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具有间歇性执行器故障的非线性系统自适应CFB控制

乃永强 杨清宇 周文兴 杨莹

乃永强, 杨清宇, 周文兴, 杨莹. 具有间歇性执行器故障的非线性系统自适应CFB控制. 自动化学报, 2020, 45(x): 1−19 doi: 10.16383/j.aas.190673
引用本文: 乃永强, 杨清宇, 周文兴, 杨莹. 具有间歇性执行器故障的非线性系统自适应CFB控制. 自动化学报, 2020, 45(x): 1−19 doi: 10.16383/j.aas.190673
Nai Yong-Qiang, Yang Qing-Yu, Zhou Wen-Xing, Yang Ying. Adaptive CFB control for a class of nonlinear systems with intermittent actuator faults. Acta Automatica Sinica, 2020, 45(x): 1−19 doi: 10.16383/j.aas.190673
Citation: Nai Yong-Qiang, Yang Qing-Yu, Zhou Wen-Xing, Yang Ying. Adaptive CFB control for a class of nonlinear systems with intermittent actuator faults. Acta Automatica Sinica, 2020, 45(x): 1−19 doi: 10.16383/j.aas.190673

具有间歇性执行器故障的非线性系统自适应CFB控制

doi: 10.16383/j.aas.190673
基金项目: 国家自然科学基金(61633001, 61673315, 61075001)
详细信息
    作者简介:

    乃永强:西安交通大学自动化科学与工程学院博士研究生. 主要研究方向为非线性系统, 自适应神经控制, 容错控制.E-mail: yongqiangnai@stu.xjtu.edu.cn

    杨清宇:西安交通大学自动化科学与工程学院教授. 主要研究方向为信息物理融合系统, 智能电网信息物理安全与隐私保护, 复杂系统故障诊断与健康管理, 工业智能控制. 本文通信作者.E-mail: yangqingyu@mail.xjtu.edu.cn

    周文兴:中国航天员科研训练中心助理研究员, 西安交通大学自动化科学与工程学院博士研究生. 主要研究方向为环境控制与生命保障技术, 测量与控制技术, 传感器融合技术, 装备健康管理技术.E-mail: zwxdzxx232@stu.xjtu.edu.cn

    杨莹:北京大学工学院教授. 主要研究方向为复杂动态过程故障诊断, 容错控制与健康管理.E-mail: yy@pku.edu.cn

Adaptive CFB Control for a Class of Nonlinear Systems with Intermittent Actuator Faults

Funds: Supported by National Natural Science Foundation of China (61633001, 61673315, 61075001)
  • 摘要: 控制系统的执行器在运行过程中经常发生各种各样不可预测的间歇性故障. 如何有效地处理这些故障仍然是控制领域的一个难题. 针对一类不确定严格反馈非线性系统, 提出一种自适应CFB (Command Filtered Backstepping) 控制方案解决了间歇性执行器故障的补偿问题. 利用神经网络逼近控制器中的未知函数, 并采用投影算子实时在线更新控制器中的估计参数使得参数估计随着故障次数的累积而不断增加的问题被消除. 考虑到未知参数间歇性跳变对系统稳定性的影响, 提出一种改进的Lyapunov函数分析了闭环系统的稳定性. 证明了所提出的控制方案能够保证所有闭环信号的有界性, 同时建立了跟踪误差与Lyapunov函数跳变幅度, 最小故障时间间隔, 设计参数之间的关系. 如果Lyapunov函数的跳变幅度越小以及两个连续故障之间的时间间隔越长, 系统的稳态跟踪指标越好. 通过迭代计算建立了暂态跟踪误差指标的均方根型界. 该界表明了通过选择恰当的设计参数, 可改善系统的暂态指标. 仿真结果表明了所提方案的有效性.
  • 图  1  控制结构图. $x_{\mathrm{c}i}$ $\dot{x}_{\mathrm{c}i}$ , $i = 2,\ldots,n$ , 为滤波器 (11) 的输出. $\alpha_i$ , $i = 1,\ldots,n$ , 为式 (12)−(14) 中定义的虚拟控制律. $\xi_i$ , $i = 1,\ldots,n-1$ 为式 (17) 中定义的滤波误差补偿信号.

    Fig.  1  Control block diagram. $x_{\mathrm{c}i}$ and $\dot{x}_{\mathrm{c}i}$ for $i = 2, \ldots,n$ are the outputs of the filter (11). $\alpha_i$ for $i = 1,\ldots,n$ is virtual control law defined in (12)−(14). $\xi_i$ for $i = 1,\ldots, n-1$ is the compensating signal of the filtered error defined in (17).

    图  2  (a) 输出 $y$ 和期望输出 $y_{\mathrm{d}}$ ; (b) 跟踪误差 $\bar{z}_1$ .

    Fig.  2  (a) Output $y$ and desired reference $y_{\mathrm{d}}$ ; (b) Tracking error $\bar{z}_1$ .

    图  3  控制输入 $u_1$ $u_2$ .

    Fig.  3  Control inputs $u_1$ and $u_2$ .

    图  4  命令滤波误差及其补偿信号. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (d) $\xi_2$ .

    Fig.  4  Command filtered errors and their compensating signals. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (d) $\xi_2$ .

    图  5  自适应参数. (a) $\|\hat{\pmb{\theta}}_1\|$ ; (b) $\|\hat{\pmb{\theta}}_2\|$ ; (c) $\|\hat{\pmb{\theta}}_3\|$ ; (d) $\hat{\rho}$ ; (e) $\hat{\beta}_1$ ; (f) $\hat{\beta}_2$ .

    Fig.  5  Adaptive parameters. (a) $\|\hat{\pmb{\theta}}_1\|$ ; (b) $\|\hat{\pmb{\theta}}_2\|$ ; (c) $\|\hat{\pmb{\theta}}_3\|$ ; (d) $\hat{\rho}$ ; (e) $\hat{\beta}_1$ ; (f) $\hat{\beta}_2$ .

    图  6  (a) 输出 $y$ 和期望输出 $y_{\mathrm{d}}$ ; (b) 跟踪误差 $\bar{z}_1$ .

    Fig.  6  (a) Output $y$ and desired reference $y_{\mathrm{d}}$ ; (b) Tracking error $\bar{z}_1$ .

    图  7  控制输入 $u_1$ $u_2$ .

    Fig.  7  Control inputs $u_1$ and $u_2$ .

    图  8  命令滤波误差及其补偿信号. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (d) $\xi_2$ .

    Fig.  8  Command filtered errors and their compensating signals. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (d) $\xi_2$ .

    图  9  自适应参数. (a) $\|\hat{\pmb{\theta}}_1\|$ ; (b) $\|\hat{\pmb{\theta}}_2\|$ ; (c) $\|\hat{\pmb{\theta}}_3\|$ ; (d) $\hat{\rho}$ ; (e) $\hat{\beta}_1$ ; (f) $\hat{\beta}_2$ .

    Fig.  9  Adaptive parameters. (a) $\|\hat{\pmb{\theta}}_1\|$ ; (b) $\|\hat{\pmb{\theta}}_2\|$ ; (c) $\|\hat{\pmb{\theta}}_3\|$ ; (d) $\hat{\rho}$ ; (e) $\hat{\beta}_1$ ; (f) $\hat{\beta}_2$ .

    图  10  (a) 输出 $y$ 和期望输出 $y_{\mathrm{d}}$ ; (b) 跟踪误差 $\bar{z}_1$ .

    Fig.  10  (a) Output $y$ and desired reference $y_{\mathrm{d}}$ ; (b) Tracking error $\bar{z}_1$ .

    图  11  控制输入 $u_1$ $u_2$ .

    Fig.  11  Control inputs $u_1$ and $u_2$ .

    图  12  命令滤波误差及其补偿信号. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (d) $\xi_2$ .

    Fig.  12  Command filtered errors and their compensating signals. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $\xi_1$ ; (f) $\xi_2$ .

    图  13  自适应参数. (a) $\|\hat{\pmb{\theta}}_2\|$ ; (b) $\|\hat{\pmb{\theta}}_3\|$ ; (c) $\hat{\rho}$ ; (d) $\hat{\beta}_1$ $\hat{\beta}_2$ .

    Fig.  13  Adaptive parameters. (a) $\|\hat{\pmb{\theta}}_2\|$ ; (b) $\|\hat{\pmb{\theta}}_3\|$ ; (c) $\hat{\rho}$ ; (d) $\hat{\beta}_1$ and $\hat{\beta}_2$ .

    图  14  (a) 输出 $y$ 和期望输出 $y_{\mathrm{d}}$ ; (b) 跟踪误差 $\bar{z}_1$ .

    Fig.  14  (a) Output $y$ and desired reference $y_{\mathrm{d}}$ ; (b) Tracking error $\bar{z}_1$ .

    图  15  控制输入 $u_1$ $u_2$ .

    Fig.  15  Control inputs $u_1$ and $u_2$ .

    图  16  命令滤波误差及其补偿信号. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $x_{\mathrm{c}4}-\alpha_3$ ; (d) $\xi_1$ ; (e) $\xi_2$ ; (f) $\xi_3$ .

    Fig.  16  Command filtered errors and their compensating signals. (a) $x_{\mathrm{c}2}-\alpha_1$ ; (b) $x_{\mathrm{c}3}-\alpha_2$ ; (c) $x_{\mathrm{c}4}-\alpha_3$ ; (d) $\xi_1$ ; (e) $\xi_2$ ; (f) $\xi_3$ .

    图  17  自适应参数. (a) $\|\hat{\pmb{\theta}}_2\|$ ; (b) $\|\hat{\pmb{\theta}}_4\|$ ; (c) $\hat{\rho}$ ; (d) $\hat{\beta}_1$ $\hat{\beta}_2$ .

    Fig.  17  Adaptive parameters. (a) $\|\hat{\pmb{\theta}}_2\|$ ; (b) $\|\hat{\pmb{\theta}}_4\|$ ; (c) $\hat{\rho}$ ; (d) $\hat{\beta}_1$ and $\hat{\beta}_2$ .

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  • 收稿日期:  2019-09-24
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