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Research on Practical Design Method for Vibration Control of a Magnetic Levitation System by Application of Inverse Problem

应用反问题的磁悬浮系统振动控制实用设计方法研究

基本信息

批准号：
09650473
负责人：
FUJII Takao
金额：
$ 2.24万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650473/
关键词：
Inverse problem Magnetic levitation HィイD2∞ィエD2 control Closed loop identification Frequency-shaping ILQ control Spillover Servo system 最適制御 ILQ オブザーバ磁気浮上制御 H∽ 制御厳密線形化ロバスト制御厳密な線形化

项目摘要

For the last three years we have tackled several problems in order to obtain a robust control design method for vibration control of a magnetic levitation system from the viewpoint of practicality and inverse problem.First, as its basis, we have established a consistent method to estimate unmodeled dynamics using closed loop identification, and then design a vibration control system using HィイD2∞ィエD2 control theory. As a result, it turned out that it is vital for suppression of spillover to shape the frequency gain characteristics of the closed-loop transfer function from sensor noise to output, called as the complementary sensitivity function, so as to have that of a notch filter.Based on this observation, we have reconsidered the basic results obtained above form the viewpoint of practicality, and tried to extend the existing useful ILQ design method so as to treat the above frequency shaping problem. The key to it lies in the extension of a usual state observer used in ILQ design to linear function observer by introducing an additional design freedom. In both cases of full-order and minimal-order state observers, we have clarified analytically the class of complementary sensitivity functions that can be shaped by the ILQ controller with such a design freedom of observer. We then proposed a novel frequency shaping method using this type of controllers, and confirmed its usefulness experimentally. As a result, we have succeeded in designing a low-order controller of dimension as reduced by one third, compared with the HィイD2∞ィエD2 controller. In the case of minimal order observer, moreover, we have proposed a two-step design method achieving nominal performance first and robust performance afterward by utilizing an additional design freedom. In this design, the resulting controller turned out to have lower dimension, compared with the one based on a full-order observer.

在过去的三年中，我们从实用性和逆问题的角度出发，研究了磁悬浮系统振动控制的鲁棒控制设计方法。首先，在此基础上，采用闭环辨识方法建立了一种一致性估计未建模动力学的方法，然后采用H∞∞∞控制理论设计了振动控制系统。因此，为了抑制溢出，塑造从传感器噪声到输出的闭环传递函数（称为互补灵敏度函数）的频率增益特性是至关重要的，从而具有陷波滤波器的频率增益特性。在此基础上，我们从实用性的角度对上述基本结果进行了重新思考，并尝试扩展现有有用的ILQ设计方法来处理上述频率整形问题。其关键在于通过引入额外的设计自由度，将ILQ设计中常用的状态观测器扩展为线性函数观测器。在全阶和最小阶状态观测器的情况下，我们解析地阐明了具有这种观测器设计自由的ILQ控制器可以形成的互补灵敏度函数的类别。在此基础上提出了一种新的频率整形方法，并通过实验验证了其有效性。因此，我们成功地设计了一种低阶控制器，其维数比H∞∞r D2控制器减少了三分之一。此外，在最小阶观测器的情况下，我们提出了一种两步设计方法，通过利用额外的设计自由度，首先实现标称性能，然后实现鲁棒性能。在此设计中，与基于全阶观测器的控制器相比，得到的控制器具有更低的维数。