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LMI Based Gain-Scheduled Sliding Mode Control for Nonlinear and Time Varying Systems

基于 LMI 的非线性和时变系统增益调度滑模控制

基本信息

批准号：
09650264
负责人：
NONAMI Kenzo
金额：
$ 2.43万
依托单位：
Chiba 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 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650264/
关键词：
Sliding Mode Control Linear Matrix Inequality Gain-Schedulling Schedulled Hyperplane Time Varying System Lyapunov Stability Theorem Magnetic Bearing Gyroscopic Effect

项目摘要

A variable structure system or sliding mode control uses a discontinuous control structure to control nonlinear systems. It is a powerful control method with increasing application in many areas of control engineering. Gain scheduling is a special type of nonlinear feedback used in a variety of control. Recent advances in robust control theory have offered a new theoretical framework and systematic gain scheduling.A linerar parameter-varying (LPV) plant definition can be described as model of linear time-varying plants or nonlinear plants which are linearized using a vector of a time-varying parameter, such as theta(t). Using LPV plant definition, the gain scheduled H_* contol design is extensively presented in terms of linear matrix inequalitiees (LMI's), the solution of which are within the scope of efficient convex optimization techniques. Here, our aims are to extend this approach to designing a sliding mode hyperplane and applying it to a practical system. All definitions and theorems given for LPV plants are also valid in our study and will not be repeated here.This reserach project deals with slidiing mode hyperplane design for a class of linearr parameter-varying (LPV) plants, the state-space matrices' of which are an affine function of time varying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertainties, We have designcd a time-varying hyperplane for a rotor-magnetic bearing system with a gyroscopic effect, which can be considered an LPV plant due to parameter dependence on rotational speed. The obtained hyperplane is continuously scheduled with respect to rotational speed. We successfully carried out experiments using a commercially available turbomolecular pump system and results were reasonable and good.

变结构系统或滑模控制使用不连续控制结构来控制非线性系统。它是一种强大的控制方法，在控制工程的许多领域得到越来越多的应用。增益调度是一种特殊类型的非线性反馈，用于各种控制。鲁棒控制理论的最新进展为系统增益调度提供了新的理论框架。线性参数变（LPV）植物定义可以描述为线性时变植物或非线性植物的模型，这些植物使用时变参数的向量（如theta(t)）进行线性化。利用LPV对象的定义，用线性矩阵不等式（LMI’s）广泛地提出了增益调度H_*控制设计，其解在有效凸优化技术的范围内。在这里，我们的目标是将这种方法扩展到设计滑模超平面并将其应用于实际系统。对于LPV工厂给出的所有定义和定理在我们的研究中也是有效的，这里不再重复。本课题研究一类线性变参数对象的滑模超平面设计，其状态空间矩阵是时变物理参数的仿射函数。本文设计了具有陀螺效应的转子磁轴承系统的时变超平面，由于其参数依赖于转速，因此可以将其视为LPV对象。得到的超平面相对于转速被连续调度。我们成功地利用市售的涡轮分子泵系统进行了实验，结果合理而良好。