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.

在过去的三年里，我们解决了几个问题，以便从实用性和反问题的角度获得磁悬浮系统振动控制的鲁棒控制设计方法。首先，作为其基础，我们建立了一致的方法来估计结果表明，塑造闭环传递函数的频率增益特性对于抑制溢出至关重要。从传感器噪声到输出，称为互补灵敏度函数，从而具有陷波滤波器的函数。基于此观察，我们从实用性的角度重新考虑了上述获得的基本结果，并尝试扩展现有的有用ILQ设计方法来处理上述频率整形问题，其关键在于通过在全阶和最小阶两种情况下引入额外的设计自由度，将ILQ设计中使用的常用状态观测器扩展到线性函数观测器。秩序国家观察员，我们有分析阐明了具有这种观察器设计自由度的 ILQ 控制器可以塑造的互补灵敏度函数的类别，然后我们提出了一种使用此类控制器的新型频率整形方法，并通过实验证实了其有效性。与HiD2控制器相比，我们成功地设计了一个低阶控制器，其维数减少了三分之一。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，实现了标称性能优先和鲁棒性能。随后，通过利用额外的设计自由度，与基于全阶观测器的控制器相比，最终的控制器尺寸更低。