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 247  全文点击 119  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
作者单位邮编
刘艳 西安交通大学 710049
阮小娥 西安交通大学 710049
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.