【作者】 杨晓燕；

【导师】 高德欣；

【作者基本信息】 青岛科技大学 ， 检测技术与自动化装置， 2011， 硕士

【摘要】 在现实世界中,理想的线性系统是并不存在的,大多数实际系统都是非线性系统,并均是在外界干扰力和时滞的影响作用下工作的。传统的方法是把非线性系统模型转化为线性化模型,随着控制理论的发展,线性模型的局限性被人们认识。为了更好的描述实际对象,研究者构造了一个关于状态变量和控制变量分别是线性的,而总体上则是非线性的系统,即双线性系统。双线性系统是形式上最简单,并且最接近线性系统的一类非线性系统。特别的,在工程、社会经济、生态、生物等过程中的很多对象都可以用双线性系统进行描述,因次对于双线性系统的研究日益重要。本文的主要研究内容概括如下:1.引入了非线性系统的基本概念以及研究现状,详细介绍了双线性系统,包括其数学模型与研究现状;并简述了非线性系统反馈线性化、最优控制与时滞系统的相关知识。研究了双线性系统的最优控制问题,给出双线性系统的数学模型和最优控制律的设计过程。针对一类受扰动双线性系统,根据二次型性能指标,通过求解Riccati方程和Sylvester方程得到消除系统干扰的前馈/反馈最优扰动抑制控制律。2.针对具有控制时滞双线性系统,提出一种基于状态反馈线性化和模型转换的精确最优控制器设计方法。研究受外部扰动且具有时滞的双线性系统,通过转换,将其转换为时滞伪线性系统模型;利用一带有控制记忆的积分变换进行精确无滞后化变换,将时滞伪线性系统模型变为相应的无时滞伪线性系统模型。最后,基于二次型理论设计了系统的前馈-反馈最优扰动抑制控制律来消除扰动对系统的影响。3.利用非线性系统中关系度的知识,将具有扰动抑制的一类不确定时滞双线性系统进行了系统变换,将满足条件的该模型转换为具有扰动抑制的线性系统的最优控制问题,通过已有的结论,得到了原双线性系统的最优控制律,同时得到了最坏扰动抑制律,仿真证明了该方法的有效性。更多还原

【Abstract】 In the real world, the ideal linear system does not exist, most practical systems are nonlinear systems, and all work with external disturbance and time-delay. The traditional method is linearization. However, with the development of control theory, the limitation of linear model is recognized. In order to describe the actual object better, the researchers constructed a nonlinear system that the state variable and control variable are linear, the whole is nonlinear, this system is the bilinear system. A bilinear system is a nonlinear system which is the simplest in form and most approximate to a linear system. Bilinear system is applied in many practise and it can describe many plants in engineering, for example, the society economy, zoology, biology, etc. This makes that the research of bilinear systems become more and more important.The major results are shown as follows:1. First, give a brief overview of nonlinear systems and current domestic; Introduce the bilinear system, including its mathematical model and current status. And give a brief description of the feedback linearization of nonlinear systems, optimal control systems and time delay. Consider the optimal control problem for the bilinear system based on state feedback, give the mathematical model of the bilinear system and the optimal control law. Then consider the optimal control problem for the bilinear system affected by measurable disturbances, by solving the Riccati equation and the Sylvester equation, a feedforword/feedback transformation is designed which is used to eliminate the influence of the disturbances.2. For the bilinear systems with time-delay, optimal controller design method is proposed based on state feedback linearization and model transformation. Researching the bilinear system with time-delay and external disturbance, through the conversion, we change it to a time-delay pseudo linear system, a linear controllable system without with time-delay is obtained by exact delay-free transformation using integral transformation with memory control. Then based on the theory of linear quadratic optimal control, a feedforword/feedback optimal disturbances rejection control law is designed which is used to eliminate the influence of the disturbances.3. Based on the knowledge of relation in nonlinear systems, we make the partial coordinate alterlate to the uncertain bilinear system with time delay and external disturbance, and the partial linearization to the system. The optimal control problem is transformed into the optimal control problem of linear system with disturbance rejection. Using the exist conclusion, the original optimal control problem is solved at 1ast. Asimulation result demonstrates the effect of the proposed method.更多还原