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Chinese Journal of Ship Research, Volume. 16, Issue 4, 132(2021)

Fractional order adaptive sliding mode control for nonlinear anti-roll of ship

Qionglin FANG
Author Affiliations
  • Institute of Navigation, Jimei University, Xiamen 361021, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (18)
    Equations (20)
    References (13)
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    Figures & Tables(18)
    [in Chinese]

    Fig. 1. [in Chinese]

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    [in Chinese]

    Fig. 2. [in Chinese]

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    P-M spectrum of waves at different ship speeds when =70°不同船速下海浪P-M谱（=70°）

    Fig. 3. P-M spectrum of waves at different ship speeds when =70°不同船速下海浪P-M谱（=70°）

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    [in Chinese]

    Fig. 4. [in Chinese]

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    Sliding mode closed loop control curve of rolling angle (v=5 m/s，=80°)横摇角滑模闭环控制曲线（v=5 m/s，=80°）

    Fig. 5. Sliding mode closed loop control curve of rolling angle (v=5 m/s，=80°)横摇角滑模闭环控制曲线（v=5 m/s，=80°）

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    Sliding mode closed loop control curve of rolling angle (v=5 m/s，=90°)横摇角滑模闭环控制曲线（v=5 m/s，=90°）

    Fig. 6. Sliding mode closed loop control curve of rolling angle (v=5 m/s，=90°)横摇角滑模闭环控制曲线（v=5 m/s，=90°）

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    Sliding mode closed loop control curve of rolling angle (v=5 m/s，=100°)横摇角滑模闭环控制曲线（v=5 m/s，=100°）

    Fig. 7. Sliding mode closed loop control curve of rolling angle (v=5 m/s，=100°)横摇角滑模闭环控制曲线（v=5 m/s，=100°）

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    Sliding mode closed loop control curve of rolling angle (v=10 m/s，=80°)横摇角滑模闭环控制曲线（v=10 m/s，=80°）

    Fig. 8. Sliding mode closed loop control curve of rolling angle (v=10 m/s，=80°)横摇角滑模闭环控制曲线（v=10 m/s，=80°）

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    Sliding mode closed loop control curve of rolling angle (v=10 m/s，=90°)横摇角滑模闭环控制曲线（v=10 m/s，=90°）

    Fig. 9. Sliding mode closed loop control curve of rolling angle (v=10 m/s，=90°)横摇角滑模闭环控制曲线（v=10 m/s，=90°）

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    Sliding mode closed loop control curve of rolling angle (v=10 m/s，=100°)横摇角滑模闭环控制曲线（v=10 m/s，=100°）

    Fig. 10. Sliding mode closed loop control curve of rolling angle (v=10 m/s，=100°)横摇角滑模闭环控制曲线（v=10 m/s，=100°）

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    [in Chinese]

    Fig. 11. [in Chinese]

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    [in Chinese]

    Fig. 12. [in Chinese]

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    System phase space control curve (v=5 m/s，= 120°)系统相空间控制曲线（v=5 m/s，= 120°）

    Fig. 13. System phase space control curve (v=5 m/s，= 120°)系统相空间控制曲线（v=5 m/s，= 120°）

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    • Table 1. Parameters of ship model

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      Table 1. Parameters of ship model

      参数数值
      总长/m2.8
      型宽/m1.35
      吃水/m0.4
      轻载重量/kg50
      最大负载/kg450
      转动惯量${I_x}$/（kg·m2）31.38
      阻尼力矩系数B1/（Nm∙rad−1∙s−1）50.23
      恢复力矩系数C1/（Nm∙rad−1）1719.5
      系数k/（Nm∙A−1）5

    • Table 2. Result comparison of different control algorithms

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      Table 2. Result comparison of different control algorithms

      v/$({\rm{m}}\cdot{\rm{s}}^{-1})$${\mu _{\rm{e}}}$/(°)${E_{\rm{Open}}}$${\sigma _{\rm{Open}}}$${E_{\rm{SMC}}}$${\sigma _{\rm{SMC}}}$${E_{\rm{FOASMC}}}$${\sigma _{\rm{FOASMC}}}$$\dfrac{{{E_{\rm{FOASMC}}}}}{{{E_{\rm{Open}}}}}$$\dfrac{{{\sigma _{\rm{FOASMC}}}}}{{{\sigma _{\rm{Open}}}}}$$\dfrac{{{E_{\rm{FOASMC}}}}}{{{E_{\rm{SMC}}}}}$$\dfrac{{{\sigma _{\rm{FOASMC}}}}}{{{\sigma _{\rm{SMC}}}}}$
      10502.512 6×10−51.186 3×10−51.232 1×10−61.221 5×10−63.189 3×10−71.749 2×10−71.27×10−21.47×10−225.89×10−214.32×10−2
      602.680 1×10−51.272 0×10−51.251 4×10−61.155 1×10−62.711 2×10−71.518 8×10−71.01×10−21.19×10−221.67×10−213.15×10−2
      702.914 9×10−51.393 8×10−51.199 3×10−61.066 3×10−62.962 7×10−71.457 5×10−71.02×10−21.05×10−224.70×10−213.67×10−2
      803.258 2×10−51.575 9×10−51.288 1×10−68.131 7×10−72.413 3×10−71.426 9×10−70.74×10−20.91×10−218.74×10−217.55×10−2
      903.810 7×10−51.876 6×10−59.003 0×10−78.338 7×10−71.375 3×10−71.083 6×10−70.36×10−20.58×10−215.28×10−212.99×10−2
      1004.934 4×10−52.495 6×10−53.402 1×10−71.402 3×10−61.841 3×10−88.054 7×10−80.04×10−20.32×10−25.41×10−25.74×10−2
      5502.950 7×10−51.412 6×10−51.215 2×10−61.030 4×10−63.240 7×10−71.487 0×10−71.10×10−226.67×10−21.05×10−214.43×10−2
      603.086 9×10−51.484 5×10−51.238 4×10−69.561 8×10−72.919 6×10−71.402 5×10−70.95×10−223.58×10−20.94×10−214.67×10−2
      703.264 7×10−51.579 4×10−51.202 6×10−69.134 2×10−72.492 6×10−71.425 5×10−70.76×10−20.90×10−220.73×10−215.61×10−2
      803.498 1×10−51.705 4×10−51.029 9×10−67.567 6×10−72.137 6×10−71.353 4×10−70.61×10−220.76×10−20.79×10−217.88×10−2
      903.810 7×10−51.876 6×10−59.003 0×10−78.338 7×10−71.375 3×10−71.083 6×10−70.36×10−215.28×10−20.58×10−212.99×10−2
      1004.247 7×10−52.118 3×10−59.596 4×10−77.083 1×10−71.179 2×10−79.110 5×10−80.28×10−20.43×10−212.29×10−212.86×10−2
      1104.907 4×10−52.480 9×10−52.321 2×10−71.471 1×10−61.960 5×10−88.185 3×10−80.04×10−20.33×10−28.45×10−25.56×10−2

    • Table 3. Result comparison of fractional orders

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      Table 3. Result comparison of fractional orders

      $\alpha $均值方差
      0.91.531 9×10−71.193 6×10−7
      0.11.368 5×10−71.095 4×10−7
      −0.21.002 4×10−81.392 1×10−7
      −0.35.751 9×10−91.228 7×10−7
      −0.47.974 9×10−91.168 3×10−7

    • Table 4. Result comparison of control law gains

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      Table 4. Result comparison of control law gains

      c均值方差
      1003.498 4×10−71.664 3×10−7
      503.636 3×10−71.728 6×10−7
      104.630 6×10−72.149 1×10−7
      55.484 0×10−72.508 9×10−7
      0.19.514 4×10−75.153 3×10−7

    • Table 5. Result comparison of sliding mode surface gains

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      Table 5. Result comparison of sliding mode surface gains

      λ均值方差
      1001.932 8×10−71.724 9×10−7
      501.837 1×10−71.608 8×10−7
      51.757 7×10−71.550 2×10−7
      11.375 3×10−71.083 6×10−7
      0.51.187 6×10−79.317 8×10−8
      0.14.178 1×10−82.628 9×10−8
      0.052.239 4×10−81.459 0×10−8
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    Qionglin FANG. Fractional order adaptive sliding mode control for nonlinear anti-roll of ship[J]. Chinese Journal of Ship Research, 2021, 16(4): 132

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    Paper Information

    Category: Ship Design and Performance

    Received: Aug. 11, 2020

    Accepted: --

    Published Online: Mar. 28, 2025

    The Author Email:

    DOI:10.19693/j.issn.1673-3185.02069

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology