摘要
非线性现象呈现的复杂性和多样性不但无法用线性系统理论解释,而且很难用统一的理论定性的描述。因此在非线性控制领域中,众多学者一般的是针对某一类的非线性系统加以分析和设计,归纳出系统特性,提出研究方法,从而取得局部成果和进展。
在实际非线性系统中由于模型简化、建模误差、外界扰动以及量测误差等因素的影响,系统模型中存在大量的不确定性。对于这些不确定性的处理一直是非线性控制领域研究的热点和难点问题。只有合理的处理不确定性,控制策略在应用到实际系统中才有可能取得理想的效果。
本文研究最小相位不确定非线性系统的鲁棒输出调节问题,即设计反馈控制律在维持闭环系统全局信号一致最终有界情况下达到跟踪参考输入和/或抑制扰动的目的。其中参考输入和非期望扰动由一被称作外系统的线性中性稳定的自治微分方程生成,统称为外系统信号。反馈控制律,或称作调节器,需要在被控对象和外系统都存在不确定性的情况下依然满足控制目标的要求。所设计的控制律基于内模和反馈镇定器的结合。
本文研究的主题着重于调节器理论与鲁棒镇定技巧的整合,扩展输出调节理论在不确定非线性系统中的应用。本文在以往研究工作的基础上,针对不确定的输出反馈非线性系统和下三角非线性系统,提出一种新的内模设计方法,即利用外系统信息和镇定过程中设计的输入项构造内模方程,在融合鲁棒镇定技巧的基础上解决其输出调节问题。而且当外系统包含未知参数时,我们同样可按照类似设计思路构造出自适应内模方程,估计出外系统的未知频率,从而完全补偿非期望扰动的影响。
同时,本文引入状态观测器用以解决系统输出反馈输出调节问题,在降低观测器设计,内模设计和镇定器设计之间的耦合作用方面进行了初步的探索
论文的结构组织如下:
第一章,介绍所选课题的背景知识,研究意义和国内外相关研究现状,说明本文的主要研究对象和贡献。
第二章,介绍论文涉及的基础概念和主要理论,包括稳定性概念,中心流形理论,浸入,高增益观测器及系统输出调节理论的初步知识。
第三章,给出输出反馈非线性系统形式,分别针对当系统不确定项在原点是否为零情况下,设计状态反馈调节器和输出反馈调节器。此不确定项被假设为由一已知平滑函数所界定。其中我们给出了一种新的内模设计思路,使得调节器既能够补偿外系统信号中非期望扰动的影响,又能够保证在系统不确定性条件下满足闭环系统有界稳定要求。
第四章,我们将上一章的内模设计方法扩展到一类包含未知参数、未知函数项和动态不确定的下三角系统,设计状态反馈和输出反馈鲁棒调节器。特别的,在输出反馈调节器设计中,我们针对具体的系统模型,分别引入普通观测器和动态增益观测器估计系统状态,结合内模设计给出满足控制目标的反馈控制律。
第五章,首先考虑由不确定外系统驱动的非线性下三角系统的鲁棒输出调节问题,设计中,我们给出一种自适应内模设计方法,估计出外系统未知频率。同时,对于一类受到未知正弦波扰动的不确定单输入严格反馈系统,此不确定满足匹配条件,我们利用标称系统的Lyapunov函数设计自适应内模方程,对系统进行二次设计,在系统存在不确定项情况下达到扰动抑制目标。
第六章,对论文内容进行总结,并指出进一步的研究方向。
The complexities and diversities nonlinear phenomena reveal are neither explained by linear system theory nor possibly characterized by unified theory. It is therefore of interest for most of the researchers in nonlinear control literature to delineate classes of nonlinear systems for which certain of analysis and design methods are readily proposed to handle the systems dynamics. The methods and results generally confined to partial nonlinear systems make considerable progress in nonlinear control theory.
Uncertainties exist in all practical systems, which possibly arise from modelling simplication, modelling error, external disturbance and measurement noise. Handling over the uncertainties in nonlinear control theory is always the interesting but difficult task. The control law can not achieve the expected performance in real control systems without compensating the uncertainty factors appropriately.
The dissertation addresses robust output regulation problem for minimum-phase uncertain nonlinear systems, which is to design a feedback control law to achieve tracking for a class of reference input and/or rejecting for a class of disturbances while maintaining close-loop system overall signals uniform ultimate boundedness. In this formulation, the reference input and the unexpected disturbance, referred to "exogenous signals", are generated by a linear and neutrally stable autonomous differential equation which is called the exosystem. The feedback control law, or alternatively regulator which is generally based on the combination of the internal model and the stabilizer, is required to preserve the expected control performance in the presence of uncertainties contained by both the controlled plant and the exosystem. The study of integrating regulator theory and robust adaptive stabilization techniques and extending the regulator theory in uncertain nonlinear systems is emphasized in this dissertation. An internal model design method is proposed for a class of uncertain output feedback nonlinear system and lower-triangular nonlinear systems. We use the exosystem information and the stabilizing input items designed in stabilizing process to construct the internal model and finally present a feedback control law with the immersion of robust stabilizing techniques. When the exosystem contains uncertain parameters, we can also construct the adaptive law to estimate the unknown frequencies of exosystem and therefore completely compensate the unexpected disturbance.
On the other hand, we introduce state observer to solve output feedback output regulation problem and attempt to probe into reducing the coupling of observer design, internal design and stabilizing design.
The chapters of the thesis are organized as follows:
In chapter 1, we introduce the background of this topic and current research situation followed by motivations, and present system models to be addressed and the main contributions of this dissertation briefly.
Chapter 2 reviews some relevant fundamental concepts and main theory including stability, center manifold theory, immersion, high-gain observer and basic knowledge of system output regulation theory.
Chapter 3 gives the forms of output feedback nonlinear system, and design state feedback regulator when the unknown nonlinearities are vanishing at the system origin and output feedback regulator when they are non-vanishing separately. The uncertain items are supposed to be bounded by a known smooth function. In the design process, we introduce a new method of constructing internal model such that the regulator obtained can compensate the exogenous unexpected disturbance while maintaining close-loop ultimate boundedness stability in the presence of system uncertainties.
Chapter 4 extends the internal model design method described in last chapter to a class of uncertain nonlinear low-triangular systems containing unknown parameters, unknown nonlinearities and unmodeled dynamics and studies robust output regulation problem using state feedback and output feedback. When addressing design of output feedback regulator, we introduce classic state observer and dynamic gain observer based on the different model form to estimate system state, and propose the feedback control law with combination of internal model to achieve control objects.
In Chapter 5, we firstly investigates robust output regulation problem of nonlinear low-triangular systems driven by uncertain exosystem. A new adaptive law is presented to estimate the unknown frequencies of exosystem in the regulator design. Then, we address the adaptive disturbance rejection problem for a class of single input strict-feedback nonlinear system subject to uncertain nonlinearity and unknown sinusoidal wave disturbance. The uncertain nonlinearity is supposed to satisfy the matching condition. We construct an adaptive internal model and redesign the system using information of Lyapunov function of the nominal systems to achieve the disturbance rejection in the presence of system uncertain nonlinearity.
In chapter 6, we summarize the dissertation and discuss open problems for future research.
引文
冯纯伯,张侃健.(2004).非线性系统的鲁棒控制[M].北京:科学出版社.
洪奕光,程代展.(2005).非线性系统的分析与控制[M].北京:科学出版社
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