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

由于在过去三年中，我们在订单中遇到了一些粗糙的控制设计方法，用于从实践和反向问题的视点对磁提升系统的振动控制。首先，作为其基础，我们有一个一致的方法来估计未建模的动力学使用封闭的环路标识，然后设计一个振动控制系统使用H-D2控制理论。作为一个结果，它被转化为一个重要的结果，因为它可以通过传感器噪音来塑造溢出效应的频率增益特征，并被称为补充的敏感性函数，因此具有一个缺口过滤器。基于这个观察，我们重新考虑了基本结果以实际的视点形式，并尝试扩展现有的有用的ILQ设计方法，因此可以处理频率塑造问题上的问题。在一个普通国家观察员的扩展中使用ILQ设计到线性功能观察器的关键是通过介绍一个额外的设计自由。在全订单和最低订单状态观察员的两个案例中，我们有一个分析性的辅助敏感性功能，可以用ILQ控制器这样的设计自由来塑造。然后，我们提出了一种新颖的频率形状方法，使用这种类型的控制器，并在实验上证实了它的有效性。作为一个结果，我们在设计一个低顺序控制器的维度被减少为一个第三个，与H-D2控制器比较。在最低限度的订单观察员的情况下，我们提出了一种两步设计方法，以实现名义性能优先和稳健性能，以利用一个额外的设计自由。在这个设计中，生成的控制器转向有较低的尺寸，并与一个基于完整的观察器进行比较。

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.