The proportional-integral-derivative (PID) controller is standard technique for controlling the industrial batch process. However, the parameter tuning and updating of PID controller has been a challenging topic for control engineers especially for the real system having initial state error, state and output disturbances. In this paper, a kind of robust optimal iterative learning control (ILC) scheme is suggested to update the PID gains for the linear system with initial state error, state and output disturbances. The quadratic performance criteria is considered, which constitute of the error and input slew rate, and the robust BIBO stability is investigated theoretically for the proposed PID type ILC scheme. In addition, the bound of the tracking error has been calculated by using Lyapunov composite energy function. Simulation examples are also given to demonstrate the effectiveness of the proposed scheme in term of its ability to deal with linear as well as nonlinear system

中文翻译：

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用于线性批处理的鲁棒优化 PID 类型 ILC

比例积分微分 (PID) 控制器是控制工业批处理过程的标准技术。然而，PID 控制器的参数整定和更新一直是控制工程师的一个具有挑战性的课题，尤其是对于具有初始状态误差、状态和输出扰动的真实系统。在本文中，提出了一种鲁棒的最优迭代学习控制 (ILC) 方案来更新具有初始状态误差、状态和输出扰动的线性系统的 PID 增益。考虑了由误差和输入转换率构成的二次性能标准，并从理论上研究了所提出的 PID 类型 ILC 方案的稳健 BIBO 稳定性。此外，利用Lyapunov复合能量函数计算了跟踪误差的界限。