Gyroscopic Effect Decoupling Control of Maglev Rotor Supported by Nonlinear Force
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摘要: 电磁轴承非线性力支承的飞轮转子各自由度之间产生的强耦合，影响轴承转子系统稳定性。为此建立了径向四自由度的非线性电磁力-刚性转子动力学模型。在此基础上，提出了一种自适应径向基神经网络和滑模控制结合的算法（Adaptive RBFNN&SMC）。基于RBFNN对非线性电磁力和陀螺效应进行整体补偿，应用双曲正切函数作为滑模鲁棒项，对滑模控制进行改进，改善了滑模算法的抖振、抑制了质量不平衡扰动和随机扰动。根据Lyapunov稳定性理论证明了系统的渐进稳定性。最后通过仿真将提出的算法与PID算法和
$ \alpha $ 阶逆系统算法对比，结果表明该算法能有效补偿非线性力、解耦系统和改善抖振问题，同时对于外界扰动具有良好的抑制效果。Abstract: The high-speed maglev flywheel supported by nonlinear force shows strong coupling dynamics, which affects the stability of the rotor-bearing system. Therefore, a four-DOF dynamic model of nonlinear magnetic force-rigid rotor was established, and an adaptive radial basis neural network and sliding mode control algorithm (adaptive RBFNN&SMC) was proposed. The nonlinear force and gyro effect was integrally compensated by the RBFNN. The hyperbolic tangent function was used as the sliding mode robust term to improve the sliding mode control, reduce the chattering of the sliding mode algorithm and suppress the mass imbalance disturbance and random disturbance. A comparation of PID, α-order inverse system and the proposed algorithm was simulated. The results shows that the algorithm proposed can effectively compensate the nonlinear force, decouple the system and improve the chattering problem. At the same time, it can suppresses the external disturbance efficiently. -
图 2 电磁轴承控制回路示意图
Figure 2. Schematic diagram of the electromagnetic bearing control circuit
图 5 开关函数、双曲正切函数曲线
Figure 5. The switching function and hyperbolic tangent function curves
图 7 本文算法下加速响应曲线
Figure 7. The acceleration response curve under the proposed algorithm
图 8 600 W·h磁悬浮飞轮实验样机本体
Figure 8. 600 W·h magnetic suspension flywheel experimental prototype
图 10 本文算法上电磁轴承x方向噪声曲线及响应曲线
Figure 10. Noise curve and response curve in the x-direction of electromagnetic bearing under the proposed algorithm
图 11 本文算法yu、xd、yd噪声干扰响应曲线
Figure 11. Disturbance response curves of yu, xd, and yd under the proposed algorithm
图 12 本文算法所有自由度受扰响应曲线
Figure 12. Disturbance response curves of all degrees of freedom under the proposed algorithm
图 13 4 500 r/min xu非零初始状态响应对比
Figure 13. Response comparison of xu with nonzero initial state at 4 500 r/min
图 14 4 500 r/min yu非零初始状态响应对比
Figure 14. Response comparison of yu with nonzero initial state at 4 500 r/min
图 15 4 500 r/min xd非零初始状态响应对比
Figure 15. Response comparison of xd with nonzero initial state at 4 500 r/min
图 16 4 500 r/min yd非零初始状态响应对比
Figure 16. Response comparison of yd with nonzero initial state at 4 500 r/min
图 18 本文算法受初始扰动解耦误差
Figure 18. Decoupling error under the proposed algorithm with initial disturbance
图 19 4 500 r/min PID控制下不同偏心距的xu响应对比
Figure 19. Response comparison of xu with different eccentricities under PID control at 4 500 r/min
图 20 4 500 r/min 本文算法下不同偏心距的xu响应对比
Figure 20. Response comparison of xu with different eccentricities under the proposed algorithm at 4 500 r/min
图 21 采用
${{\rm{sgn}}} \left( {{{\boldsymbol{s}}}} \right)$ 的控制电流曲线Figure 21. Control current curve using sgn(s)
图 22 采用
$\tan ({{\boldsymbol{s}}/}{\boldsymbol{\delta}} ) $ 的控制电流曲线Figure 22. Control current curve using
$\tan ({{\boldsymbol{s}}/}{\boldsymbol{\delta}} ) $ 表 1 系统计算参数
Table 1. System calculation parameters
参数 数值 参数 数值 $\;{{\boldsymbol{\varLambda }}}$ ${\text{diag}}\left( {80,80,80,80} \right)$ ${k_{i} }$ 0 ${{\boldsymbol{\phi}} ^{ - 1} }$ ${\text{diag}}\left( {15,15,15,15} \right)$ $ {k_{\text{d}}} $ 8.34 ${{\boldsymbol{\gamma}} }$ ${\text{diag}}\left( {20,20,20,20} \right)$ ${l_{\text{u}}}/{\text{m}}$ 0.273 ${\boldsymbol{\nu}} $ 20 ${l_{\text{d}}}/{\text{m}}$ 0.282 ${\boldsymbol{\delta}} $ $5 \times {10^{ - 3}}$ $m/{\text{kg}}$ 56.8 ${b_{j} }$ 10 $J/({\text{kg}} \cdot {{\text{m}}^{-2}})$ 1.14 ${ { {\boldsymbol{c} } }_{i} }$ $[ { - 3}\quad { - 2}\quad{ - 1}\quad 0\quad \\ 1\quad 2\quad 3 ] \times {10^{ - 6} }$ ${J_{\textit{z}}}/({\text{kg}} \cdot {{\text{m}}^{-2}})$ 0.93 ${k_{\text{p}}}$ $16\;680 $ $e_0/{\text{m}}$ $1.59 \times {10^{ - 6}}$ 
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