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.     

分数阶控制器的数字实现及其特性

针对分数阶控制器数值计算和应用难的问题,研究了分数阶控制器的数字实现方法和控制特性．取Grunwald-Letnikov定义有限项,并直接离散化,得到有限记忆数字实现法;利用Tustin算子生成函数把分数阶微分由复频域变换到Z域,然后用连分式展开式CFE(continued fraction expansion)近似展开,可得到Tustin CFE数字实现法．两种方法的频域对比分析表明Tustin CFE法优于有限记忆法．采用设计的分数阶控制器的数字实现方法,对分数阶控制器和传统PID控制器的控制性能进行了对比实验分析．研究结果表明:分数阶控制器对非线性具有较强的控制能力．     

分数阶控制系统

随着基于分数阶次的数学理论日益完善,分数阶控制系统也越来越广泛地被研究和讨论。为了完善分数阶控制系统的理论体系,给出了分数阶系统的总体综述。介绍了分数微积分的定义,给出了分数阶线性定常系统的传递函数和状态空间描述,简要介绍了分数阶控制系统的复频域分析和分数阶控制器及控制器的设计方法,并分析了几种设计方法的优缺点。分数系统的研究必然能找到合适的切入点广泛地进入现代控制领域,为真正实现工业控制自动化提供强有力的理论依据。     

复杂系统的分数阶内模控制器设计

针对高阶复杂系统提出一种分数阶内模控制器设计方法。利用微粒群算法(PSO)进行模型化简,基于内模控制(IMC)原理设计分数阶控制器,该控制器仅有一个可调参数,并根据鲁棒性能指标给出控制器参数整定的解析表达式。仿真结果表明,该方法可以使系统同时具有良好的目标值跟踪特性、扰动抑制特性以及克服参数变化的鲁棒性。     

分数阶模糊免疫PID控制器的设计

为改善分数阶PID控制器的控制性能,借鉴整数阶模糊免疫PID控制器,把模糊免疫调节与分数阶PID控制器结合起来,设计了分数阶模糊免疫PID控制器。仿真结果表明了该方法的有效性,不但提高了分数阶PID控制器跟踪性能,而且还具有良好的鲁棒性和抗干扰性。     

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。     

基于模糊估计的可调分数阶PID控制器设计

可变分数阶微分环节直接影响分数阶PID控制器性能,设计分数阶PID控制器需要根据被控对象传递函数凭经验调整微分阶次。采用Oustaloup间接离散法数字实现分数阶微积分,再基于模糊估计由特定分数阶次近似得到任意分数阶次微积分环节,根据参数整定规则确立各环节系数,设计了一种可调分数阶次的PID控制器。仿真实验证明,此方法得到的微积分环节对控制系统性能没有影响,根据整数阶被控对象传递函数调节微分阶次,分数阶PID控制器有较好的控制效果。     

一种分数阶预测控制器的研究与实现

本论文研究了一种新型预测控制器RTD-A的分数阶实现方法及应用. 与常规控制器比较, RTD-A控制器具有参数意义明确, 易于整定和实施的优点. 论文将RTD-A控制器扩展到分数阶形式, 并与经Z-N法整定的分数阶PI?D1控制器和Wang-Juang-Chan法整定的PID控制器进行了比较. 所提出的分数阶预测控制器在设定值跟踪, 克服负荷扰动, 鲁棒性等方面都有较理想的控制性能. 仿真结果验证了这种分数阶预测控制器的有效性.     

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.     

分数阶PIλDμ控制器的一种状态空间实现

首先回顾了分数阶微积分、分数阶系统和分数阶PIλDμ控制器的数学描述,对于一类分数阶SISO被控对象,提出了一种基于整数阶微分算子的分数阶PIλDμ控制器的S平面状态空间实现.同时,在Matlab Simulink仿真平台实现了基于Oustaloup连续滤波器法的分数阶微分算子和该状态空间实现,并基于遗传算法整定了状态空间参数.仿真结果验证了该状态空间的有效性与正确性.     

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.     

含有分数阶PID控制器的随机动力系统可靠性分析

随着粘弹性材料在工程结构中的广泛应用,刻画工程结构中粘弹性材料遗传特性和长记忆性的分数阶微积分成为研究的热点,特别是具有分数阶微积分特点的PID控制器更是从理论上和应用上受到关注.本文研究高斯白噪声激励下含有分数阶PID控制器的随机结构动力系统的可靠性问题.利用慢变过程的特征以及广义积分的性质,对分数阶PID控制器在数学上进行了近似处理,之后应用能量包络随机平均法确定了可靠性函数满足的后向Kolmogorov方程以及首次穿越时间统计矩满足的广义Pontryagin方程.结果表明：在分数阶控制器中,较小的分数阶α和较大的分数阶β均可以得到较为理想的可靠性结果,并且这些均与蒙特卡洛仿真结果一致,验证了方法的有效性和正确性.     

Optimal design of fractional order PID controller for time-delay systems: an IWLQR technique

ABSTRACT

In this paper, an optimal design based state feedback gain of fractional order proportional integral derivative (PID) controller for time delay system is proposed. The proposed optimal design is called as IWLQR, which will be the joined execution of both the invasive weed optimization (IWO) and linear quadratic regulator (LQR). The proposed technique modifies a fractional order proportional integral derivative (FOPID) regulator among a high order time delay scheme that achieves an elevated performance for a wide area. In the proposed methodology, the gain of the FOPID controller is tuned to achieve the desired responses which are determined using the LQR theory and the weight matrices of the LQR is anticipated with the assistance of IWO technique. The uniqueness of the projected technique is to reduce the fault in a PID regulator among the higher order time delay scheme by the aid of the increase limits of the regulator. The objective of the proposed control method is chosen in view of the set point parameters and the accomplished parameters from the time delay system. The projected method is employed to achieve the avoidance of high order time delay and the dependability restrictions such as tiny overrun, resolving time and fixed condition defect. This technique is carried out in MATLAB/Simulink platform and the results are separated by the earlier regulator junction representation like Z-N system, Wang technique, curve fitting technique, regression technique which illustrates the superior presentation of the anticipated abstaining in the existing work.     

开关磁阻电机分数阶PI调速控制器设计

在开关磁阻电机调速系统中,基于常规的PI控制,设计了分数阶PI转速闭环调速控制系统。在速度环和电流环中,分数阶积分用于积分环节,把分数阶微积分的扩展系统参数稳定域及比整数阶好的时域和频率特性用于非线性的开关磁阻电机调速控制系统中。采用直接离散法,将连续分数阶积分通过双线性变换离散化,并用连分式近似展开获得分数阶积分算子的数字实现。在MATLAB/Simulink中,建立了三相6/4极开关磁阻电机调速系统的仿真模型,与常规PI控制进行了比较,结果验证了该方法的有效性。     

Optimum design of fractional order PID controller for AVR system using chaotic ant swarm

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared to PID controller, the tuning of FOPID is more complex and remains a challenge problem. This paper focuses on the design of FOPID controller using chaotic ant swarm (CAS) optimization method. The tuning of FOPID controller is formulated as a nonlinear optimization problem, in which the objective function is composed of overshoot, steady-state error, raising time and settling time. CAS algorithm, a newly developed evolutionary algorithm inspired by the chaotic behavior of individual ant and the self-organization of ant swarm, is used as the optimizer to search the best parameters of FOPID controller. The designed CAS-FOPID controller is applied to an automatic regulator voltage (AVR) system. Numerous numerical simulations and comparisons with other FOPID/PID controllers show that the CAS-FOPID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.     

一种复杂系统的最优分数阶内模控制器设计

针对复杂系统提出了一种最优分数阶内模控制器设计方法。引入一种带混沌算子的人群搜索优化算法（Seeker Optimization Algorithm,SOA）将系统模型降阶简化,在此基础上完成了一种新的分数阶内模控制器的设计和参数最优整定。仿真结果表明,降阶模型很好地逼近了原系统,设计的控制器可以使系统具有良好的动态性能及克服参数变化的鲁棒性。     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.