Independent Cascade Control Method for Permanent Magnetic Levitation Platform
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摘要:
针对各悬浮单元磁力特性差异导致的倾斜问题，设计一种用于无接触传送的永磁悬浮平台，提出了具有气隙偏差积分反馈的分散式串级控制方法. 首先，分析了悬浮平台的动力学模型与平衡条件，获得各悬浮单元气隙与平台三自由度之间的变换关系；其次，根据悬浮单元系统特点设计了双闭环串级控制系统，外环是以气隙为被控对象的主调节回路，内环是以转角为被控对象的随动回路，并引入气隙偏差进行积分反馈；最后，通过悬浮实验进行验证. 结果表明：引入积分反馈后，起浮后各磁悬浮单元气隙一致，向不同位置施加0.1 kg重物，各悬浮单元气隙同步增大0.12 mm；悬浮平台能够通过调节内环转角弥补磁力特性差异并实现偏载下水平悬浮，但系统的调节时间比无积分反馈的分散串级控制系统增加约1.4倍.
Abstract:Aiming at tilt caused by the difference of magnetic characteristics of each MLU (magnetic levitation unit), a permanent magnetic levitation platform is designed for contactless transportation; and an independent cascade control method is presented, which allows integral feedback of air gap deviation. Firstly, the dynamic model and equilibrium conditions of the levitation are analyzed to establish the transformation relationship between the air gap of each suspension unit and three degrees of freedom of the platform. Secondly, given each MLU features, the cascade control system with a double closed-loop is designed, in which the outer loop plays a major regulating role for the air gap, the inner loop works as a follow-up control for the rotation angle, and air gap error among each MLU runs as the integral feedback. Finally, the levitation experiment is conducted to verify the proposed controller. The results show that, when introducing the integral feedback, the air gap of each MLU is the same after levitating, and the air gap increases 0.12 mm synchronously when 0.1 kg of weight is applied to different positions. The platform adjusts the rotational angle to control the difference of magnetic characteristics and fulfill the horizontal levitation under eccentric load. However, the adjusting time of the system is about 1.4 times that of the independent cascade control system without integrated feedback.
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Key words:
- magnetic levitation /
- PD control /
- cascade control systems /
- integrated feedback
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图 1 永磁悬浮平台的三维模型
Figure 1. Three-dimensional model of permanent magnetic levitation platform
图 2 永磁悬浮平台的运动分析简图
Figure 2. Schematic diagram of motion analysis for permanent magnetic levitation platform
图 3 具有偏差积分反馈的分散串级控制系统框图
Figure 3. Block diagram of independent cascade control method with integral feedback of air gap deviation
图 4 永磁悬浮平台的实验系统
Figure 4. Experimental system of permanent magnetic levitation platform
图 5 无积分反馈时系统起浮实验结果
Figure 5. Experimental results during system floating without integral feedback
图 6 有积分反馈时系统起浮实验结果
Figure 6. Experimental results during system floating with integral feedback
图 8 无积分反馈时在Ⅰ加载的实验结果
Figure 8. Experimental results of loading at position Ⅰ without integral feedback
图 9 有积分反馈时在Ⅰ加载的实验结果
Figure 9. Experimental results of loading at position Ⅰ with integral feedback
图 10 悬浮平台的气隙阶跃实验结果
Figure 10. Experimental results of air gap step for levitated platform
表 1 施加偏载后悬浮系统的稳态气隙
Table 1. Steady-state air gap length of levitation system under eccentric load
mm 加载位置编号 无气隙偏差补偿 有气隙偏差补偿 1 2 3 4 1 2 3 4 0 3.94 3.92 4.11 4.17 4.00 4.00 4.00 4.00 Ⅰ 4.15 4.02 4.08 4.24 4.12 4.12 4.12 4.12 Ⅱ 4.05 4.16 4.21 4.11 4.12 4.12 4.12 4.12 Ⅲ 3.90 4.0 4.33 4.26 4.12 4.12 4.12 4.12 Ⅳ 4.00 3.87 4.20 4.39 4.12 4.12 4.12 4.12 
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表 2 施加偏载后永磁体的转角
Table 2. Rotational angle of permanent magnet under eccentric load
（°） 加载位置编号 无气隙偏差补偿 有气隙偏差补偿 1 2 3 4 1 2 3 4 0 59.5 52.9 55.2 59.1 58.4 56.3 53.1 59.6 Ⅰ 64.3 54.7 54.6 60.9 61.4 57.8 53.6 61.1 Ⅱ 61.9 57.4 57.0 57.7 60.4 58.6 54.5 59.7 Ⅲ 58.6 54.3 59.3 61.2 58.8 57.7 55.3 60.8 Ⅳ 60.9 51.9 57.0 64.2 60.2 56.2 54.4 61.9
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