复杂分数阶多自主体系统的运动一致性

复杂环境中,许多自然现象的动力学特性不能应用整数阶方程描述,而只能用分数阶（非整数阶）动力学的智能个体合作行为来解释. 本文假设多自主体 系统存在个体差异,采用不同的分数阶动力学特性组成复杂分数混合阶微分方程. 应用分数阶系统的Laplace变换和频域理论,研究了有向网络拓扑下,时延分数混合阶多自主体系统的运动一致性. 由于整数阶系统是分数阶系统的特殊情况,本文的结论可以推广到整数阶与分数阶混合的多自主体系统中. 最后,应用仿真实例对本文结论进行了验证.     

分数阶系统的分数阶PID控制器设计

对于一些复杂的实际系统,用分数阶微积分方程建模要比整数阶模型更简洁准确.分数阶微积分也为描述动态过程提供了一个很好的工具.对于分数阶模型需要提出相应的分数阶控制器来提高控制效果.本文针对分数阶受控对象,提出了一种分数阶PID控制器的设计方法.并用具体实例演示了对于分数阶系统模型,采用分数阶控制器比采用古典的PID控制器取得更好的效果.     

一类不确定分数阶混沌系统同步的自适应滑模控制方法

针对一类系统不确定及受外界干扰的分数阶混沌系统,本文首先将分数阶微积分应用到滑模控制中,构造了一个具有分数阶积分项的滑模面.针对系统不确定及外界干扰项,基于分数阶Lyapunov稳定性理论与自适应控制方法,设计了一种滑模控制器以及分数阶次的参数自适应律,实现了两不确定分数阶混沌系统的同步控制,并辨识出相应误差系统中不确定项及外界干扰项的边界.在分数阶系统稳定性分析中使用的分数阶Lyapunov稳定性理论及相关函数都可以很好地运用到其它分数阶系统同步控制方法中.最后数值仿真验证了所提控制方法的可行性与有效性.     

不确定混沌系统用分数阶系统同步与参数辨识

针对不确定整数阶混沌系统的同步和参数辨识问题,提出一种新的策略即用分数阶混沌系统来同步整数阶混沌系统并实现不确定参数的辨识。首先引入预控制量并利用主动控制构造同步误差方程,然后用分数阶混沌系统稳定性理论和自适应控制理论,设计同步控制器及参数的自适应率,最终实现整数阶混沌系统用分数阶混沌系统同步和参数辨识。数值仿真实现参数不确定整数阶Lorenz系统用分数阶Lorenz系统进行同步和参数辨识仿真,结果表明提出方法的有效性。     

计及时滞的互联电网负荷频率控制最优分数阶PID控制器设计

分数阶PID控制器相比于传统整数阶PID控制器,具有控制性能好、鲁棒性强等诸多优势,可应用于电网的负荷频率控制(load frequency control,LFC)中.针对网络化时滞互联电网的LFC问题,提出了一种基于计算智能的分数阶PID控制器参数优化整定方案.该方案选择时滞LFC系统时域输出响应构建优化目标函数,采用最近提出的灰狼优化算法获得最优的分数阶PID控制器参数,所设计的控制器能确保一定时滞区间内LFC系统的稳定性.仿真算例表明,所设计的LFC最优分数阶PID控制器比传统整数阶PID控制器的控制性能更优,时滞鲁棒性更强.     

分数阶PD控制器在时滞伺服系统中的研究

分数阶微积分理论的发展推动了分数阶微积分在各个领域的广泛应用,分数阶控制算法的研究也成为近几年的研究热点.目前分数阶控制理论的研究主要集中在理论分析,对于目前所研究的这类工程性较强的控制对象,成熟的研究成果较少.针对实际工程中含有时滞的伺服系统模型,将Flat phase法和系统稳定性裕度条件相结合,设计了分数阶PD控制器.此PD控制器结构简单,对参数变化稳定性好,控制精度高.为了对比仿真实验,文章还设计了整数阶PID控制器.仿真结果表明,分数阶控制器比传统整数阶PID控制器的控制精度更高,鲁棒性更好.     

基于模糊分数阶PIλDμ控制的AC/DC变换器

作为AC/DC电力变换装置的核心,控制系统控制效果的好坏直接影响电压输出波形的质量.为了进一步提高AC/DC电力变换装置的控制性能,增强系统的鲁棒性和稳态性,提出一种模糊控制与分数阶PIλ Dμ控制相结合的复合控制策略,并将其用于十二脉波整流电路的控制系统中.采用模糊控制器可以很好地实现对控制参数的自适应调整,分数阶PIλDμ控制器在非线性系统的控制过程中能够取得比整数阶PID控制器更好的控制效果.仿真和实验结果表明,改进后的控制器具有较强的灵活性和鲁棒性,稳态性和自适应能力得到增强,适用于非线性时变系统.     

航天器近距离相对轨道的滑模控制

基于滑模控制原理,研究了近距离追踪航天器与目标航天器交会对接时,相对运动轨道的控制问题.首先,建立非线性航天器相对运动模型;其次,利用滑模控制原理和分数阶导数的相关性质,设计了整数阶PD控制器和分数阶PD~α控制器;最后,分别运用整数阶和分数阶控制器对未扰和受扰系统实施控制.数值仿真结果表明,整数阶与分数阶控制器均能实现对未扰和受扰系统的控制,验证了方法的有效性.同时发现,在时效性上,分数阶控制器明显优于整数阶控制器;在能效性上,达到相同控制目标时,分数阶控制器的能量消耗大于整数阶控制器.     

分数阶PI^λD^μ控制器控制性能的研究

现实控制系统研究中存在很多分数阶系统,因此对系统提出了分数阶PI~λD~μ控制器,控制器将传统整数阶PID控制器的微分与积分阶数扩展到分数,增加了两个参数微分阶数μ和积分阶数λ.为了对比研究分数阶系统分别在分数阶PI~λD~μ控制器控制下和在整数阶PID控制器控制下的系统性能,针对一个典型的分数阶系统,分别设计两类控制器,再进行性能比较.实验仿真结果表明,与整数阶PID控制器相比,该系统在分数阶PI~λD~μ控制器控制下整个闭环系统具备较好的动、静态性能,并且鲁棒性较强,说明分数阶PI~λD~μ控制器控制性能的优越性以及当被控系统为分数阶系统时应该设计分数阶PI~λD~μ控制器.     

一类分数阶系统的分析及控制器设计

针对一类与传统一阶惯性环节传递函数结构类似的分数阶系统,推导出该类分数阶系统稳定的参数取值范围,并给出了不同时间响应与分数阶阶次的对应关系.然后基于该类分数阶系统同时设计了分数阶PIλ控制器和整数阶PI控制器,控制器参数采用粒子群优化算法得到.结果表明:在控制该类对象时两者均能取得很好的控制效果,证明了本文所提方法的有效性.但由于整数阶PI控制器比分数阶PIλ控制器简单且便于实现,因此在工程应用中针对该类分数阶对象选择PI控制器即可满足要求.     

Robust stability analysis for fractional‐order systems with time delay based on finite spectrum assignment

In this paper, the robust stability of a fractional‐order time‐delay system is analyzed in the frequency domain based on finite spectrum assignment (FSA). The FSA algorithm is essentially an extension of the traditional pole assignment method, which can change the undesirable system characteristic equation into a desirable one. Therefore, the presented analysis scheme can also be used as an alternative time‐delay compensation method. However, it is superior to other time‐delay compensation schemes because it can be applied to open‐loop poorly damped or unstable systems. The FSA algorithm is extended to a fractional‐order version for time‐delay systems at first. Then, the robustness of the proposed algorithm for a fractional‐order delay system is analyzed, and the stability conditions are given. Finally, a simulation example is presented to show the superior robustness and delay compensation performance of the proposed algorithm. Moreover, the robust stability conditions and the time‐delay compensation scheme presented can be applied on both integer‐order and fractional‐order systems.     

Smith Predictor Based Fractional‐Order‐Filter PID Controllers Design for Long Time Delay Systems

In this paper, an original model‐based analytical method is developed to design a fractional order controller combined with a Smith predictor and a modified Smith predictor that yield control systems which are robust to changes in the process parameters. This method can be applied for integer order systems and for fractional order ones. Based on the Bode's ideal transfer function, the fractional order controllers are designed via the internal model control principle. The simulation results demonstrate the successful performance of the proposed method for controlling integer as well as fractional order linear stable systems with long time delay.     

Consensus of Multi-agent Systems with Feedforward Nonlinear Dynamics and Digraph

This paper considers a high-order consensus problem of multi-agent system with feedforward nonlinear and time-varying input delay in a directed network. In order to achieve the consensus, we propose a low gain distributed protocol which can get rid of impacts of feedforward nonlinearity and an arbitrarily bounded input delay on the consensus problem. Moreover, for any upper bound time-varying delay and strongly connected diagraph, the proposed controller can solve the consensus problem of multi-agent systems with feedforward nonlinearity if the designed parameter θ is great than the threshold value. Finally, several numerical simulations are presented to demonstrate the validity of the theoretical results.     

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.     

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative (FO-PID) controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system (MLS), which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller. An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored. The controller parameters are tuned using dynamic particle swarm optimization (dPSO) technique. Effectiveness of the proposed control scheme is verified by simulation and experimental results. The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers. It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.      

基于时延控制的伪码多普勒补偿算法

针对高动态或者弱信号条件下,伪码多普勒对卫星导航系统信号捕获的影响将会凸显,导致捕获性能明显降低的问题,提出了一种基于时延控制的码多普勒补偿方法,利用数字延迟滤波器来补偿码多普勒引入的本地码和接收信号的相位不匹配。同时,给出了包括码多普勒补偿在内的新的卫星导航系统信号捕获结构。仿真结果表明：新方法能够很好地进行码多普勒补偿,采用三阶Farrow结构的分数延迟滤波器就可以使捕获损耗降低到0.3 dB以下。     

网络控制系统分数阶PI~λD~μ控制器研究

针对带延时的分数阶的网络控制系统,采用分数阶的P I D控制器对系统进行仿真,并与不存在网络时延的系统进行对比。仿真结果表明,网络时延使系统敏感性增加,但分数阶控制器本身的鲁棒性,仍可保证系统具有良好的控制效果。     

Relationship Between Integer Order Systems and Fractional Order Systems and Its Two Applications

Existence of periodic solutions and stability of fractional order dynamic systems are two important and difficult issues in fractional order systems (FOS) field. In this paper, the relationship between integer order systems (IOS) and fractional order systems is discussed. A new proof method based on the above involved relationship for the non existence of periodic solutions of rational fractional order linear time invariant systems is derived. Rational fractional order linear time invariant autonomous system is proved to be equivalent to an integer order linear time invariant non-autonomous system. It is further proved that stability of a fractional order linear time invariant autonomous system is equivalent to the stability of another corresponding integer order linear time invariant autonomous system. The examples and state figures are given to illustrate the effects of conclusion derived.      

Proportional integral-fractional filter controller design for first order lag plus time delay system

In this work, a design approach of proportional integral-fractional filter (PI-FF) controller for first order plus time delay (FOPTD) system is proposed in order to enhance the feedback control system performances characteristics. The controller design method is drawn up such that the transfer function of the overall closed-loop system is equivalent to the transfer function of the general fractional Bagley–Torvik reference model whose behaviour ranges from relaxation to oscillation for different values of the fractional order derivative and the damping ratio-like parameter. The tuning parameters of the PI-FF controller are derived analytically from the FOPTD process model and the general fractional Bagley–Torvik reference model parameters. Illustrative examples were presented to test the effectiveness and the usefulness of the proposed PI-FF controller on the feedback control system performance characteristics enhancement.