分数阶观测器分析与设计研究
发布时间：2019-06-19 17:09
【摘要】：随着计算机科学的快速发展,分数阶理论已经在流体力学、信号分析以及电力电子等诸多领域开始得到应用。分数阶微积分是整数阶微积分的扩展,即微积分的阶次是分数。由于分数阶系统具有记忆性和遗传性,因此对系统动态过程的描述更为合理和精确。另外,分数阶控制器本身提供了更多的调节参数,并且参数整定的选择范围更广。分数阶微积分的特性以及在理论研究的不断突破,这使得分数阶控制的应用方面也得到了越来越多的重视。在实际应用中,对于系统而言,并非所有的状态变量都能够容易测得。因此,分数阶微分系统观测器的设计,具有重要的理论意义与应用价值,也是分数阶控制理论在实际工程应用中一个亟待解决的问题。本论文对分数阶滤波器以及分数阶观测器方面进行研究。主要进行的工作有:(1)提出一种分数阶观测器的设计方法。针对一类非线性系统,通过引入连续频率分布等价模型以及利用间接李雅普诺夫方法,获得全维观测器动态误差系统渐近稳定的充分条件,并结合LMI工具求解观测器增益。(2)提出分数阶滤波器设计方法。离散化近似处理是对分数阶滤波器数字实现的关键,离散化近似处理方法即是对于分数阶生成函数和展开方法上的选择。利用几种常见的离散化方法进行滤波器设计。分析各种离散法的性能,比较出符合滤波器设计的要求。分析出滤波器的阶次选择。(3)针对电动扭矩加载系统的数学模型,在分数阶滤波器的基础上设计分数阶抗干扰观测器,同时验证对抗干扰以及抗扰动的性能。然后与传统的PI控制进行对比显示分数阶干扰观测器的优越性。
[Abstract]:With the rapid development of computer science, fractional order theory has been applied in many fields, such as fluid mechanics, signal analysis, power electronics and so on. Fractional calculus is an extension of integer calculus, that is, the order of calculus is fraction. Because of the memory and heredity of the fractional system, the description of the dynamic process of the system is more reasonable and accurate. In addition, the fractional controller itself provides more adjustment parameters, and the selection range of parameter tuning is wider. The characteristics of fractional calculus and the continuous breakthrough in theoretical research have made more and more attention to the application of fractional order control. In practical application, not all state variables can be easily measured for the system. Therefore, the design of fractional differential system observer has important theoretical significance and application value, and it is also an urgent problem to be solved in practical engineering application of fractional control theory. In this paper, the fractional filter and fractional observer are studied. The main work is as follows: (1) A design method of fractional observer is proposed. For a class of nonlinear systems, the sufficient conditions for the asymptotic stability of the full-order observer dynamic error system are obtained by introducing the continuous frequency distribution equivalent model and the indirect Leonov method, and the observer gain is solved by combining the LMI tool. (2) the fractional filter design method is proposed. Discrete approximate processing is the key to the digital realization of fractional filter. Discrete approximate processing method is the choice of fractional generation function and expansion method. Several common discretization methods are used to design the filter. The performance of various discrete methods is analyzed, and the requirements of filter design are compared. The order selection of the filter is analyzed. (3) aiming at the mathematical model of the electric torque loading system, the fractional anti-interference observer is designed on the basis of the fractional filter, and the performance of anti-interference and anti-disturbance is verified at the same time. Then compared with the traditional PI control, the advantages of the fractional disturbance observer are shown.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713
[Abstract]:With the rapid development of computer science, fractional order theory has been applied in many fields, such as fluid mechanics, signal analysis, power electronics and so on. Fractional calculus is an extension of integer calculus, that is, the order of calculus is fraction. Because of the memory and heredity of the fractional system, the description of the dynamic process of the system is more reasonable and accurate. In addition, the fractional controller itself provides more adjustment parameters, and the selection range of parameter tuning is wider. The characteristics of fractional calculus and the continuous breakthrough in theoretical research have made more and more attention to the application of fractional order control. In practical application, not all state variables can be easily measured for the system. Therefore, the design of fractional differential system observer has important theoretical significance and application value, and it is also an urgent problem to be solved in practical engineering application of fractional control theory. In this paper, the fractional filter and fractional observer are studied. The main work is as follows: (1) A design method of fractional observer is proposed. For a class of nonlinear systems, the sufficient conditions for the asymptotic stability of the full-order observer dynamic error system are obtained by introducing the continuous frequency distribution equivalent model and the indirect Leonov method, and the observer gain is solved by combining the LMI tool. (2) the fractional filter design method is proposed. Discrete approximate processing is the key to the digital realization of fractional filter. Discrete approximate processing method is the choice of fractional generation function and expansion method. Several common discretization methods are used to design the filter. The performance of various discrete methods is analyzed, and the requirements of filter design are compared. The order selection of the filter is analyzed. (3) aiming at the mathematical model of the electric torque loading system, the fractional anti-interference observer is designed on the basis of the fractional filter, and the performance of anti-interference and anti-disturbance is verified at the same time. Then compared with the traditional PI control, the advantages of the fractional disturbance observer are shown.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN713
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