Robust Model Predictive Iterative Learning Control With Iteration-varying Reference Trajectory
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摘要: 迭代学习模型预测控制是针对间歇过程的先进控制方法.它能通过迭代高精度跟踪给定参考轨迹，并保证时域上的闭环稳定性.然而，现有的迭代学习模型预测控制算法大多基于线性/线性化系统，且没有考虑参考轨迹变化的情况.本文基于线性参变系统提出一种能有效跟踪变参考轨迹的鲁棒迭代学习模型预测控制算法.首先，采用线性参变模型准确涵盖原始非线性系统的动态特性.然后，将鲁棒H∞控制与传统迭代学习模型预测控制相结合，抑制变参考轨迹带来的跟踪误差波动，通过优化线性矩阵不等式约束下的目标函数求得控制输入.深入分析了鲁棒迭代学习模型预测控制的鲁棒稳定性和迭代收敛性.最后，通过对数值例子和连续搅拌反应釜系统的仿真验证了所提出算法的有效性.Abstract: Model predictive iterative learning control (MPILC) is a popular approach to control systems with repetitive nature like batch systems, as it is capable of tracking the plant reference trajectory with high accuracy and guaranteed closed-loop stability. However, the existing MPILCs are mostly based on linear/linearized system with no consideration of reference trajectory variation. In this paper, a robust MPILC (RMPILC) based on the linear parameter varying (LPV) model is derived to track the iteration-varying reference trajectory. The LPV model is chosen to represent the dynamic property of nonlinear systems accurately. Robust H∞ control is incorporated with MPILC to restrain the fluctuation of tracking errors, with control inputs solved by optimizing the objective function constrained by linear matrix inequalities. The robust stability and convergence condition of the system controlled by RMPILC are analyzed. The effectiveness of the proposed controller is verified through the simulations on a numerical example and a continuous stirred tank reactor (CSTR) system.1) 本文责任编委 魏庆来
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图 6 RMPILC控制下第5批次当$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的跟踪曲线
Fig. 6 The tracking trajectories in the fifth batch when $\varepsilon=5.8, 10, 15$
图 7 RMPILC控制下$\varepsilon=5.8$、$\varepsilon=10$和$\varepsilon=15$时的不变集$\Omega_{\tilde{x}_k}$在原状态空间的象集
Fig. 7 The image set of $\Omega_{\tilde{x}_k}$ when $\varepsilon=5.8, 10, 15$
图 8 CSTR反应温度$T$参考轨迹
Fig. 8 The reference trajectories of CSTR reaction temperature $T$
图 9 RMPILC控制下反应温度$T$参考轨迹跟踪曲线
Fig. 9 The tracking trajectories for $T$ under RMPILC control
图 10 RMPILC控制下控制输入$T_c$轨迹
Fig. 10 The trajectories of control input $T_c$ under RMPILC
表 1 $F_k(t)$优化值
Table 1 Optimized feedback control law
批次($k$) $F_k(61)$ 2 [$-$46.7539 $-$24.0899 $-$5.0529 0.0000] 3 [$-$42.9654 $-$25.0475 $-$3.7597 0.0000] 4 [$-$57.4573 $-$29.2520 $-$5.4621 $-$0.0000] 5 [$-$16.9782 $-$7.8604 $-$1.2311 $-$0.0000] 6 [$-$37.0429 $-$26.9746 $-$3.0976 0.0000] 7 [$-$41.3123 $-$27.2625 $-$2.9534 $-$0.0000] 8 [$-$54.1913 $-$32.1226 $-$4.9777 0.0000] 
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表 2 $F_k(t)$优化值
Table 2 Optimized feedback control law
批次$k$ $F_k(200)$ 2 [-7.8076 -12.6079 -7.9428 -0.0000] 3 [-8.4202 -12.9000 -8.2264 -0.0000] 4 [-7.8744 -12.6839 -7.9521 -0.0000] 5 [-8.9258 -13.1178 -8.4572 -0.0000] 6 [-9.7286 -13.2893 -9.0092 0.0000] 7 [-6.9490 -11.3713 -7.6883 0.0000] 8 [-7.5195 -12.4532 -8.0074 -0.0000] 9 [-7.7803 -12.6691 -7.9535 -0.0000]
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[1] 陆宁云, 王福利, 高福荣, 王姝.间歇过程的统计建模与在线监测.自动化学报, 2006, 32(3):400-410 http://www.aas.net.cn/CN/abstract/abstract15815.shtmlLu Ning-Yun, Wang Fu-Li, Gao Fu-Rong, Wang Shu. Statistical modeling and online monitoring for batch processes. Acta Automatic Sinica, 2006, 32(3):400-410 http://www.aas.net.cn/CN/abstract/abstract15815.shtml [2] 赵春晖, 王福利, 姚远, 高福荣.基于时段的间歇过程统计建模、在线监测及质量预报.自动化学报, 2010, 36(3):366-374 http://www.aas.net.cn/CN/abstract/abstract13676.shtmlZhao Chun-Hui, Wang Fu-Li, Yao Yuan, Gao Fu-Rong. Phase-based statistical modeling, online monitoring and quality prediction for batch processes. Acta Automatic Sinica, 2010, 36(3):366-374 http://www.aas.net.cn/CN/abstract/abstract13676.shtml [3] 池荣虎, 侯忠生, 黄彪.间歇过程最优迭代学习控制的发展:从基于模型到数据驱动.自动化学报, 2017, 43(6):917-932 http://www.aas.net.cn/CN/abstract/abstract19070.shtmlChi Rong-Hu, Hou Zhong-Sheng, Huang Biao. Optimal iterative learning control of batch processes:from model-based to data-driven. Acta Automatica Sinica, 2017, 43(6):917-932 http://www.aas.net.cn/CN/abstract/abstract19070.shtml [4] 席裕庚, 李德伟, 林姝.模型预测控制-现状与挑战.自动化学报, 2013, 39(3):221-236 http://www.aas.net.cn/CN/abstract/abstract17874.shtmlXi Yu-Geng, Li De-Wei, Lin-Shu. Model predictive control-status and challenges. Acta Automatic Sinica, 2013, 39(3):221-236 http://www.aas.net.cn/CN/abstract/abstract17874.shtml [5] 柴天佑, 李少远, 王宏.网络信息模式下复杂工业过程建模与控制.自动化学报, 2013, 39(5):469-470 http://www.aas.net.cn/CN/abstract/abstract17922.shtmlChai Tian-You, Li Shao-Yuan, Wang Hong. Networked cooperative modeling and control for complex industrial process. Acta Automatic Sinica, 2013, 39(5):469-470 http://www.aas.net.cn/CN/abstract/abstract17922.shtml [6] 孔小兵, 刘向杰.双馈风力发电机非线性模型预测控制.自动化学报, 2013, 39(5):636-643 http://www.aas.net.cn/CN/abstract/abstract17920.shtmlKong Xiao-Bing, Liu Xiang-Jie. Nonlinear model predictive control for DFIG-based wind power generation. Acta Automatic Sinica, 2013, 39(5):636-643 http://www.aas.net.cn/CN/abstract/abstract17920.shtml [7] Shen C, Shi Y, Buckham B. Trajectory tracking control of an autonomous underwater vehicle using Lyapunov-based model predictive control. IEEE Transactions on Industrial Electronics, 2018, 65(7):5796-5805 doi: 10.1109/TIE.2017.2779442 [8] Bone G M. A novel iterative learning control formulation of generalized predictive control. Automatica, 1995, 31(10):1483-1487 doi: 10.1016/0005-1098(95)00051-W [9] Shi J, Zhou H, Cao Z, Jiang Q. A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm. Journal of Process Control, 2014, 24(10):1527-1537 doi: 10.1016/j.jprocont.2014.07.004 [10] Lee K S, Chin I S, Lee H J, J. H. Lee. Model predictive control technique combined with iterative learning for batch processes. Aiche Journal, 1999, 45(10):2175-2187 doi: 10.1002/aic.690451016 [11] Oh S K, Lee J M. Iterative learning model predictive control for constrained multivariable control of batch processes. Computers & Chemical Engineering, 2016, 93(4):284-292 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ae599f5dfecdeac1d4c9c967fa90bf4d [12] Oh S K, Lee J M. Iterative learning control integrated with model predictive control for real-time disturbance rejection of batch processes. Journal of Chemical Engineering of Japan, 2017, 50(6):415-421 doi: 10.1252/jcej.16we333 [13] Lu J, Cao Z, Wang Z, Gao F. A two-stage design of two-dimensional model predictive iterative learning control for non-repetitive disturbance attenuation. Industrial & Engineering Chemistry Research, 2015, 54(21):5683-5689 http://cn.bing.com/academic/profile?id=b8a21f6d9a18ec531b27f79609e45b4f&encoded=0&v=paper_preview&mkt=zh-cn [14] Chu B, Owens D H, Freeman C T. Iterative learning control with predictive trial information:convergence, robustness, and experimental verification. IEEE Transactions on Control Systems Technology, 2016, 24(3):1101-1108 doi: 10.1109/TCST.2015.2476779 [15] Wu S, Jin Q, Zhang R, Zhang J, Gao F. Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties. ISA Transactions, 2017, 69:273-280 doi: 10.1016/j.isatra.2017.04.006 [16] Liu X, Kong X. Nonlinear fuzzy model predictive iterative learning control for drum-type boiler-turbine system. Journal of Process Control, 2013, 49:26-35 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d4d20a46865dd07ddfcdfd03c32bf88e [17] Jia L, Han C, Chiu M S. Dynamic R-parameter based integrated model predictive iterative learning control for batch processes. Journal of Process Control, 2017, 49:26-35 doi: 10.1016/j.jprocont.2016.11.003 [18] Yu Q, Hou Z. Data-driven predictive iterative learning control for a class of multiple-input and multiple-output nonlinear systems. Transactions of the Institute of Measurement & Control, 2016, 38(3):266 http://cn.bing.com/academic/profile?id=4ac1c0c9ac0fc9e1cd72c350a2eda742&encoded=0&v=paper_preview&mkt=zh-cn [19] 胡超芳, 解倩倩.非线性系统有输入饱和时基于平方和的鲁棒模型预测控制器.控制理论与应用, 2016, 33(3):321-328 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy201603007Hu Chao-Fang, Xie Qian-Qian. Sum of squares-robust model predictive controller for nonlinear system with input saturation. Control Theory & Applications, 2016, 33(3):321-328 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy201603007 [20] 赵敏, 李少远.约束非线性系统切换鲁棒预测控制.控制理论与应用, 2010, 27(4):495-500 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy201004013Zhao Min, Li Shao-Yuan. Switching robust model predictive control strategy for constrained nonlinear system. Control Theory & Applications, 2010, 27(4):495-500 http://d.old.wanfangdata.com.cn/Periodical/kzllyyy201004013 [21] Oh S K, Lee J M. Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories. Journal of Process Control, 2015, 36:64-78 doi: 10.1016/j.jprocont.2015.09.008 [22] Xiao T F, Li X D, Ho J K L. An adaptive discrete-time ILC strategy using fuzzy systems for iteration-varying reference trajectory tracking. International Journal of Control Automation & Systems, 2015, 13(1):222-230 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=998990e497b44b81bf7b4ea09ef55305 [23] Chi R, Hou Z, Jin S. A data-driven adaptive ILC for a class of nonlinear discrete-time systems with random initial states and iteration-varying target trajectory. Journal of Franklin Institute, 2015, 352(6):2407-2424 doi: 10.1016/j.jfranklin.2015.03.014 [24] 黄鹤, 李德伟, 席裕庚.基于多步控制策略的混合H2/H∞鲁棒预测控制器设计.自动化学报, 2012, 38(6):944-950 http://www.aas.net.cn/CN/abstract/abstract13713.shtmlHuang He, Li De-Wei, Xi Yu-Geng. On design of mixed H2/H∞ RMPC based on multi-step control strategy. Acta Automatic Sinica, 2012, 38(6):944-950 http://www.aas.net.cn/CN/abstract/abstract13713.shtml [25] 王幼琴, 赵忠盖, 刘飞.一种间歇过程多批次融合线性变参数建模方法.信息与控制, 2017, 46(1):46-52 http://d.old.wanfangdata.com.cn/Periodical/xxykz201701008Wang You-Qin, Zhao Zhong-Gai, Liu Fei. A multi-batch fusion linear parameter varying modeling method for batch process. Information and Control, 2017, 46(1):46-52 http://d.old.wanfangdata.com.cn/Periodical/xxykz201701008 [26] Li W. Research and application of robust gain-scheduling based on LPV System[Ph.D. dissertation], National University of Defense Technology, 2009 [27] 孙海乔, 陈珺, 刘飞.鲁棒预测迭代学习控制在间歇过程中的运用.信息与控制, 2015, 44(2):129-134 http://d.old.wanfangdata.com.cn/Periodical/xxykz201502002Sun Hai-Qiao, Chen Jun, Liu Fei. Robust predictive and iterative learning control as applied to batch process. Information and Control, 2015, 44(2):129-134 http://d.old.wanfangdata.com.cn/Periodical/xxykz201502002 [28] Ouellett D V. Schur complement and statistics. Linear Algebra & Its Applications, 1981, 36:187-295 http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ026406551/ [29] Lee K S, Lee J H. Convergence of constrained model-based predictive control for batch processes. IEEE Transactions on Automatic Control, 2000, 45(10):1928-1932 doi: 10.1109/TAC.2000.881002 [30] Orukpe P E, Jaimoukha I M, El-Zobaidi H M H. Model predictive control based on mixed control approach. In: Proceedings of American Control Conference. NewYork, USA: IEEE, 2007. 6147-6150 [31] Magni L, Nicolao G D, Magnani L, Scattolini R, A stabilizing model-based predictive control for nonlinear systems. Automatica, 2001, 37(9):1351-1362 doi: 10.1016/S0005-1098(01)00083-8 [32] Ding B, Xie L, Cai W. Robust MPC for polytopic uncertain systems with time-varying delays. International Journal of Control, 2008, 81(8):1239-1252 doi: 10.1080/00207170701613699 [33] 姜頔, 刘向杰.核电站蒸汽发生器水位的软约束预测控制.自动化学报, 2019, 45(6):1111-1121 http://www.aas.net.cn/CN/abstract/abstract19510.shtmlJiang Di, Liu Xiang-Jie. Soft Constrained MPC on water level control in steam generator of a nuclear power plant. Acta Automatic Sinica, 2019, 45(6):1111-1121 http://www.aas.net.cn/CN/abstract/abstract19510.shtml -
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