【作者】 陈岚峰；

【导师】 薛定宇；

【作者基本信息】 东北大学 ， 系统仿真与应用， 2020， 博士

【摘要】 分数阶控制系统的研究是把微积分阶次推广到实数或者是复数,是对整数阶控制系统扩展和延伸。其中,研究分数阶微积分算子的近似方法和使分数阶与控制理论相结合是一个比较新颖的研究方向。现实生活中的很多现象和系统都体现出分数阶的特点,它是一种较整数阶更为普遍的存在。对于实际的系统控制,使用分数阶控制器往往能够获得更好的控制效果。因此,本文针对于分数阶系统的建模与控制方法以及其微积分算子的近似方法进行研究。主要工作如下:首先,研究系统的分数阶建模。因为许多实际系统都表现出分数阶的特性,为这些系统建立精确的数学模型就显得十分必要。但是,由于分数阶阶次的存在又使得对于建立分数阶系统变得十分的复杂和繁琐。相较时域建模,频域建模不需要大量繁琐的计算,所以本研究是基于频域建立的分数阶模型。在介绍几种常见的建立分数阶模型方法的基础上,提出基于粒子群(PSO)算法的最优辨识。使用该方法能够对相对复杂的无理分数阶模型参数进行精确的辨识,并且能够实现无理分数阶模型的有理化,以及对特殊分数阶系统及具有扰动信号存在的系统实现参数辨识,都得到了很好的辨识效果,通过辨识精度和拟合曲线说明该方法的正确性和可行性。其次,针对离子聚合物金属复合材料(IPMC)的驱动特性建立分数阶模型。在搭建了驱动特性实验环境的基础上,测量实验数据得到响应。提出利用Levy算法、Sanathanan和Koerner(SANKO)的递归算法、最优SANKO算法以及粒子群(PSO)算法分别为系统辨识模型。比较辨识的模型和实验数据的拟合精度及拟合效果,说明粒子群算法建立的模型更为精准,与实验数据拟合效果更好,可用于建立精确的系统分数阶模型。然后,针对分数阶系统设计最优分数阶控制器,以提高其控制指标和性能。由于分数阶控制器的整定参数相对于较多,所以设计的控制器更为灵活,可以很好地提高系统的控制性能。在研究了控制器参数对控制指标影响的基础上,为上一章辨识的IPMC驱动器设计最优控制器,提出基于最优化算法和给定的控制指标分别设计出整数阶和分数阶控制器,并对控制效果进行比较,从而说明分数阶控制效果更好。对设计的IPMC系统分数阶控制的可行性进行了 Simulink仿真验证。最后,针对分数阶算子与系统的整数阶近似方法进行了研究。基于连分式近似法、Carlson近似法、Matsuda近似法、Oustaloup滤波器近似法等广泛使用的方法,提出对有理分数阶模型使用Oustaloup改进的滤波器实现高阶近似,拟合效果很好。对无理分数阶模型分别采用基于频域响应近似和基于Charef技术近似,得到了很好的拟合效果,仿真说明这些方法可以用来实现分数阶模型的高阶整数阶近似,以便有利于在工程实际中应用。更多还原

【Abstract】 The research of fractional-order control systems is an extension of the integer-orders.The order of calculus is generalized to real numbers or complex numbers.Among them,the approximation of fractional calculus operators and the combination of fractional calculus and control theory are relatively new research directions.Many phenomena and systems in real-life reflect the characteristics of fractional-orders,which is a more common existence than the integer-orders.For practical system control,it is often possible to obtain better control effects by using fractional-order controllers.Therefore,the modeling and control of fractional-order systems and the approximation of fractional calculus operators are studied in this thesis.The main research work is as follows.Firstly,the fractional-order modeling of the system is studied.Because many practical systems exhibit the characteristics of fractional-orders,it is necessary to establish accurate mathematical models for these systems.However,due to the existence of fractional-order,it becomes very complicated and cumbersome for establishing a fractional-order system.Compared with time domain modeling,frequency domain modeling does not require a lot of cumbersome calculations.So,the establishment of a fractional-order model based on the frequency domain is in this research.Based on the introduction to several commonly used methods of establishing fractional-order models,an optimum identification method based on Particle swarm optimization(PSO)algorithm is proposed.This method is used to identify the parameters of a relatively complex irrational fractional-order model and realize the rationalization of the irrational fractional-order model.The parameters identification of the special fractional-order system or that with disturbance signals,the identification effects are good.The correctness and feasibility of the method are explained by the identification accuracy and fitting curves obtained.Secondly,the fractional-order model is established for the driving characteristics of ionic polymer metal composites(IPMC).Based on the experimental environment of driving characteristics,the experimental data of response is measured.The models are established for the driving system by Levy algorithm,recursion of Sanathanan and Koerner(SANKO)algorithm,optimum SANKO algorithm and the Particle swarm optimization(PSO)algorithm which is proposed.Comparing the fitting accuracy and fitting effect of the identifying models with experimental data,the model identifyied by the PSO algorithm is more accurate.The model can fit better with experimental data.It can be used to build an accurate systematic fractional-order model.Then,the fractional-order optimum controller is designed for the identifying fractional-order system to improve its control index and performance.Since the setting parameters of the fractional-order controller are more than the integer-order,the designed controller is more flexible and can improve the control performance of the system.Based on the study of controller parameters influence on the control indicators,the optimum controller for the IPMC driver identified in the previous is designed.The integer-order controller and the fractional-order controller are designed separately based on the optimization algorithm and the given control index.By comparing the control effects,the fractional-order controller is better.Then,verify the feasibility of the IPMC fractional-order control by Simulink simulation.Finally,the approximation of fractional-order operators and the integer-order approximation of fractional-order systems have been studied.Based on the widely used methods such as continued fraction approximation,Carlson approximation,Matsuda approximation and oustaloup filter approximation,the high-order approximation for rational fractional-order models by modified Oustaloup filter is proposed.The fitting effect is very good.The approximation for the irrational fractional-order model is by frequency domain response and Charef technology,the fitting effect is very good.The simulation shows these methods can be used to implement high-order integer-order approximations for fractional-order models.It can be used to facilitate application in engineering practice.更多还原