## Abstract and Applied Analysis

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

#### Abstract

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 ${H}_{\infty }$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 748981, 21 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495699

Digital Object Identifier
doi:10.1155/2012/748981

Mathematical Reviews number (MathSciNet)
MR2922917

Zentralblatt MATH identifier
1242.93095

#### Citation

Wang, Limin; Dong, Weiwei. Optimal Iterative Learning Fault-Tolerant Guaranteed Cost Control for Batch Processes in the 2D-FM Model. Abstr. Appl. Anal. 2012 (2012), Article ID 748981, 21 pages. doi:10.1155/2012/748981. https://projecteuclid.org/euclid.aaa/1355495699

#### References

• Anon, “Automatic control of batch-process temperature,” Food Industries, vol. 8, no. 5, pp. 237–244, 1936.
• E. Korovessi and A. A. Linninger, Batch Processes, CRC/Taylor and Francis, Boca Raton, Fla, USA, 2006.
• D. Ye and G. H. Yang, “Delay-dependent reliable H$\infty$ control for linear time-varying delay systems via adaptive approach,” in American Control Conference (ACC '07), pp. 3991–3996, July 2007.
• D. Yue and J. Lam, “Reliable memory feedback design for a class of non-linear time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 14, no. 1, pp. 39–60, 2004.
• D. Yue, J. Lam, and D. W. C. Ho, “Reliable H$\infty$ control of uncertain descriptor systems with multiple time delays,” IEE Proceedings: Control Theory and Applications, vol. 150, no. 6, pp. 557–564, 2003.
• Y. Wang, J. Shi, D. Zhou, and F. Gao, “Iterative learning fault-tolerant control for batch processes,” Industrial and Engineering Chemistry Research, vol. 45, no. 26, pp. 9050–9060, 2006.
• Y. Wang, D. Zhou, and F. Gao, “Iterative learning reliable control of batch processes with sensor faults,” Chemical Engineering Science, vol. 63, no. 4, pp. 1039–1051, 2008.
• Y. Wang, Y. Yang, D. Zhou, and F. Gao, “Active fault-tolerant control of nonlinear batch processes with sensor faults,” Industrial and Engineering Chemistry Research, vol. 46, no. 26, pp. 9158–9169, 2007.
• F. Gao, Y. Yang, and C. Shao, “Robust iterative learning control with applications to injection molding process,” Chemical Engineering Science, vol. 56, no. 24, pp. 7025–7034, 2001.
• D. Gorinevsky, “Loop shaping for iterative control of batch processes,” IEEE Control Systems Magazine, vol. 22, no. 6, pp. 55–65, 2002.
• Z. Xiong and J. Zhang, “Product quality trajectory tracking in batch processes using iterative learning control based time-varying perturbation models,” Industrial and Engineering Chemistry Research, vol. 42, no. 26, pp. 6802–6814, 2003.
• J. Shi, F. Gao, and T. J. Wu, “From two-dimensional linear quadratic optimal control to iterative learning control. Paper 1. Two-dimensional linear quadratic optimal controls and system analysis,” Industrial and Engineering Chemistry Research, vol. 45, no. 13, pp. 4603–4616, 2006.
• J. Shi, F. Gao, and T. J. Wu, “From two-dimensional linear quadratic optimal control to iterative learning control. Paper 2. Iterative learning controls for batch processes,” Industrial and Engineering Chemistry Research, vol. 45, no. 13, pp. 4617–4628, 2006.
• J. Shi, F. Gao, and T. J. Wu, “Single-cycle and multi-cycle generalized 2D model predictive iterative learning control (2D-GPILC) schemes for batch processes,” Journal of Process Control, vol. 17, no. 9, pp. 715–727, 2007.
• J. Shi, F. Gao, and T. J. Wu, “Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system,” Journal of Process Control, vol. 15, no. 8, pp. 907–924, 2005.
• J. Shi, F. Gao, and T. J. Wu, “Robust iterative learning control design for batch processes with uncertain perturbations and initialization,” AIChE Journal, vol. 52, no. 6, pp. 2171–2187, 2006.
• J. Shi, F. Gao, and T. J. Wu, “Integrated design and structure analysis of robust Iterative learning control system based on a two-dimensional model,” Industrial and Engineering Chemistry Research, vol. 44, no. 21, pp. 8095–8105, 2005.
• S. S. L. Chang and T. K. C. Peng, “Adaptive guaranteed cost control of systems with uncertain parameters,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 474–483, 1972.
• A. Dhawan and H. Kar, “Optimal guaranteed cost control of 2-DčommentComment on ref. [19a?]: We split this reference to [19a,19b, 19c?]. Please check. discrete uncertain systems: an LMI approach,” Signal Processing, vol. 87, no. 12, pp. 3075–3085, 2007.
• A. Dhawan and H. Kar, “An lmi approach to robust optimal guaranteed cost control of 2-d discrete systems described by the roesser model,” Signal Processing, vol. 90, no. 9, pp. 2648–2654, 2010.
• A. Dhawan and H. Kar, “An improved LMI-based criterion for the design of optimal guaranteed cost controller for 2-D discrete uncertain systems,” Signal Processing, vol. 91, no. 4, pp. 1032–1035, 2011.
• I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems & Control Letters, vol. 8, no. 4, pp. 351–357, 1987.
• S. Boyd, L. E. Ghaoui, E. Feron et al., Linear Matrix Inequality in System and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994.