任意初态偏移下连续系统两阶段迭代学习控制

doi:10.12341/jssms21691

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (7): 1700-1714.DOI: 10.12341/jssms21691

• • 上一篇

任意初态偏移下连续系统两阶段迭代学习控制

李国军, 卢甜甜, 范英盛

浙江警察学院公共基础部, 杭州 310053

收稿日期:2021-12-06 修回日期:2022-03-08 发布日期:2022-08-31
通讯作者: 卢甜甜,Email:lutiantian@zjjcxy.cn.
基金资助:
北京东方计量测试研究所刘尚合院士专家工作站静电研究基金(BOIMTLSHJD20182001)资助课题.

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李国军, 卢甜甜, 范英盛. 任意初态偏移下连续系统两阶段迭代学习控制[J]. 系统科学与数学, 2022, 42(7): 1700-1714.

LI Guojun, LU Tiantian, FAN Yingsheng. Two-Phase Iterative Learning Control for Continuous Systems with Random Initial State Shifts[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1700-1714.

Two-Phase Iterative Learning Control for Continuous Systems with Random Initial State Shifts

LI Guojun, LU Tiantian, FAN Yingsheng

Basic Courses Department, Zhejiang Police College, Hangzhou 310053

Received:2021-12-06 Revised:2022-03-08 Published:2022-08-31

针对任意初态偏差下的一阶状态跟踪系统,文章采取了两阶段迭代学习控制策略.首先,借助差分项将一阶非线性微分方程转换成线性非齐次微分方程,并根据一阶线性非齐次微分方程解的特点和初态偏差值选择合适的控制增益,确保系统稳定并在某个固定时刻达到稳态偏差输出.其次,在系统已经达到固定偏差输出的前提下,文中提供了两种固定偏差修正方法,即偏差修正控制和变轨迹控制.理论分析表明,文章所提的两阶段迭代学习控制策略能够确保系统在指定区间达到完全跟踪.最后的仿真验证了所提算法的有效性.

关键词： 迭代学习控制, 一阶微分方程, 初始修正, 收敛

Aiming at the first-order state tracking systems with arbitrary initial state shifts, this paper presents a two-phase iterative learning control strategy. Firstly, by means of difference terms, the first-order nonlinear differential equation is converted into a first-order linear non-homogeneous differential equation. Utilizing the form of solution of the first-order linear non-homogeneous differential equation and the initial state shifts, we can select the appropriate control gain to ensure that the systems are stable and reach the stable output at a fixed time. Secondly, on the premise that the systems have reached the fixed output, two methods are proposed for rectifying the fixed shifts, namely, shifts rectifying control and alternative trajectory control. Theoretical analysis shows that the two-phase iterative learning control strategy proposed in this paper can ensure that the systems achieve complete tracking in the specified interval. The final simulations verify the effectiveness of the proposed algorithm.

Key words: Iterative learning control, first-order differential equation, initial rectifying, convergence

MR(2010)主题分类:

93C05
93C15

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