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双层模型预测控制系统的多包镇定域分析与系统设计

朱宇轩 李少远

朱宇轩, 李少远. 双层模型预测控制系统的多包镇定域分析与系统设计. 自动化学报, 2018, 44(2): 262-269. doi: 10.16383/j.aas.2018.c160394
引用本文: 朱宇轩, 李少远. 双层模型预测控制系统的多包镇定域分析与系统设计. 自动化学报, 2018, 44(2): 262-269. doi: 10.16383/j.aas.2018.c160394
ZHU Yu-Xuan, LI Shao-Yuan. Analysis and System Design of Multi-convex Hull Stabilization Domain for Double-layered Model Predictive Control System. ACTA AUTOMATICA SINICA, 2018, 44(2): 262-269. doi: 10.16383/j.aas.2018.c160394
Citation: ZHU Yu-Xuan, LI Shao-Yuan. Analysis and System Design of Multi-convex Hull Stabilization Domain for Double-layered Model Predictive Control System. ACTA AUTOMATICA SINICA, 2018, 44(2): 262-269. doi: 10.16383/j.aas.2018.c160394

双层模型预测控制系统的多包镇定域分析与系统设计

doi: 10.16383/j.aas.2018.c160394
基金项目: 

国家自然科学基金 61521063

国家自然科学基金 61590924

详细信息
    作者简介:

    朱宇轩  上海交通大学硕士研究生.主要研究方向为模型预测控制.E-mail:xuan1788@163.com

    通讯作者:

    李少远   上海交通大学自动化系教授.主要研究方向为预测控制, 模糊控制, 自适应控制理论与应用.本文通信作者.E-mail:syli@sjtu.edu.cn

Analysis and System Design of Multi-convex Hull Stabilization Domain for Double-layered Model Predictive Control System

Funds: 

National Natural Science Foundation of China 61521063

National Natural Science Foundation of China 61590924

More Information
    Author Bio:

     Master student at Shanghai Jiao Tong University. Her main research interest is model predictive control

    Corresponding author: LI Shao-Yuan  Professor at the Institute of Automation, Shanghai Jiao Tong University. His research interest covers predictive control, fuzzy system, adaptive control theory and applications. Corresponding author of this paper
  • 摘要: 针对双层模型预测控制(Model predictive control,MPC)中出现的由于系统状态在动态控制(Dynamic control,DC)过程中超出约束集,导致下层优化不可行的问题,本文在综合控制方法的基础上提出一种新的动态控制策略,引入多包镇定域(Multi-convex hull stabilization domain,MHSD)的概念.通过离线计算多包镇定域,并根据系统每一时刻的实测状态值,在线决定(Dynamic control)层的镇定域以及相应的控制时域,结合变约束思想,保证动态控制过程递归可行,从而有效控制在大范围内变化的系统状态.另外,本文通过设计非线性反馈控制器,扩大了终端不变集和多包镇定域的范围,提高了DC层对稳态目标值的跟踪效果.本文的控制算法可以使得DC层在目标跟踪过程中保证递归可行性,并最大程度地实现无静差跟踪.仿真算例验证了本文算法对稳定系统和不稳定系统都有效.
    1)  本文责任编委 谢永芳
  • 图  1  双层模型预测控制结构

    Fig.  1  The structure of the double-layered MPC

    图  2  纸机系统的多包镇定域

    Fig.  2  The stabilization region set of the AS DPS

    图  3  控制时刻$k$从31到60对应的纸机系统控制过程

    Fig.  3  Control process of the paper system with the control moment $k$ from 31 to 60

    图  4  控制时刻$k$从61到90对应的纸机系统控制过程

    Fig.  4  Control process of the paper system with the control moment $k$ from 61 to 90

    图  5  控制时刻$k$从31到60对应的双积分系统控制过程

    Fig.  5  Control process of the double-integrator system with the control moment $k$ from 31 to 60

    图  6  三组仿真中的系统状态轨迹

    Fig.  6  The state trajectories of the three scenarios

    表  1  本文符号及其含义

    Table  1  The meanings of the notations in this paper

    符号含义
    $x^*$ $x$的最优值
    ${\bf R}^n$ $n$维欧氏空间
    $k$离散采样间隔
    $x$系统状态, $x \in {\bf R}^{n_x}$
    $u$系统输入, $u \in {\bf R}^{n_u}$
    $x_s(u_s)$稳态状态(输入)
    $x_t(u_t)$期望稳态状态(输入)
    $\bar{x}(\bar{u})$状态(输入)上界
    $I_n $ $n$维单位矩阵
    $Q_s, R_s$适维权重矩阵
    $N_i$第$i$个镇定域所对应的控制时域
    ${\| x\|}_{Q_s}^2$ $x^{\rm T}$$Q_s$$x$
    $x(k+i|k)$ $k$时刻对未来状态的预测值
    $u(k+i|k) $ $k$时刻对未来输入的预测值
    下载: 导出CSV

    表  2  纸机系统的稳态目标计算结果

    Table  2  The results of the SSTC in the AS DPS system

    $k$$u_{s, 1}$$u_{s, 2}$$x_{s, 1}$$x_{s, 2}$
    $1\sim90$-0.39-0.41-0.32-0.33
    下载: 导出CSV

    表  3  双积分器系统的稳态目标计算结果

    Table  3  The results of SSTC in the double-integrator system

    k$u_t$$x_t$$u_s$$x_s$
    $1\sim30$(0, 0)(2, -2)(0, 0)(2, 0.5)
    $31\sim60$(0, 0)(0, -2)(-0.1, 0.2)(-0.38, 0.2998)
    $61\sim90$(0, 0)(0, 0)(0, 0)(0, 0)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-05-13
  • 录用日期:  2016-12-20
  • 刊出日期:  2018-02-20

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