Control Systems Design of Nonlinear Systems and Negative Imaginary Systems

本项目属于控制系统理论与应用的工程领域。该项目的目的是为一般非线性系统或负虚数（NI）系统或两者开发新的控制器设计技术。由于这是两个独立的任务，因此将分别描述它们。非线性系统控制非线性系统的一种常见的、简单的方法是首先在一个工作点对非线性系统进行线性化，丢弃非线性元素，然后控制由此产生的线性系统。虽然这种控制器设计方法已被证明是富有成效的，但没有测量系统的线性化模型有多精确，因此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。相反，控制器是为这样的系统设计的，不承认它们的非线性行为。因此，学生将研究这些（通常被丢弃的）非线性元素对线性化模型的影响，并使用它来开发更合适的控制器设计方法。所采取的方法将是通过反馈控制鲁棒处理非线性元素。本文采用的新颖工程方法是将非线性视为对线性系统的扰动。这项研究的结果将为实践控制工程师提供有用的工具，以确定他们的线性化模型和控制器的准确性，并协助设计控制器，为此类系统产生更理想的结果。负虚系统在过去的十年中已经有很多工作来分析NI系统的性质并扩展NI系统的定义。研究方法合成这些系统的控制器也进行了。然而，这些合成方法不允许控制工程师自由地设计系统，使其具有他们想要的特性。因此，本项目旨在回答以下研究问题：-与使用适用于任何系统的方法设计的控制器相比，如何利用负虚系统的独特特性来设计具有改进性能的控制器？所采取的办法如下：首先，看看当前适用于所有系统的控制器设计算法和方法。利用NI系统的特性，尝试修改所讨论的控制器设计方法，改变或放松假设，并根据NI系统的特性添加约束。这将导致当前理论的修改版本，只适用于NI系统，产生比一般理论更理想的结果。（如果这被证明是不可行的）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。表现出负虚数特性的现实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的系统（“共定位”）。具有这些特性的控制问题的例子包括：-大空间结构的振动控制；-纳米定位系统，如控制原子力显微镜。这是一个重要的工程研究领域，因为负虚系统在世界上经常发生，所以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。

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.