| 引用本文: | 刘艳,阮小娥.线性时不变系统PID–型迭代学习控制律的单调收敛形态[J].控制理论与应用,2020,37(9):1873~1879.[点击复制] |
| LIU Yan,RUAN Xiao-e.Monotonic convergence characteristics of PID-type iterative learning control for linear time-invariant systems[J].Control Theory and Technology,2020,37(9):1873~1879.[点击复制] |
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| 线性时不变系统PID–型迭代学习控制律的单调收敛形态 |
| Monotonic convergence characteristics of PID-type iterative learning control for linear time-invariant systems |
| 摘要点击 2709 全文点击 1022 投稿时间：2019-09-08 修订日期：2020-04-16 |
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| DOI编号 10.7641/CTA.2020.90759 |
| 2020,37(9):1873-1879 |
| 中文关键词 迭代学习控制 积分补偿 Lebesgue-p范数 收敛性 |
| 英文关键词 iterative learning control integral compensation Lebesgue-p norm convergence |
| 基金项目 国家自然科学基金 |
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| 中文摘要 |
| 传统的迭代学习控制机理中, 积分补偿是典型的策略之一, 但其跟踪效用并不明确. 本文针对连续线性时
不变系统, 对传统的PD–型迭代学习控制律嵌入积分补偿, 利用分部积分法和推广的卷积Young不等式, 在Lebesgue-
p范数意义下, 理论分析一阶和二阶PID–型迭代学习控制律的收敛性态. 结果表明, 当比例、积分和导数学习增益满
足适当条件时, 一阶PID–型迭代学习控制律是单调收敛的, 二阶PID–型迭代学习控制律是双迭代单调收敛的. 数值
仿真验证了积分补偿可有效地提高系统的跟踪性能. |
| 英文摘要 |
| For conventional iterative learning control (ILC) mechanism, the integral compensation is one of typical
strategies but the effect on the tracking performance is ambiguous. This paper exploits the embedment of the integral compensation
into the conventional PD-type ILC rule for linear continuous-time-invariant systems. By taking advantages of
the generalized Young inequality of convolution integral, the convergence characteristics of the first-order and the secondorder
PID-type ILCs are analyzed, while the tracking error is measured in the form of Lebesgue-p norm. The theoretical
analysis manifests that the first-order PID-type ILC is monotonously convergent whilst the second-order PID-type ILC is
bi-iteratively monotonously convergent under the assumption that the proportional, integral and derivative learning gains
appropriately chosen. Numerical simulations present that an appropriate integration action may enhance the tracking performance. |