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Abstract and Applied Analysis
Volume 2012, Article ID 748981, 21 pages
Research Article

Optimal Iterative Learning Fault-Tolerant Guaranteed Cost Control for Batch Processes in the 2D-FM Model

1College of Sciences, Liaoning Shihua University, Fushun 113001, China
2Fok Ying Tung Graduate School, Hong Kong University of Science and Technology, Hong Kong
3Department of Control Science and Engineering, Zhejiang University, Zhejiang 310027, China

Received 2 January 2012; Accepted 22 February 2012

Academic Editor: Pavel Drábek

Copyright © 2012 Limin Wang and Weiwei Dong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops the optimal fault-tolerant guaranteed cost control scheme for a batch process with actuator failures. Based on an equivalent two-dimensional Fornasini-Marchsini (2D-FM) model description of a batch process, the relevant concepts of the fault-tolerant guaranteed cost control are introduced. The robust iterative learning reliable guaranteed cost controller (ILRGCC), which includes a robust extended feedback control for ensuring the performances over time and an iterative learning control (ILC) for improving the tracking performance from cycle to cycle, is formulated such that it cannot only guarantee the closed-loop convergency along both the time and the cycle directions but also satisfy both the performance level and a cost function having upper bounds for all admissible uncertainties and any actuator failures. Conditions for the existence of the controller are derived in terms of linear matrix inequalities (LMIs), and a design procedure of the controller is presented. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop system cost. Finally, an illustrative example of injection molding is given to demonstrate the effectiveness and advantages of the proposed 2D design approach.