基于指数衰减性能要求的离散系统最优控制的研究

发布时间：2018-04-28 16:07

本文选题：离散系统 + 指数衰减　；参考：《青岛科技大学》2017年硕士论文

【摘要】：随着社会不断进步和科学技术快速发展,计算机性能和控制技术水平得到不断的提高,离散系统的研究在控制理论领域中也愈加受到众多学者的关注。在实际工程中,时滞现象所涉及的领域较为广泛,几乎所有实际控制系统中都普遍带有时滞现象,时滞的存在通常会造成系统性能变差。此外,控制系统工作时或多或少会受到外界的干扰,致使系统的动态性能和稳态性能变差。因此,针对离散系统的时滞问题及扰动问题的分析具有重要意义。本文首先对离散系统进行了简单的概述。接着对时滞系统进行了综述性地介绍,并介绍了这一领域内对时滞现象的研究方法以及研究动态。对最优控制的理论知识以及其发展状况加以概述,阐述了含有时滞系统的最优控制理论的发展现状。最后,对振动领域中的振动控制问题加以概述,重点介绍了振动主动控制技术,并对振动主动控制方法的研究进展及其最优控制问题加以阐述。其次,针对选取的离散系统,研究了状态变量中含有时滞的最优控制问题。通过加入指数衰减得到一个新的离散系统,针对该离散系统对最优控制问题展开研究。本文提出通过引入灵敏度参数,将原系统的最优控制问题转变成一个既不含有超前项也不含有时滞项的两点边值(TPBV)问题,通过级数求和得到最优控制律。最后通过实验仿真表明该算法的可行性。接着,分析研究了引入指数衰减的含有随机扰动的离散系统。首先对随机噪声扰动项进行卡尔曼滤波估计,其次通过分离原理对原系统进行分析,进而得到最优控制律。最后通过MATLAB仿真表明该方法的可行性。最后选取含有柔性基础的悬臂梁振动模型为研究对象,对基于指数衰减性能的含有外界扰动的离散系统的最优控制问题进行研究。根据振动力学知识,可以推导获得含有柔性基础悬臂梁的振动微分方程,再结合压电方程得到含有柔性基础悬臂梁系统的状态空间表达式。将该连续系统离散化得到的离散系统就是我们要研究的含有持续扰动的离散系统。采用含扰动离散系统的最优控制对该系统进行研究,并通过实验仿真验证其可行性。
[Abstract]:With the continuous progress of society and the rapid development of science and technology, the performance of computer and the level of control technology have been continuously improved, and the study of discrete systems has been paid more and more attention by many scholars in the field of control theory. In practical engineering, the delay phenomenon involves a wide range of fields, almost all practical control systems generally have time delay phenomenon, the existence of time delay will usually lead to the system performance deterioration. In addition, the control system is more or less disturbed by external disturbance, which makes the dynamic and steady-state performance of the control system worse. Therefore, it is of great significance to analyze the time-delay problem and perturbation problem of discrete systems. In this paper, a brief overview of discrete systems is given. Then, this paper gives a general introduction to the time-delay system, and introduces the research methods and the research trends of the time-delay phenomenon in this field. The theoretical knowledge of optimal control and its development are summarized, and the development of optimal control theory with time delay is expounded. Finally, the vibration control problems in the field of vibration are summarized, the active vibration control technology is introduced, and the research progress of the active vibration control method and its optimal control are described. Secondly, the optimal control problem with time delay in state variables is studied for the selected discrete systems. A new discrete system is obtained by adding exponential attenuation, and the optimal control problem of the discrete system is studied. In this paper, by introducing sensitivity parameters, the optimal control problem of the original system is transformed into a two-point boundary value TPBV problem with neither lead term nor delay term. The optimal control law is obtained by summing up the series. Finally, the feasibility of the algorithm is demonstrated by experimental simulation. Then, the discrete systems with stochastic perturbations with exponential attenuation are studied. Firstly, the stochastic noise disturbance is estimated by Kalman filter, and then the optimal control law is obtained by analyzing the original system by the separation principle. Finally, the feasibility of the method is demonstrated by MATLAB simulation. Finally, the vibration model of cantilever beam with flexible foundation is selected as the research object, and the optimal control problem of discrete system with external disturbance based on exponential attenuation performance is studied. According to the knowledge of vibration dynamics, the vibration differential equation of cantilever beam with flexible foundation can be derived, and the state space expression of cantilever beam system with flexible foundation can be obtained by combining piezoelectric equation. The discrete system obtained by discretization of the continuous system is a discrete system with persistent perturbations that we are going to study. The optimal control of the discrete system with disturbance is used to study the system, and the feasibility of the system is verified by experimental simulation.
【学位授予单位】：青岛科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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