International Journal of Control, Automation and Systems 18(X) (2020) 1-11 http://dx.doi.org/10.1007/s12555-019-1033-1 ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555 Robust Optimal PID type ILC for Linear Batch Process Furqan Memon and Cheng Shao* Abstract: 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 Keywords: Discrete-time system, iterative learning control (ILC), parameter optimal ILC, PID iterative learning control. 1. INTRODUCTION Due to the PID controller’s better good performance, simple structure, and robustness, it is still considered as a standard tool to solve the automatic control problem of in- dustrial processes. However, the better performance of the PID controller depends strongly on the proper choice of the PID parameters. Some efforts are made to update PID parameters, such as fuzzy logic [1], neural network [2], adaptive [3] and etc. For batch/repetitive processes, itera- tive learning control (ILC) is known as an effective control strategy to optimize control performance from iteration to iteration. Hence, it is motivated to apply ILC schemes to update PID parameters for the batch processes. ILC is an effective control technique to realize perfect tracking for the batch process. The main principle of ILC is to use the error informa- tion from the previous iteration to enhance the input or learning gains for the subsequent trial, such that perfect or bounded tracking of the reference trajectory can be at- tained. ILC method for computing such input was first ad- dressed in 1978 by Uchiyama [4] and later mathematically formulated by Arimoto et al. in 1984 [5]. Afterward, sig- nificant research efforts have been devoted to the ILC de- sign to deal with actual batch process, for the improve- ment of tracking performance and convergence rate. In or- der to deal with linear and non-linear batch processes, re- searchers have recommended many techniques for attain- ing perfect tracking in both continuous- and discrete-time domains [6, 7]. The efficacy of ILC has been demonstrated in literature with the applications in the field of robotics, mechatronics, manufacturing, building control, nuclear fusion, rehabilitation, and in network control [8–16]. ILC consists of many varieties, which have been de- veloped to expedite the convergence rate of tracking er- ror such as optimal ILC [9], [11] parameter optimization [17, 18], Model Predictive Control ILC [19, 20] and oth- ers. As known, the major challenge to ILC is to acquire error convergence iteratively even if there is uncertainty in the plant model. The robustness of the various ILC tech- niques against model uncertainty has been studied in the literature, such as inverse model-based ILC [21], norm- optimal ILC [22] and two dimensional learning systems [23, 24]. The robustness against model uncertanity in ILC design has also been investigated in frequency domain [25, 26]. There are some ILC approaches that explicitly considered model uncertainty to improve robust conver- gence and performance, such as author in [27] used the convex optimization methods to calculate the LMI dealing with time-varying model uncertainty. In [28], the author investigates the use of time-varying filtering and [29] de- velops an averaging technique over uncertain models for a robustly converging algorithm. Recently, a robust worst- case norm-optimal ILC technique [30] is presented, which Manuscript received December 11, 2019; revised May 6, 2020; accepted June 2, 2020. Recommended by Associate Editor Changsun Ahn under the direction of Editor Kyoung Kwan Ahn. This work is partly financially supported by the High-tech Research and Development Program of China (2014AA041802). The first author is also thankful to the China Scholarship Council (CSC) for providing financial support for his Ph.D. studies at Dalian University of Technology, China. Furqan Memon and Cheng Shao are with the Institute of Advanced Control, Dalian University of Technology, Dalian 116024, Liaoning, China (e-mails: furqan@mail.dlut.edu.cn, cshao@dlut.edu.cn). * Corresponding author. c ICROS, KIEE and Springer 2020