果.

In this paper,we firstly use the backstepping method to design the continuous-time state feedback controller,continuous-time observer and continuous-time observer-based controller for a class of nonlinear systems.Then,we obtain the state feedback sampled-data controller and the sampled-data controller based on the continuous-time observer,respectively by discretizing the continuous-time state feedback controller and the continuous-time observer-based controller using zero-hold method.Correspondingly,we employ the Euler method to discretize the continuous-time observer and use the zero-hold method to discretize the continuous-time observerbased controller,then we obtain the sampled-data observer and the sampled-data controller based on the sampled-data observer.This paper proves that the state feedback sampled-data controller and the sampled-data controller based on continuous-time observer can guarantee the asymptotic stability of the closed-loop system.The paper also proves that the sampled-data controller based on sampled-data observer can guarantee that the states of plant are bound,and the boundaries are dependent on the designed parameters and sampling period.Finally,we complete the design of sampled closed-loop system after choosing an appropriate sampling period.An example applied to ship course-keeping control shows that the three types of sampleddata controllers can achieve favorable performance.