基于敏感传递函数的分数阶PI~λD~μ控制器的设计

发布时间：2018-03-01 12:40

本文关键词： 分数阶微积分分数阶PI~γ、PI~γD~μ控制器敏感传递函数稳定域参数整定液位控制　出处：《天津科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：过去我们用整数阶微积分方程描述自然界中的事物,但随着科学技术的发展,我们发现,自然界中许多现象依靠传统整数阶微分方程式是不能精确描述的。其实,现实的世界本质上大部分都是分数阶的。所以,分数阶模型理所应当就成为描述自然界现象的数学模型。分数阶微积分对于我们所能看到的、所能感受到的、所能控制的自然世界中的事物具有很大的影响。本文首先介绍分数阶微积分理论的发展及背景,然后,以THJSK-1型水箱综合实验平台为实验背景,研究水箱综合控制系统、水箱模型的建立、时滞系统及其特点以及分数阶算子的近似,并在此基础之上,利用可应用于分数阶系统的敏感传函的界与系统幅值裕度和相角裕度的关系,研究了滞后系统的PIλ、PIλDμ控制器的参数稳定域和参数整定方法,给出了满足要求的控制器参数的完整区域。本文做了以下工作：(1)根据水箱实验设备及工作原理,通过水箱液位控制实验建立了单容水箱的数学模型,并验证了模型的正确性与有效性。(2)针对建立的时滞系统,应用敏感传函的界与系统幅值裕度和相角裕度的关系,研究其分数阶PIλ、PIλDμ控制器的参数整定。并与传统的控制器参数下的控制效果相比较,通过MATLAB仿真验证了分数阶控制器能够获得比整数阶更好的动态性能。本文的主要创新点是利用敏感传函的界与系统的幅值裕度和相角裕度直接相关,给出了系统相对稳定性的信息。采用一种代数方法,在控制器的参数稳定域内,按敏感传函的界进行PIλ、PIλDμ控制器的参数整定。具体的仿真实例和水箱实验证明了该方法设计的PIλ控制器具有良好的动态性能和鲁棒性,验证了该方法的有效性。
[Abstract]:In the past, we used to describe things in nature with integral order calculus, but with the development of science and technology, we found that many phenomena in nature can not be accurately described by traditional integer order differential equations. The real world is essentially fractional. So fractional order models are, of course, mathematical models that describe natural phenomena. Fractional calculus is what we can see and feel. This paper first introduces the development and background of fractional calculus theory, and then, taking the THJSK-1 water tank synthesis experimental platform as the experimental background, studies the water tank integrated control system. The establishment of the water tank model, the characteristics of the time-delay system and the approximation of fractional order operators. On the basis of this, the relationship between the bounds of sensitive transmissions applicable to fractional order systems and the amplitude margin and phase margin of the system is used. In this paper, the parameter stability region and parameter tuning method of Pi 位 N Pi 位 D 渭 controller for hysteretic systems are studied, and the complete region of controller parameters satisfying the requirements is given. The following work is done: 1) according to the experimental equipment and working principle of water tank, The mathematical model of a single tank is established through the water tank level control experiment, and the correctness and validity of the model are verified. For the time-delay system established, the relation between the bounds of the sensitive function and the amplitude margin and the phase angle margin of the system is applied. The parameter tuning of the fractional Pi 位 PI-位 D 渭 controller is studied, and the control effect is compared with that of the traditional controller. The MATLAB simulation shows that the fractional order controller can achieve better dynamic performance than the integer order. The main innovation of this paper is that the bounds of the sensitive function are directly related to the amplitude margin and the phase angle margin of the system. The information of the relative stability of the system is given. An algebraic method is used in the parameter stability domain of the controller. The parameter tuning of Pi 位 PI-位 D 渭 controller is carried out according to the bounds of sensitive transmissions. The simulation examples and water tank experiments show that the Pi 位 controller designed by this method has good dynamic performance and robustness, and the effectiveness of the proposed method is verified.
【学位授予单位】：天津科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TP273

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