基于多面体终端域的Hammerstein-Wiener非线性预测控制

李妍; 毛志忠; 王琰; 袁平; 贾明兴

doi:10.3724/SP.J.1004.2011.00629

基于多面体终端域的Hammerstein-Wiener非线性预测控制

doi: 10.3724/SP.J.1004.2011.00629

1.
东北大学信息科学与工程学院沈阳 110004;
2.
辽阳市发展和改革委员会辽阳 111000

详细信息

通讯作者:
李妍

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- 文章访问数: 2178
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- 被引次数: 0
出版历程
- 收稿日期: 2010-05-25
- 修回日期: 2010-09-21
- 刊出日期: 2011-05-20

Predictive Control of Hammerstein-Wiener Nonlinearity Based on Polytopic Terminal Region

1.
School of Information Science and Engineering, Northeastern University, Shenyang 110004;
2.
Liaoyang Municipal Development and Reform Commission, Liaoyang 111000

More Information

Corresponding author: LI Yan

摘要

摘要: 许多实际系统都可以表示成一种中间为线性动态子系统、输入输出端为非线性静态子系统的Hammerstein-Wiener型非线性模型. 针对输入和输出受约束的Hammerstein-Wiener型非线性系统, 提出一种基于多面体终端域的预测控制综合算法. 离线设计时, 通过构造一系列多面体不变集, 扩大了终端域; 在多面体不变集内, 设计非线性控制律, 减少了常规线性控制律设计的保守性. 在线计算时, 通过求解有限个线性矩阵不等式(Linear matrix inequalities, LMIs)优化问题, 不仅可以满足实时性要求, 而且能够改善控制性能. 仿真结果表明了采用多面体不变集的优越性.
- Hammerstein-Wiener非线性模型 /
- 模型预测控制 /
- 多面体终端域 /
- 稳定性 /
- 线性矩阵不等式
Abstract: Many actual systems are often represented as the Hammerstein-Wiener nonlinear models, where a linear dynamic subsystem is surrounded by two static nonlinear subsystems at its input and output. For Hammerstein-Wiener nonlinear systems with the input and output constraints, a predictive control synthesis algorithm based on polytopic terminal region is proposed. At the offline stage, by constructing a series of the polytopic invariant sets, the terminal region is enlarged; in the polytopic invariant set, the nonlinear controller is designed, then the conservation of conventional linear control law design is reduced. At the online stage, by solving a finite number of linear matrix inequality optimization problems, not only the real-time demand can be satisfied, but also the control performance can be improved. Simulation results show the advantages of adopting polyhedron invariant set.
- Hammerstein-Wiener nonlinear models /
- model predictive control (MPC) /
- polytopic terminal region /
- stability /
- linear matrix inequalities (LMIs)

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参考文献(1)

[1]

Henson M A. Nonlinear model predictive control: current status and future directions. Computers and Chemical Engineering, 1998, 23(2): 187--202 [2] Ding Bao-Cang, Xi Yu-Geng, Li Shao-Yuan. Stability analysis on predictive control of discrete-time systems with input nonlinearity. Acta Automatica Sinica, 2003, 29(6): 827-834[3] Xu Xiang-Yuan, Mao Zong-Yuan. The analysis and research of predictive control based on Hammerstein model. Control Theory and Applications, 2000, 17(4): 529-532(徐湘元, 毛宗源. 基于Hammerstein模型预测控制的分析与研究. 控制理论与应用, 2000, 17(4): 529-532)[4] Ding Bao-Cang, Li Shao-Yuan. Design and analysis of Hammerstein nonlinear control systems with constraints. Control and Decision, 2003, 18(1): 24-28(丁宝苍, 李少远. 具有约束的Hammerstein非线性控制系统的设计与分析. 控制与决策, 2003, 18(1): 24-28)[5] Ding B C, Xi Y G. A two-step predictive control design for input saturated Hammerstein systems. International Journal of Robust and Nonlinear Control, 2006, 16(7): 353-367 [6] Zhang H T, Li H X, Chen G R. Dual-mode predictive control algorithm for constrained Hammerstein systems. International Journal of Control, 2008, 81(10): 1609-1625 [7] Niu Yong-Xiao, Ding Bao-Cang, Sun He-Xu. Robust stability of two-step predictive control for systems with input nonlinearities. Control and Decision, 2006, 21(4): 457-461(牛永肖, 丁宝苍, 孙鹤旭. 输入非线性系统的两步法预测控制的鲁棒稳定性. 控制与决策, 2006, 21(4): 457-461)[8] Bloemen H H J, Van D B T J J, Verbruggen H B. Model-based predictive control for Hammerstein systems. In: Proceedings of the 39th IEEE Conference on Decision and Control. Sydney, Australia: IEEE, 2000. 4963-4968[9] Bloemen H H J, Boom T J J V D, Verbruggen H B. Model-based predictive control for Hammerstein-Wiener systems. International Journal of Control, 2001, 74(5): 482-495 [10] Kouvaritakis B, Rossiter J A, Schuurmans J. Efficient robust predictive control. IEEE Transactions on Automatic Control, 2000, 45(8): 1545-1549 [11] Wan Z, Kothare M V. Efficient robust constrained model predictive control with a time varying terminal constraint set. Systems and Control Letters, 2003, 48(5): 375-383 [12] Pluymers B, Suykens J A K, Moor B D. Min-max feedback MPC using a time-varying terminal constraint set and comments on ``efficient robust constrained model predictive control with a time-varying terminal constraint set''. Systems and Control Letters, 2005, 54(12): 1143-1148 [13] Wan Z, Pluymers B, Kothare M V, Moor B D. Comments on: ``Efficient robust constrained model predictive control with a time varying terminal constraint set'' by Wan and Kothare. Systems and Control Letter, 2006, 55(7): 618-621 [14] Zheng Peng-Yuan, Xi Yu-Geng, Li De-Wei. Improved synthesis approach of robust constrained model predictive controller. Control and Decision, 2008, 23(9): 1040-1044(郑鹏远, 席裕庚, 李德伟. 一种改进的鲁棒约束预测控制器的综合设计方法. 控制与决策, 2008, 23(9): 1040-1044)[15] Wan Z Y, Kothare M V. An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica, 2003, 39(5): 837-846 [16] Ding Bao-Cang, Yang Peng. Synthesizing off-line robust model predictive controller based on nominal performance cost. Acta Automatica Sinica, 2006, 32(2): 304-310(丁宝苍, 杨鹏. 基于标称性能指标的离线鲁棒预测控制器综合. 自动化学报. 2006, 32(2): 304-310)[17] Ding Bao-Cang, Zou Tao, Li Shao-Yuan. Varying-horizon off-line robust predictive control for time-varying uncertain systems. Control Theory and Applications, 2006, 23(2): 240-244(丁宝苍, 邹涛, 李少远. 时变不确定系统的变时域离线鲁棒预测控制. 控制理论与应用, 2006, 23(2): 240-244)[18] Lee Y I, Kouvaritakis B. Robust receding horizon predictive control for systems with uncertain dynamics and input saturation. Automatica, 2000, 36(10): 1497-1504 [19] Lee Y I, Kouvaritakis B. A linear programming approach to constrained robust predictive control. IEEE Transactions on Automatic Control, 2000, 45(9): 1765-1770 [20] Lee Y I, Kouvaritakis B. Superposition in efficient robust constrained predictive control. Automatica, 2002, 38(5): 875-878 [21] Cannon M, Deshmukh V, Kouvaritakis B. Nonlinear model predictive control with polytopic invariant sets. Automatica, 2003, 39(8): 1487-1494 [22] Cannon M, Kouvaritakis B, Deshmukh V. Enlargement of polytopic terminal region in NMPC by interpolation and partial invariance. Automatica, 2004, 40(2): 311-317 [23] Zou Zhi-Qiang, Xu Li-Hong, Yuan Meng. A nonlinear model predictive control based on polytopic description system. Journal of Tongji University (Natural Science), 2006, 34(6): 813-817(邹志强, 徐立鸿, 袁梦. 一种基于多面体描述系统的非线性预测控制. 同济大学学报(自然科学版), 2006, 34(6): 813-817)[24] Zou Zhi-Qiang. Roubst Control Research of Parameter Time-Varying Linear System with Polytopic Uncertainty [Ph.D. dissertation], Tongji University, China, 2006(邹志强. 参数时变多面体不确定线性系统的鲁棒控制研究 [博士学位论文], 同济大学, 中国, 2006)[25] Zhang F Z. The Schur Complement and Its Applications. New York: Springer, 2005[26] Gahinet P, Nemirovski A, Laub A J, Chilali M. LMI Control Toolbox for Use with Matlab. Natick: The Math Works, 1995[27] Jin Wei-Qiang, Li Ji-Shun. The design of electrode regulation system for electric arc furnace. Industrial Heating, 2008, 37(2): 45-47(金伟强, 李济顺. 电弧炉电极调节系统的设计. 工业加热, 2008, 37(2): 45-47)[28] Wu Le-Bin, Wang Xuan-Yin, Li Qiang. Fuzzy-immune PID control of a 6-DOF parallel platform for docking simulation. Journal of Zhejiang University (Engineering Science), 2008, 42(3): 387-391(吴乐彬, 王宣银, 李强. 对接模拟并联六自由度平台的模糊免疫PID控制. 浙江大学学报(工学版), 2008, 42(3): 387-391)[29] Zhang Y W, Gui W H. Compensation for secondary uncertainty in electro-hydraulic servo system by gain adaptive sliding mode variable structure control. Journal of Central South University of Technology, 2008, 15(2): 256-263 [30] Wang Yan. Study and Application of Electric Arc Model for AC Electric Arc Furnace [Ph.D. dissertation], Northeastern University, China, 2009(王琰. 交流电弧炉电弧模型研究及其应用 [博士学位论文], 东北大学, 中国, 2009)

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