Model-Free Adaptive Control for Single-Degree-of-Freedom Magnetically Levitated System
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摘要:
针对单自由度磁悬浮系统的非线性及难以建立精确数学模型的问题，将全格式无模型自适应控制（FFDL-MFAC）方法应用于单自由度磁悬浮系统，首先，采用无模型自适应控制算法、伪梯度估计算法、伪梯度重置算法和单自由度磁悬浮系统的动态化数据模型，设计单自由度磁悬浮系统的控制器；然后，仿真分析MFAC控制参数对单自由度磁悬浮系统控制效果的影响及对阶跃响应信号、干扰信号和噪声信号的响应特性；最后，在磁悬浮球实验装置上进行实验验证. 研究结果表明：全格式无模型自适应控制方法只需采集单自由度磁悬浮系统在工作状态下的I/O数据，无需建立单自由度磁悬浮系统精确数学模型，通过设定全格式无模型自适应控制器参数即可使控制器具备良好的自适应性和鲁棒性，实现高精度稳定悬浮控制；与PID相比，FFDL-MFAC将系统的超调量降低了0.005，稳定悬浮位移的误差均方根减小了0.2607.
Abstract:Aiming at the problem of nonlinear and difficult to establish accurate mathematical model of a single-degree-of-freedom magnetically levitated system, the model-free adaptive control method based on full-format dynamic linearization (FFDL-MFAC) was applied to a single-degree-of-freedom magnetically levitated system. Firstly, model-free adaptive control algorithm, pseudo gradient estimation algorithm, pseudo gradient reset algorithm and dynamic data model of single degree of freedom magnetic levitation system were used to design the controller of single degree of freedom magnetic levitation system. Then the influence of MFAC control parameters on the control effect of the single-degree-of-freedom magnetically levitated system and the response characteristics of step response signal, interference signal and noise signal are analyzed by simulation, and the experimental verification was carried out on the magnetic levitation ball experimental device. Finally, the experimental verification was carried out on the magnetic levitation ball experimental device. The results show that the FFDL-MFAC method only needs to collect the I/O data of the single-degree-of-freedom magnetically levitated system under the working state, and does not need to establish an accurate mathematical model of the single-degree-of-freedom magnetically levitated system. The high precision and stable suspension control can be realized by setting the parameters of the model free adaptive controller, and the controller has good adaptability and robustness. Compared with PID, FFDL-MFAC reduces the overshoot of the system by 0.005, and the root mean square error of stable suspension displacement is reduced by 0.2607.
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Key words:
- magnetic levitation /
- adaptive algorithms /
- model-free adaptive control /
- pseudo-gradient
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图 1 单自由度磁悬浮系统示意
Figure 1. Schematic diagram of single degree-of-freedom magnetically levitated system
图 8 MFAC与PID算法对干扰信号的响应
Figure 8. Response of MFAC and PID algorithm to interfering signal
图 9 MFAC与PID算法对白噪声的响应
Figure 9. Response of MFAC and PID algorithms to white noise signal
图 11 铁球悬浮位移与传感器测量位移的关系
Figure 11. Relationship between the suspension displacement of the iron ball and the displacement measured by the sensor
表 1 单自由度磁悬浮系统的物理参数
Table 1. Physical parameters of a single-degree-of-freedom magnetically levitated system
符号 参数 值 m 小球质量/g 94 Ka 放大系数 6.508 A 系数 0.02012 B 系数/（A·m−1） 39.433 
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表 2 阶跃信号响应下MFAC与PID控制器的性能对比
Table 2. Performances comparison between MFAC and PID controller under step signal response
控制器 超调量 稳定时间/s eRMS PID 0.005 0.205 1.2484 FFDL-MFAC 0 0.070 0.6350
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表 3 干扰信号下MFAC与PID控制器的性能对比
Table 3. Performance comparison between MFAC and PID controller under interfering signal response
控制算法 eRMS PID 1.3341 FFDL-MFAC 0.7405
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