Iterative learning fault-tolerant control for batch processes based on T-S fuzzy model

doi:10.11949/j.issn.0438-1157.20161608

Abstract

Abstract:

Batch processes are not with highly nonlinearity, but also suffer from the actuator failures. Study of the stability of nonlinear batch processes under failure conditions is of great significance. With considering on the actuator gain faults and the highly nonlinearity, a new T-S fuzzy model-based iterative learning fault-tolerant control method is proposed for nonlinear batch process. Firstly, the T-S fuzzy model is employed to represent the nonlinear batch process. Then a 2D compound iterative learning fault-tolerant controller is proposed by exploiting the 2D and repetitive nature of batch processes, and the equivalent 2D Rosser model of the fuzzy model is constructed. Lastly, the sufficient condition guaranteeing the system stable is given through a Lyapunov function method, and the controller gains are designed in terms of linear matrix inequalities (LMIs). Simulation to a highly nonlinear continuous stirred tank reactor (CSTR) demonstrates the feasibility and efficiency of the proposed method.

Key words: batch processes, 2D T-S fuzzy model, fuzzy iterative learning fault-tolerant control, process control, stability, systems engineering

摘要：

间歇过程不仅具有强非线性，同时还会受到诸如执行器等故障影响，研究非线性间歇过程在具有故障的情况下依然稳定运行至关重要。针对执行器增益故障及系统所具有的强非线性，提出一种新的基于间歇过程的T-S模糊模型的复合迭代学习容错控制方法。首先根据间歇过程的非线性模型，利用扇区非线性方法建立其T-S模糊故障模型，再利用间歇过程的二维特性与重复特性，在2D系统理论框架内，设计2D复合ILC容错控制器，进而构建此T-S模糊模型的等价二维Rosser模型，接着利用Lyapunov方法给出系统稳定充分条件并求解控制器增益。针对强非线性的连续搅拌釜进行仿真，结果表明所提出方法具有可行性与有效性。

关键词: 间歇过程, 2D T-S模糊模型, 模糊迭代学习容错控制, 过程控制, 稳定, 系统工程

CLC Number:

TB114.43

WANG Limin, YANG Jisheng, YU Jingxian, LI Bingyun, GAO Furong. Iterative learning fault-tolerant control for batch processes based on T-S fuzzy model[J]. CIESC Journal, 2017, 68(3): 1081-1089.

王立敏, 杨继胜, 于晶贤, 李秉芸, 高福荣. 基于T-S模糊模型的间歇过程的迭代学习容错控制[J]. 化工学报, 2017, 68(3): 1081-1089.

References 29

[1]	SHAO C, GAO F R, YANG Y. Robust stability of optimal iterative learning control and application to injection molding machine[J]. Automatica, 2003, 29(1):72-79.
[2]	WANG Y Q, ZHOU D H, GAO F R. Iterative learning fault-tolerant control for batch processes[J]. Industrial and Engineering Chemistry Research, 2006, 45(26):9050-9060.
[3]	WANG L M, MO S Y, QU H Y, et al. H∞ design of 2D controller for batch processes with uncertainties and interval time-varying delays[J]. Control Engineering Practice, 2013, 21(10):1321-1333.
[4]	WANG Y Q, ZHOU D H, GAO F R. Iterative learning reliable control of batch processes with sensor faults[J]. Control Engineering Science, 2008, 63(4):1039-1051.
[5]	杨国军, 李秀喜, 陈赟, 等. 间歇过程实时优化[J]. 化工学报, 2011, 62(10):2839-2844. YANG G J, LI X X,CHEN Y, et al. Real-time optimization for batch process[J]. CIESC Journal, 2011, 62(10):2839-2844.
[6]	叶凌箭, 马修水, 宋执环. 不确定性间歇过程的一种实时优化控制方法[J]. 化工学报, 2014, 65(9):3535-3543. YE L J, MA X S, SONG Z H. A real-time optimization approach for uncertain batch processes[J]. CIESC Journal, 2014, 65(9):3535-3543.
[7]	SHI J, GAO F R, WU T J. Robust design of integrated feedback and iterative learning control of a batch process based on a 2D roesser system[J]. Journal of Process Control, 2005, 15(8):907-924.
[8]	SHI J, GAO F R, WU T J, et al. Robust iterative learning control design for batch processes with uncertain perturbations and initialization[J]. AIChE J., 2006, 52(6):2171-2187.
[9]	SHI J, GAO F R, WU T J. Two-dimensional linear quadratic optimal control to iterative learning control[J]. Industrial and Engineering Chemical Research, 2006, 45(13):4603-4616.
[10]	SHI J, GAO F R, WU T J. Two-dimensional linear quadratic optimal controls and system analysis[J]. Industrial and Engineering Chemical Research, 2006, 45(13):4617-4628.
[11]	SHI J, YANG B, CAO Z K, et al. Two-dimensional generalized predictive control (2D-GPC) scheme for the batch processes with two-dimensional (2D) dynamics[J]. Multi dimensional Systems and Signal Processing, 2015, 26(4):941-966.
[12]	LIU T, WANG Y Q.A synthetic approach for robust constrained iterative learning control of piecewise affine batch processes[J]. Automatic, 2012, 48(11):2762-2775.
[13]	WANG L M, CHEN X, GAO F R. Delay-range-dependent robust BIBO stabilization of a class of uncertain 2-D discrete delayed systems via LMI approach[C]//The 19th World Congress of the International Federation of Automatic Control (IFAC). Cape Town, South Africa, 2014, 19(1):10994-10999.
[14]	蒋丽英,王树青.基于MPCA-MDPLS的间歇过程的故障诊断[J]. 化工学报, 2005, 56(3):482-486. JIANG L Y, WANG S Q. Fault diagnosis for batch processes based on MPCA-MDPLS[J]. Journal of Chemical Industry and Engineering(China), 2005, 56(3):482-486.
[15]	郭金玉, 袁堂明, 李元. 一种不等长的多模态间歇过程故障检测方法[J]. 化工学报, 2016, 67(7):2916-2924. GUO J Y, YUAN T M, LI Y. Fault detection method for uneven-length multimode batch processes[J]. CIESC Journal, 2016, 67(7):2916-2924.
[16]	齐咏生, 王普, 高学金, 等. 一种基于改进MPCA的间歇过程监控与故障诊断方法[J]. 化工学报, 2009, 60(11):2838-2846. QI Y S, WANG P, GAO X J,et al. Batch process monitoring and fault diagnosis based on improved multi-way principal component analysis[J]. CIESC Journal, 2009, 60(11):2838-2846.
[17]	刁英湖, 陆宁云, 姜斌. 一种针对间歇过程过渡状态的故障诊断方法[J]. 化工学报, 2008, 59(7):1778-1782. DIAO Y H, LU N Y, JIANG B. Fault diagnosis during batch process transition[J]. Journal of Chemical Industry and Engineering(China), 2008, 59(7):1778-1782.
[18]	祁鹏程, 赵忠盖, 刘飞. 含时滞测量值下间歇过程的双维状态估计[J]. 化工学报, 2016, 67(9):3784-3792. QI P C, ZHAO Z G, LIU F. Two dimensional state estimation in batch process with delayed measurements[J]. CIESC Journal, 2016, 67(9):3784-3792.
[19]	邸丽清, 熊智华, 阳宪惠. 基于MKPLS和SQP方法的间歇过程迭代优化控制[J]. 化工学报, 2007, 58(12):3102-3107. DI L Q, XIONG Z H, YANG X H. Iterative optimal control for batch processes based on MKPLS and SQP methods[J]. Journal of Chemical Industry and Engineering(China), 2007, 58(12):3102-3107.
[20]	叶凌箭, 宋执环, 马修水. 间歇过程的批间自优化控制[J]. 化工学报, 2015, 66(7):2573-2580. YE L J, SONG Z H, MA X S. Batch-to-batch self-optimizing control for batch processes[J]. CIESC Journal, 2015, 66(7):2573-2580.
[21]	王志文, 刘毅, 高增梁. 时变间歇过程的2D-PID自适应控制方法[J]. 化工学报, 2016, 67(3):991-997. WANG Z W, LIU Y, GAO Z L.D-PID adaptive control method for time-varying batch processes[J]. CIESC Journal, 2016, 67(3):991-997.
[22]	叶凌箭, 马修水, 宋执环. 基于输入轨迹参数化的间歇过程迭代学习控制[J]. 化工学报, 2016, 67(3):743-750. YE L J, MA X S, SONG Z H. Iterative learning control of batch process with input trajectory parameterization[J]. CIESC Journal, 2016, 67(3):743-750.
[23]	史洪岩, 苑明哲, 王天然, 等. 间歇过程动态优化方法综述[J]. 信息与控制, 2012, 41(1):75-82. SHI H Y, YUAN M Z, WANG T R, et al. A survey on dynamic optimization methods of batch processes[J]. Information and Control, 2012, 41(1):75-82.
[24]	常玉清, 王姝, 谭帅, 等. 基于多时段MPCA模型的间歇过程监测方法研究[J]. 自动化学报, 2010, 36(9):1312-1320. CHANG Y Q, WANG S, TAN S, et al. Research on multistage-based MPCA modelling and monitoring method for batch processes[J]. Acta Automatica Sinica, 2010, 36(9):1312-1320.
[25]	谢磊, 何宁, 王树青.步进MPCA及其在间歇过程监控中的应用[J]. 高校化学工程学报, 2004, 16(5):643-647. XIE L, HE N, WANG S Q. Step-by-step adaptive MPCA applied to an industrial batch process[J]. Journal of Chemical Engineering of Chinese Universities, 2004, 16(5):643-647.
[26]	董久祥.T-S模糊系统的若干控制问题研究[D].沈阳:东北大学, 2009. DONG J X. Research of some control problems based on T-S fuzzy system[D]. Shenyang:Northeastern University, 2009.
[27]	TANG G Y, HUANG D M, DENG Z.T-S fuzzy model based generalized predictive control of vehicle yaw stability[J]. Kybernetes, 2012, 41(9):1261-1268.
[28]	HAN L, QIU C, XIAO J. Finite-time H∞ control synthesis for nonlinear switched systems using T-S fuzzy model[J]. Neurocomputing, 2016, 171(C):156-170.
[29]	TANAKA K, WANG H O. Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach[M]. New York:John Wiley & Sons, 2001.