Control Systems Design of Nonlinear Systems and Negative Imaginary Systems

非线性系统和负虚系统的控制系统设计

• 批准号: 2324441
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2324441
• 关键词: Control; Systems; Design; Nonlinear; Negative

This project lies within the engineering field of control systems theory and applications. The aim of this project is to develop new controller design techniques for either general non-linear systems, or Negative Imaginary (NI) systems, or both. As these are two discrete tasks, they will be described separately.Non-linear SystemsA common, simple method for controlling nonlinear systems is to first linearise the nonlinear system at an operating point, discarding the nonlinear elements, and to subsequently control the resultant linear system. While this method of controller design has proven fruitful, there is no measure of how accurate this linearized model of the system is and therefore how well the controller designed for the linear model will behave on the true non-linear system. Instead, controllers are designed for such systems with no acknowledgement of their non-linear behaviours.Therefore, the student will investigate the effect of these (usually discarded) nonlinear elements on the linearised model, and use this to develop a more appropriate controller design method. The approach taken will be to robustly handle the nonlinear elements via feedback control. The novel engineering approach applied here is to treat the nonlinearities as perturbations to the linear system.The result of this research would be to provide useful tools for practising control engineers to both determine the accuracy of their linearised models and their controllers, and to assist in designing controllers which produce more desirable results for such systems. Negative Imaginary SystemsThere has been much work over the last decade to analyse the properties of NI systems and to extend the definition of NI systems. Research in methods to synthesise controllers for these systems has also been carried out. However, these synthesis methods do not allow the control engineer the freedom to design the system to have the properties they desire. Therefore, this project aims to answer the following research question:- How can the unique properties of negative imaginary systems be leveraged in designing a controller which has improved properties when compared to controllers designed using methods applicable to any system?The approach taken will be as follows:1. First, look at current controller design algorithms and methodologies which are applicable to all systems.2. Using the properties of NI systems, attempt to modify the controller design methods in question, changing or relaxing assumptions and adding constraints based on the properties of NI systems.3. This will result in a modified version of the current theories, applicable only to NI systems, which yield more desirable results than the generic theory would.4. (If this proves infeasible) New theories will attempt to be developed from first principles to directly leverage the properties of NI systems.The main type of real world system which exhibits the negative imaginary property are systems with force actuators and position sensors located in the same place ('co-located'). Examples of control problems with these properties include:- vibration control of large space structures;- nano-positioning systems, such as the control of atomic force microscopes.This is an important area of engineering research because negative imaginary systems occur frequently in the world, so having more powerful tools to design controllers for these systems would be beneficial to practising control engineers.

该项目属于控制系统理论和应用的工程领域。该项目的目的是开发新的控制器设计技术，无论是一般的非线性系统，或负虚（NI）系统，或两者兼而有之。非线性系统控制非线性系统的一种常见的简单方法是首先在一个工作点上将非线性系统线性化，丢弃非线性元件，然后控制得到的线性系统。虽然这种控制器设计方法已被证明是富有成效的，但没有测量系统的这种线性化模型有多精确，因此没有测量为线性模型设计的控制器在真正的非线性系统上的表现有多好。因此，学生将研究这些（通常被丢弃的）非线性元件对线性化模型的影响，并利用这些影响来开发更合适的控制器设计方法。所采取的方法是通过反馈控制来鲁棒地处理非线性元件。这里应用的新的工程方法是处理的非线性扰动的线性system.The结果的研究将提供有用的工具，为实践控制工程师，以确定其线性化模型和控制器的精度，并协助设计控制器，产生更理想的结果，这样的系统。在过去的十年里，有很多工作来分析NI系统的性质，并扩展NI系统的定义。还研究了为这些系统合成控制器的方法。然而，这些综合方法不允许控制工程师自由地设计具有他们期望的特性的系统。因此，该项目旨在回答以下研究问题：-如何利用负虚系统的独特属性设计控制器，与使用适用于任何系统的方法设计的控制器相比，该控制器具有更好的性能？所采取的办法如下：1.首先，看看目前的控制器设计算法和方法，适用于所有的系统.利用NI系统的特性，尝试修改控制器的设计方法，根据NI系统的特性，改变或放宽假设条件，增加约束条件.这将导致当前理论的修改版本，仅适用于NI系统，其产生比一般理论更理想的结果。(If这证明是不可行的）新的理论将试图从第一原理发展到直接利用NI系统的特性。表现出负虚特性的真实的世界系统的主要类型是力致动器和位置传感器位于同一位置（“共同定位”）的系统。具有这些性质的控制问题的例子包括：-大型空间结构的振动控制;-纳米定位系统，如原子力显微镜的控制。这是工程研究的一个重要领域，因为负虚系统在世界上经常出现，因此拥有更强大的工具来设计这些系统的控制器将有利于实践控制工程师。