未知有界扰动切换系统的PID控制:区间观测器方法  

Interval Observer Based PID Control for Switching Systems with Unknown Bounded Disturbances

作　　者：李新 洪琦格 程凯杰 朱良宽[2] LI Xin;HONG Qige;CHENG Kaijie;ZHU Liangkuan(College of Computer and Control Engineering,Northeast Forestry University,Harbin 150040,China;College of Mechanical and Electrical Engineering,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学计算机与控制工程学院,哈尔滨150040 [2]东北林业大学机电工程学院,哈尔滨150040

出　　处：《小型微型计算机系统》2025年第2期493-503,共11页Journal of Chinese Computer Systems

基　　金：国家博士后基金第73批面上项目(2023M730528)资助;黑龙江省优秀青年(YQ2023F002)资助;黑龙江省博士后项目(LBH-Z22053)资助;中央高校基本科研业务费专项资金项目(2572023CT15-05,2572022BF05)资助。

摘　　要：本文研究了一类具有未知有界扰动的离散时间非线性切换系统的基于区间观测器的PID控制问题.基于正系统理论为这类切换系统设计了一种区间观测器用于估计系统状态的上下界,并根据估计的系统状态边界设计了离散时间PID控制律.随后,利用增广技术以及多Lyapunov稳定性分析方法,以线性矩阵不等式的形式给出了保证估计误差系统和闭环系统全局一致渐近稳定的充分条件.此外,通过求解线性矩阵不等式,得到了区间观测器增益和PID控制器增益,进一步保证了闭环系统的H∞性能.最后,通过一个数值仿真验证了所提方法的正确性和有效性.This paper is concerned with the problem of PID control based on interval observer for a class of discrete-time nonlinear switching systems with unknown bounded disturbances.An interval observer is designed for the switching systems with unknown bounded disturbances to estimate the upper and lower bounds of the system state based on positive system theory,and a discrete-times PID control law is given based on the estimated system state bounds.In addition,sufficient conditions to ensure globally consistent asymptotic stability of the estimation error system and the closed-loop system are given in the form of linear matrix inequalities(LMIs)using the augmentation technique and the multi-Lyapunov stability analysis method.Furthermore,the interval observer gain and the PID controller gain are obtained by solving the LMIs,which further ensures the H∞performance of the closed-loop system.Finally,a numerical simulation verifies the correctness and effectiveness of the proposed method.

关 键 词：区间观测器 切换系统 PID控制 有界扰动 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]