Feedforward decoupling and internal model control for rotor of magnetically suspended control and sensing gyroscope
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摘要:
磁悬浮控制敏感陀螺以洛伦兹力磁轴承（LFMB）为力矩器驱动转子偏转。针对磁悬浮控制敏感陀螺转子径向转动自由度间存在耦合的问题以及转子偏转高精度快响应要求，提出一种前馈解耦内模控制方法。根据洛伦兹力磁轴承的工作原理建立了转子偏转动力学模型，并设计了前馈解耦矩阵实现转子径向偏转解耦，在此基础上，采用二自由度内模控制器（2-DOF IMC）对转子进行高精度快响应偏转控制。MATLAB仿真结果表明所提出的控制方法可有效实现对陀螺转子偏转的完全解耦，且转子偏转响应时间较交叉PID算法减少57.1%，受0.1sin（2π
t ）°正弦信号扰动影响产生的偏转波动幅值较交叉PID算法减少76%。-
关键词:
- 磁悬浮控制敏感陀螺 /
- 洛伦兹力磁轴承(LFMB) /
- 径向偏转 /
- 前馈解耦 /
- 二自由度内模控制
Abstract:Magnetically suspended control and sensing gyroscope takes Lorentz force magnetic bearing (LFMB) as torquer to drive the rotor to tilt. As there is coupling between the two radial rotation degrees of freedom and it requires that rotor tilts with high precision and fast response, feedforward decoupling and internal model controller is proposed. Dynamic model for rotor tilting is established based on basic structure of LFMB. Feedforward decoupling matrix is designed to perform tilting decoupling in radial direction, and then on this basis, two-degree-of-freedom internal model controller (2-DOF IMC) is adopted to perform rotor tilting control with high precision and fast response. Simulation results by MATLAB indicate that the proposed method can realize full decoupling for rotor tilting, response time is reduced by 57.1% than that of cross PID controller, and tilting fluctuation amplitude produced by 0.1sin(2π
t )° disturbance signal is reduced by 76% than that of cross PID controller. -
图 6 灵敏度函数与补灵敏度函数Bode图
Figure 6. Bode diagrams of sensitivity function and penalty sensitivity function
表 1 转子偏转系统参数
Table 1. Parameters of rotor tilting system
参数 数值 Jz/ (kg·m2) 0.016 6 Ω/Hz 100 λ2 0.003 Kp 15 Kd 3 n 200 L/m 0.115 8 kL 0.5 kH 0.2 lr/m 0.078 Jr/ (kg·m2) 0.009 7 λ1 0.08 τ/s 0.002 Ki 0.001 B/T 0.4 lm/m 0.059 ωL/Hz 80 ωH/Hz 400 kr 0.05 
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