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基于LMI的过渡态主控回路闭环控制律优化设计

缪柯强 王曦 朱美印

缪柯强, 王曦, 朱美印等 . 基于LMI的过渡态主控回路闭环控制律优化设计[J]. 北京航空航天大学学报, 2022, 48(5): 841-854. doi: 10.13700/j.bh.1001-5965.2020.0661
引用本文: 缪柯强, 王曦, 朱美印等 . 基于LMI的过渡态主控回路闭环控制律优化设计[J]. 北京航空航天大学学报, 2022, 48(5): 841-854. doi: 10.13700/j.bh.1001-5965.2020.0661
MIAO Keqiang, WANG Xi, ZHU Meiyinet al. Optimal design of transient main closed-loop control law based on LMI[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(5): 841-854. doi: 10.13700/j.bh.1001-5965.2020.0661(in Chinese)
Citation: MIAO Keqiang, WANG Xi, ZHU Meiyinet al. Optimal design of transient main closed-loop control law based on LMI[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(5): 841-854. doi: 10.13700/j.bh.1001-5965.2020.0661(in Chinese)

基于LMI的过渡态主控回路闭环控制律优化设计

doi: 10.13700/j.bh.1001-5965.2020.0661
基金项目: 

国家科技重大专项 2017-V-0015-0067

详细信息
    通讯作者:

    王曦, E-mail: xwang@buaa.edu.cn

  • 中图分类号: V233.7

Optimal design of transient main closed-loop control law based on LMI

Funds: 

National Science and Technology Major Project 2017-V-0015-0067

More Information
  • 摘要:

    针对涡扇发动机过渡态多变量控制设计难的问题,提出了一种基于抽功法在过渡态加减速线上的准稳态工作点处提取线性模型的方法,并在此基础上提出了一种过渡态主控回路闭环控制律的优化设计方法。通过功率输入和功率提取解决过渡态动态特征提取难题,基于增益调度可作为非线性动态控制策略的基本原理,将稳态多变量控制规律的线性矩阵不等式(LMI)设计方法推广到涡扇发动机过渡态主控回路闭环控制的设计中,并通过最小化矩阵迹优化闭环极点配置。针对2种不同过渡态主控回路闭环控制策略,分别设计了最小化矩阵迹寻优的过渡态主控回路的多变量闭环控制律,并进行从慢车到中间状态的基于涡扇发动机非线性动态模型的双通道过渡态性能仿真验证,结果表明:方案1过渡态控制双通道N1N2的调节时间不大于5.0 s,超调量不大于0.8%;方案2过渡态控制双通道πTN2的调节时间不大于5.6 s,超调量不大于0.8%。

     

  • 图 1  基于增益调度的过渡态控制系统结构

    Figure 1.  Structure of transient control system based on gain-schedule

    图 2  基于增益调度的主控回路控制系统结构

    Figure 2.  Structure of main loop control system based on gain-schedule

    图 3  发动机最大工作范围

    Figure 3.  Maximum working area of engine

    图 4  系统闭环极点随矩阵迹增大的位置变化

    Figure 4.  Position change of system closed-loop poles with the increase of matrix trace

    图 5  方案1低压转子转速N1响应曲线

    Figure 5.  Response curves of low-pressure rotor speed N1 in case 1

    图 6  方案1高压转子转速N2响应曲线

    Figure 6.  Response curves of high-pressure rotor speed N2 in case 1

    图 7  方案1燃油流量Wf响应曲线

    Figure 7.  Response curves of fuel flow Wf in case 1

    图 8  方案1喷口面积A8响应曲线

    Figure 8.  Response curve of exhaust nozzle area A8 in case 1

    图 9  方案1风扇喘振裕度SM响应曲线

    Figure 9.  Response curve of compressor surge margin in case 1

    图 10  方案1高压涡轮后温度T48响应曲线

    Figure 10.  Response curve of temperature T48 after high-pressure turbine in case 1

    图 11  方案2涡轮落压比πT响应曲线

    Figure 11.  Response curves of turbine pressure ratio πT in case 2

    图 12  方案2高压转子转速N2响应曲线

    Figure 12.  Response of high-pressure rotor speed N2 in case 2

    图 13  方案2燃油流量Wf响应曲线

    Figure 13.  Response curve of fuel flow Wf in case 2

    图 14  方案2喷口面积A8响应曲线

    Figure 14.  Response curve of nozzle throat area A8 in case 2

    图 15  方案2风扇喘振裕度SM响应曲线

    Figure 15.  Response curve of compressor surge margin in case 2

    图 16  方案2高压涡轮后温度T48响应曲线

    Figure 16.  Response curve of temperature T48 after high-pressure turbine in case 2

    图 17  方案1转动愦量拉偏测试低压转子转速N1响应曲线

    Figure 17.  Response curves of low-pressure rotor speed N1 with moment of inertia error in case 1

    图 18  方案1转动愦量拉偏测试高压转子转速N2响应曲线

    Figure 18.  Response curves of high-pressure rotor speed N2 with moment of inertia error in case 1

    图 19  方案2转动愦量拉偏测试涡轮落压比πT响应曲线

    Figure 19.  Response curves of turbine pressure ratio πT with moment of inertia error in case 2

    图 20  方案2转动愦量拉偏测试高压转子转速N2响应曲线

    Figure 20.  Response curves of high-pressure rotor speed N2 with moment of inertia error in case 2

    图 21  闭环过渡态控制器逻辑框

    Figure 21.  Logic diagram of closed-loop transient controller

    图 22  方案1最优控制器与传统控制器N1响应曲线对比

    Figure 22.  Comparison of N1 response curve between optimal controller designed in case 1 and traditional controller

    图 23  方案1最优控制器与传统控制器N2响应曲线对比

    Figure 23.  Comparison of N2 response curve between optimal controller designed in case 1 and traditional controller

    图 24  最小化迹寻优和最大化迹寻优闭环极点对比

    Figure 24.  Comparison of poles of closed-loop system designed with minimized trace optimization and poles of closed-loop system designed with maximized trace optimization

    表  1  稳态点条件

    Table  1.   Conditions of steady state point

    编号 n2cor SM
    1 10 588 5
    2 10 265 5
    3 9 943 5
    4 10 588 18
    5 10 265 24
    6 9 943 28
    7 10 588 33
    8 10 265 33
    9 9 943 33
    下载: 导出CSV

    表  2  方案1基状态矩阵

    Table  2.   Basis state matrix in case 1

    Ai a11 a21 a12 a22
    A1 -6.36 -0.09 6.63 -4.18
    A2 -9.10 0.13 5.75 -3.68
    A3 -4.71 -0.16 3.82 -2.29
    A4 -6.55 0.13 5.57 -3.72
    A5 -5.29 -0.22 5.15 -3.54
    A6 -2.90 -0.22 3.56 -2.17
    A7 -5.81 0.47 3.56 -4.17
    A8 -4.55 -0.34 4.60 -4.58
    A9 -2.52 -0.32 3.80 -3.22
    下载: 导出CSV

    表  3  方案1基输入矩阵

    Table  3.   Basis input matrix in case 1

    Bi b11 b21 b12 b22
    B1 2.99 -0.10 0.31 0.67
    B2 2.55 -0.14 0.46 0.68
    B3 1.45 -0.02 0.72 0.67
    B4 1.98 -0.01 0.48 0.66
    B5 1.46 -0.04 0.64 0.70
    B6 0.56 0 0.99 0.75
    B7 0.42 0.02 0.92 1.00
    B8 0.65 0.01 0.99 1.06
    B9 0.36 0.01 1.00 1.15
    下载: 导出CSV

    表  4  方案1最优基控制参数KP

    Table  4.   Optimal basis control parameter KP in case 1

    KPi, opt kP11 kP21 kP12 kP22
    KP1, opt -0.47 -0.05 -0.06 -2.05
    KP2, opt -0.56 -0.10 0.29 -2.09
    KP3, opt -0.99 -0.08 0.71 -2.21
    KP4, opt -0.72 -0.02 0.26 -2.12
    KP5, opt -0.94 -0.11 0.65 -2.09
    KP6, opt -2.40 -0.19 2.72 -2.23
    KP7, opt -3.16 -0.03 2.78 -1.58
    KP8, opt -2.06 -0.09 1.84 -1.52
    KP9, opt -3.63 -0.23 3.03 -1.62
    下载: 导出CSV

    表  5  方案1最优基控制参数KI

    Table  5.   Optimal basis control parameter KI in case 1

    KIi, opt kI11 kI21 kI12 kI22
    KI1, opt -2.97 -0.59 3.41 -7.77
    KI2, opt -4.95 -0.76 4.23 -6.73
    KI3, opt -4.33 -0.68 5.23 -4.67
    KI4, opt -4.62 0.05 5.12 -7.42
    KI5, opt -4.65 -0.96 7.07 -6.52
    KI6, opt -6.33 -0.83 14.32 -4.44
    KI7, opt -19.44 0.62 22.69 -6.22
    KI8, opt -8.69 -0.69 17.76 -6.21
    KI9, opt -8.34 -0.86 23.52 -4.36
    下载: 导出CSV

    表  6  方案2基输出矩阵

    Table  6.   Basis output matrix in case 2

    Ci c11 c21 c12 c22
    C1 -0.64 0 1.18 1
    C2 -1.13 0 1.27 1
    C3 -0.55 0 1.21 1
    C4 -0.88 0 1.14 1
    C5 -0.64 0 1.28 1
    C6 0.01 0 1.33 1
    C7 -0.02 0 0.64 1
    C8 -0.14 0 1.09 1
    C9 0.25 0 1.27 1
    下载: 导出CSV

    表  7  方案2基前馈矩阵

    Table  7.   Basis feedforward matrix in case 2

    Di d11 d21 d12 d22
    D1 0.73 0 0 0
    D2 0.75 0 0 0
    D3 0.67 0 0 0
    D4 0.74 0 0 0
    D5 0.68 0 0 0
    D6 0.37 0 0 0
    D7 0.38 0 0 0
    D8 0.45 0 0 0
    D9 0.26 0 0 0
    下载: 导出CSV

    表  8  方案2最优基控制参数KP

    Table  8.   Optimal basis control parameter KP in case 2

    KPi, opt kP11 kP21 kP12 kP22
    KP1, opt -1.06 -0.29 0.40 -1.84
    KP2, opt -0.86 -0.08 0.32 -2.01
    KP3, opt -1.08 -0.35 0.78 -1.91
    KP4, opt -0.85 0.10 0.11 -2.01
    KP5, opt -1.02 -0.39 0.60 -1.69
    KP6, opt 1.18 -0.18 -0.73 -1.84
    KP7, opt 0.58 1.05 -0.06 -2.01
    KP8, opt -0.30 -0.51 0.57 -1.02
    KP9, opt -0.05 0.78 0.06 -2.43
    下载: 导出CSV

    表  9  方案2最优基控制参数KI

    Table  9.   Optimal basis control parameter KI in case 2

    KIi, opt kI11 kI21 kI12 kI22
    KI1, opt -6.99 -1.50 1.39 -7.98
    KI2, opt -6.18 -0.68 1.80 -6.84
    KI3, opt -5.98 -1.35 3.30 -4.52
    KI4, opt -5.75 0.50 -0.23 -6.88
    KI5, opt -5.78 -1.48 1.70 -6.83
    KI6, opt -0.65 -1.31 2.95 -3.24
    KI7, opt -2.45 2.22 2.64 -6.21
    KI8, opt -3.98 -1.53 5.18 -5.63
    KI9, opt -1.35 0.78 2.15 -6.24
    下载: 导出CSV

    表  10  过渡态控制器参数KP

    Table  10.   Parameter KP of transient controller

    KPi, opt kP11 kP21 kP12 kP22
    KP1, opt -0.13 0 0 1.32
    KP2, opt -0.16 0 0 1.64
    KP3, opt -0.17 0 0 1.69
    下载: 导出CSV

    表  11  过渡态控制器参数KI

    Table  11.   Parameter KI of transient controller

    KIi, opt kI11 kI21 kI12 kI22
    KI1, opt -7.23 0 0 72.3
    KI2, opt -0.88 0 0 8.8
    KI3, opt -1.34 0 0 13.4
    下载: 导出CSV
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  • 收稿日期:  2020-11-26
  • 录用日期:  2021-04-16
  • 网络出版日期:  2022-05-20

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