2.765

2022影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

肖宇 徐晓东 阳春华

肖宇, 徐晓东, 阳春华. 一类具有复杂执行器动态的双曲线型偏微分方程输出调节. 自动化学报, 2024, 50(2): 200−212 doi: 10.16383/j.aas.c221007
引用本文: 肖宇, 徐晓东, 阳春华. 一类具有复杂执行器动态的双曲线型偏微分方程输出调节. 自动化学报, 2024, 50(2): 200−212 doi: 10.16383/j.aas.c221007
Xiao Yu, Xu Xiao-Dong, Yang Chun-Hua. Output regulation for a class of hyperbolic PDEs with complex actuator dynamics. Acta Automatica Sinica, 2024, 50(2): 200−212 doi: 10.16383/j.aas.c221007
Citation: Xiao Yu, Xu Xiao-Dong, Yang Chun-Hua. Output regulation for a class of hyperbolic PDEs with complex actuator dynamics. Acta Automatica Sinica, 2024, 50(2): 200−212 doi: 10.16383/j.aas.c221007

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

doi: 10.16383/j.aas.c221007
基金项目: 国家重点研发项目(2022YFB3304700)资助
详细信息
    作者简介:

    肖宇:中南大学自动化学院硕士研究生. 2021年获得中南大学学士学位. 主要研究方向为分布参数系统自适应控制与输出调节. E-mail: yu_xiao@csu.edu.cn

    徐晓东:中南大学自动化学院教授. 2017年获得阿尔伯塔大学博士学位. 主要研究方向为无限维系统的鲁棒/最优控制和故障估计. 本文通信作者. E-mail: XiaodongXu@csu.edu.cn

    阳春华:中南大学自动化学院教授. 2002年获得中南大学博士学位. 主要研究方向为复杂工业过程建模与优化控制, 智能自动化系统与装置. E-mail: ychh@csu.edu.cn

Output Regulation for a Class of Hyperbolic PDEs With Complex Actuator Dynamics

Funds: Supported by National Key R&D Program of China (2022YFB3304700)
More Information
    Author Bio:

    XIAO Yu Master student at the School of Automation, Central South University. He received his bachelor degree from Central South University in 2021. His research interest covers adaptive control and output regulation of distributed parameter systems

    XU Xiao-Dong Professor at the School of Automation, Central South University. He received his Ph.D. degree from the University of Alberta in 2017. His research interest covers robust/optimal control and fault estimation of infinite-dimensional systems. Corresponding author of this paper

    YANG Chun-Hua Professor at the School of Automation, Central South University. She received her Ph.D. degree from Central South University in 2002. Her research interest covers modeling and optimal control of complex industrial process, intelligent automation systems and devices

  • 摘要: 本文研究了一类具有边界执行器动态特性的双曲线型偏微分方程(Partial differential equation, PDE)系统的输出调节问题. 特别地, 执行器由一组非线性常微分方程(Ordinary differential equation, ODE)描述, 控制输入出现在执行器的一端而非直接作用在PDE系统上, 这使得控制任务变得相当困难. 基于几何设计方法和有限维与无限维反步法, 本文提出了显式表达的输出调节器, 实现了该类系统的扰动补偿及跟踪控制. 并且我们采用Lyapunov稳定性理论严格证明了闭环系统及跟踪误差在范数意义上的指数稳定性. 仿真实例对比验证了所提出控制方法的有效性.
    1)  11 本文使用的符号说明如下: $ {\bf{R}} $为所有实数的集合; $ {\bf{C}} $为所有复数的集合; $ \left|\cdot\right| $表示欧几里得范数; 对于一个时变的信号$ \omega \left( {x,t} \right) \in {\bf{R}}, x \in \left[0,1\right] $, 令$ \left\| {\omega \left( x \right)} \right\|_{L_2} = \sqrt {\int_0^1 {{\omega ^2}\left( x \right)\mathrm{d}x} } $表示其$ L_2 $范数. 此外, 令$ {v_x}\left( {x,t} \right) $和$ {v_t}\left( {x,t} \right) $分别表示偏导$ \frac{{\partial v\left( {x,t} \right)}}{{\partial x}} $和$ \frac{{\partial v\left( {x,t} \right)}}{{\partial t}} $. 为避免混淆, 时间和空间变量在一些函数中常被忽略, 例如: $ v\left( {x,t} \right) = v\left( x \right),v\left( {x,t} \right) = v $.
  • 图  1  一类典型的流程工业多反应器串联系统信号流图

    Fig.  1  A typical signal flow graph of multi-reactor series system in process industry

    图  2  输出反馈闭环控制系统结构框图

    Fig.  2  The block diagram of output-feedback closed-loop control system

    图  3  状态反馈控制下的被控输出$y\left(t\right)$及参考信号$y_r\left(t\right) = 2\cos \left(t\right)$

    Fig.  3  The controlled output $y\left(t\right)$ under the state-feedback control and the reference signal $y_r\left(t\right) = 2\cos \left(t\right)$

    图  4  状态反馈控制器$U\left(t\right)$轨迹

    Fig.  4  The trajectory of state-feedback controller $U\left(t\right)$

    图  5  输出反馈控制下的被控输出$y\left(t\right)$及参考信号$y_r\left(t\right) = 2\cos \left(t\right)$

    Fig.  5  The controlled output $y\left(t\right)$ under the output-feedback control and the reference signal $y_r\left(t\right) = 2\cos \left(t\right)$

    图  6  输出反馈控制器$\hat U\left(t\right)$轨迹

    Fig.  6  The trajectory of output-feedback controller $\hat U\left(t\right)$

    图  7  PDE子系统观测误差的范数$\left\| {{{\tilde u}_1}} \right\|$和$\left\| {{{\tilde u}_2}} \right\|$

    Fig.  7  The norms $\left\| {{{\tilde u}_1}} \right\|$ and $\left\| {{{\tilde u}_2}} \right\|$ of observer errors of PDE subsystem

    图  8  执行器状态观测误差${X_1} - {{\hat X}_1}$和${X_2} - {{\hat X}_2}$

    Fig.  8  The observer errors ${X_1} - {{\hat X}_1}$ and ${X_2} - {{\hat X}_2}$ of actuator states

    图  9  PDE子系统受到的常值扰动${D_i} = Q_i^\mathrm{T}{v_{d1}},i = 1, 2 ,3$及相应的扰动观测值${\hat D_i} = Q_i^\mathrm{T}{\hat v_{d1}},i = 1, 2 ,3$

    Fig.  9  The constant perturbations ${D_i} = Q_i^\mathrm{T} {v_{d1}}$, $i = 1, 2 ,3$ to PDE subsystem and the corresponding disturbance observations ${\hat D_i} = Q_i^\mathrm{T}{\hat v_{d1}},i = 1, 2 ,3$

    图  10  执行器受到的周期性扰动${d_i} = q_i^\mathrm{T}{v_{d2}},i = 0,1 ,2$以及相应的扰动观测值${{\hat d}_i} = q_i^\mathrm{T}{{\hat v}_{d2}},i = 0,1 ,2$

    Fig.  10  The periodic perturbations ${d_i} = q_i^\mathrm{T} {v_{d2}}$, $i = 0, 1 ,2$ to actuator and the corresponding disturbance observations ${{\hat d}_i} = q_i^\mathrm{T}{{\hat v}_{d2}}$, $i = 0, 1 ,2$

    图  11  采用控制器(79)的系统被控输出 $y\left(t\right)$及参考信号$y_r\left(t\right) = 2\cos \left(t\right)$

    Fig.  11  The system controlled output $y\left(t\right)$ and reference signal $y_r\left(t\right) = 2\cos \left(t\right)$ using the controller (79)

    图  12  控制器(79)轨迹

    Fig.  12  The trajectory of controller (79)

  • [1] Xu C, Sallet G. Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, 2002, 7: 421-442 doi: 10.1051/cocv:2002062
    [2] Landet I S, Pavlov A, Aamo O M. Modeling and control of heave-induced pressure fluctuations in managed pressure drilling. IEEE Transaction Control System Technology, 2012, 21(4): 1340-1351
    [3] Boskovic D M, Krstic M. Backstepping control of chemical tubular reactors. Computers & Chemical Engineering, 2002, 26(7-8): 1077-1085
    [4] Deutscher J. Output regulation for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. Automatica, 2017, 85: 34-42 doi: 10.1016/j.automatica.2017.07.027
    [5] Xu X, Dubljevic S. Output regulation boundary control of first-order coupled linear mimo hyperbolic pide systems. International Journal of Control, 2020, 93(3): 410-23 doi: 10.1080/00207179.2018.1475749
    [6] Deutscher J, Gehring N, Kern R. Output feedback control of general linear heterodirectional hyperbolic ode-pde-ode systems. Automatica, 2018, 95: 472-480 doi: 10.1016/j.automatica.2018.06.021
    [7] Xu X, Dubljevic S. Output regulation for a class of linear boundary controlled first-order hyperbolic pide systems. Automatica, 2017, 85: 43-52 doi: 10.1016/j.automatica.2017.07.036
    [8] Deutscher J, Gabriel J. Minimum time output regulation for general linear heterodirectional hyperbolic systems. International Journal of Control, 2020, 93(8): 1826-1838 doi: 10.1080/00207179.2018.1533648
    [9] Zhang J, Qi J, Dubljevic S, Bo S. Output regulation for a first-order hyperbolic PIDE with state and sensor delays. European Journal of Control, 2022, 65: 100643 doi: 10.1016/j.ejcon.2022.100643
    [10] Irscheid A, Deutscher J, Gehring N, Joachim R. Output regulation for general heterodirectional linear hyperbolic PDEs coupled with nonlinear ODEs. Automatica, 2023, 148: 110748 doi: 10.1016/j.automatica.2022.110748
    [11] Deutscher J. Finite-time output regulation for linear 2×2 hyperbolic systems using backstepping. Automatica, 2017, 75: 54-62 doi: 10.1016/j.automatica.2016.09.020
    [12] Owens B A, Mann B P. Linear and nonlinear electromagnetic coupling models in vibration-based energy harvesting. Journal of Sound and Vibration, 2012, 331(4): 922-937 doi: 10.1016/j.jsv.2011.10.026
    [13] Susto G A, Krstic M. Control of pde-ode cascades with neumann interconnections. Journal of Franklin Institute, 2010, 347(1): 284-314 doi: 10.1016/j.jfranklin.2009.09.005
    [14] Xu X, Tian Y, Yuan Y, Luan X, Liu F, Dubljevic S. Output regulation of linearized column froth flotation process. IEEE Transaction Control System Technology, 2020 29(1): 249-262
    [15] Li J, Wu Z, Liu Y. Adaptive stabilization for an uncertain reaction-diffusion equation with dynamic boundary condition at control end. System & Control Letters, 2022, 162, 105-180
    [16] Liu W J, Krstic M. Backstepping boundary control of burgers’ equation with actuator dynamics. System & Control Letters, 2000, 41(4): 291-303
    [17] Wang J, Krstic M. Output-feedback control of an extended class of sandwiched hyperbolic pde-ode systems. IEEE Transaction on Automatic Control, 2020, 66(6): 2588-2603
    [18] Wang J, Krstic M. Delay-compensated control of sandwiched ode-pde-ode hyperbolic systems for oil drilling and disaster relief. Automatica, 2020, 120: 109-131
    [19] Wang J, Krstic M. Event-triggered output-feedback backstepping control of sandwich hyperbolic pde systems. IEEE Transaction Automatic Control, 2022, 67(1): 220-235 doi: 10.1109/TAC.2021.3050447
    [20] Wang J, Krstic M. Output feedback boundary control of a heat pde sandwiched between two odes. IEEE Transaction Automatic Control, 2019, 64(11): 4653-4660 doi: 10.1109/TAC.2019.2901704
    [21] Li J, Wu Z, Wen C. Adaptive stabilization for a reaction-diffusion equation with uncertain nonlinear actuator dynamics. Automatica, 2021, 128: 109-594
    [22] Xiao Y, Yuan Y, Yang C, Luo B, Xu X, Dubljevic S. Adaptive neural tracking control of a class of hyperbolic PDE with uncertain actuator dynamics. IEEE Transactions on Cybernetics, DOI: 10.1109/TCYB.2022.3223168
    [23] Zhang B, Yang C, Zhu H, Shi P, Gui W. Controllable-domain-based fuzzy rule extraction for copper removal process control. IEEE transactions on fuzzy systems, 2017 26(3): 1744-1756
    [24] Lin Z, Stoorvogel A A, Saberi A. Output regulation for linear systems subject to input saturation. Automatica, 1996, 32(1): 29-47 doi: 10.1016/0005-1098(95)00110-7
    [25] Raghavan S, Hedrick J K. Observer design for a class of nonlinear systems. International Journal of Control, 1994, 59(2): 515-528 doi: 10.1080/00207179408923090
    [26] Vazquez R, Krstic M, Coron J M. Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system. In: Proceedings of Conference on Decision and Control and European Control Conference. Orlando, USA: 2011. 4937−4942
    [27] Kailath T. Linear Systems. Englewood Cliffs, NJ: Prentice Hall, 1980.
    [28] Khalil H. Nonlinear systems (3rd edition). NJ: Prentice Hall, 2002.
  • 加载中
计量
  • 文章访问数:  149
  • HTML全文浏览量:  66
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-12-30
  • 录用日期:  2023-05-18
  • 网络出版日期:  2023-06-14

目录

    /

    返回文章
    返回