Fault-tolerant iterative learning control for batch processes with time-varying state delays and uncertainties

Abstract

A proportional-derivative (PD)-type iterative learning control (ILC) combined with fault-tolerant control (FTC) for a discrete-time batch process with time-varying delays and uncertainties is presented in this paper. The main goals of paper are to drive the considered output profile to the desired reference with the avoidance of possible process faults, delays and uncertainties. First, the nonlinear estimation problem is simplified to the linear one by introducing an appropriate system reparametrisation to deal with the problem of the simultaneous estimation of state and process fault. Second, to solve the problem of time-varying delays and uncertainties, this paper makes use of the two-dimensional (2-D) and repetitive characteristics of batch processes and introduces the state error, tracking error and estimation error to establish the dynamics model of FTILC that is eventually converted into a linear repetitive process model. Then, sufficient conditions based on the Lyapunov–Krasovskii theory and $H_{\mathrm{\infty }}$ methodology are established to ensure the robust stability along the trial in according with linear matrix inequalities (LMIs) for all uncertainties. Finally, this paper manifests the effectiveness of the proposed sufficient conditions by a simulation of injection moulding process.

Keywords:

• Batch processes
• iterative learning control
• fault-tolerant
• time-delay

Disclosure statement

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

If anyone who wants to get the simulation data can contact the corresponding author by email ([email protected]).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the Natural Science Foundation of Jiangsu Province, China (Grant No.BK20201159).

Notes on contributors

Hua Chen

Hua Chen was born in Jiangsu Province, China, on November 18, 1978. He received the B.S. degree from the Department of Mathematics at Yangzhou University, China, 2001, received the M.S. degree from the Department of Management Sciences and Engineering at Nanjing University, China in 2009, and received the Ph.D. degree from the Department of Control Science and Engineering at University of Shanghai for Science and Technology, China in 2012. Currently, he is a professor in the School of Mathematics at Hohai University. His main research interests include modelling and control of complex nonlinear systems, stability analysis, time delay systems, motion control of underactuated systems such as wheeled mobile robots, unmanned surface vehicles, and inspection robots, etc.

Rui Xu

Rui Xu was born in Zaozhuang, China. She M. S. candidate in the School of Mathematics at Hohai University. Her research interests cover nonlinear systems, time delay systems and iterative learning control.

Yao Tang

Yao Tang was born in Suqian, China. She M. S. candidate in the School of Mathematics at Hohai University. Her researc nterests cover fault diagnosis and fault-tolerant control.

Xinyuan Long

Xinyuan Long was born in Lianyungang, China. She M. S. candidate in the School of Mathematics at Hohai University. Her research interests cover nonlinear systems and non-fragile control.