一种改进的永磁同步电机分数阶速度控制器

为了实现永磁同步电机伺服系统的高性能速度控制,针对现有分数阶PI(FO-PI)控制器设计中存在的截止频率有效范围有限的问题,在频域设计的基础上,提出一种改进的分数阶控制器,在FO-PI基础上引入校正传递函数,保持分数阶控制性能的同时拓展控制器截止频率的选取范围,并设计三维作图法实现改进控制器的参数整定。最后通过仿真实验来验证改进分数阶速度控制器的有效性。仿真实验结果表明,所提出的改进分数阶速度控制器可以满足更高截止频率的要求,较传统FO-PI及整数阶PI控制器,可以提高速度控制的跟踪性能、动态性能和抗扰动性能。     

直流位置伺服系统的二自由度分数阶控制

为提高直流位置伺服系统的控制性能,提出了一种2自由度（two degree-of-freedom,2DOF）分数阶控制方法．通过设计一种2DOF控制结构,实现了系统的跟随和抗扰特性的解耦控制;将内模控制（internal model control,IMC）与分数阶控制相结合,选用分数阶滤波器,推导出了跟随控制器和抗扰控制器设计方法;根据控制性能的要求,利用系统截止频率和最大灵敏度指标,实现了2DOF控制器参数的解析整定．仿真实验结果表明,2DOF分数阶控制方法具有良好的位置跟随特性和抗干扰能力．     

一种整数阶系统的分数阶(PID)~γ控制方法

针对常见的1阶、2阶和1阶加积分系统,提出了一种分数阶(fractional order,FO)控制器设计方法.基于内模控制(internal model control,IMC)原理,采用分数阶滤波器推导出了一种分数阶(PID)γ控制器,该控制器仅包含两个可调整参数,有效降低了分数阶控制器整定的难度,并基于系统相位裕量φm和截止频率ωc,实现了分数阶(PID)γ控制器的参数整定.仿真结果表明,所提出的方法不但设计简单,参数整定方便,而且可使系统获得良好的设定值跟踪特性和干扰抑制特性,以及克服系统参数摄动的鲁棒性.     

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.     

基于理想Bode传递函数的分数阶PID频域设计方法及其应用

基于理想Bode传递函数,提出一种简便的分数阶PID控制器频域设计方法.采用传递函数模型匹配与辨识方法,将分数阶PID控制器5个参数的复杂设计问题转化为单个参数的一维搜索问题进行求解;结合短记忆法实现分数阶PID控制器数字化.该方法已成功应用于直流电机调速控制系统,能够达到期望的响应性能,具有强鲁棒性.实验结果验证了所提出设计方法的有效性.     

基于序列二次规划法的新型分数阶PIλ-PDμ控制器设计

针对被控对象具有分数阶特性的系统需要相应的分数阶控制器来提高控制效果, 提出一种新型的分数阶PI^λ-PD^μ控制器, 系统的前向通道采用分数阶PI^λ控制器, 被控对象的内反馈环采用分数阶PD^μ控制器, 利用序列二次规划法辨识分数 阶PI^\lambdaD^μ控制器的参数, 并设计了一种结构变换法求取分数阶PI^λ-PD^μ控制器的参数; 然后, 基于Oustaloup滤波器采用整数阶近似及模型降阶法对分数阶被控对象进行求解. 系统仿真结果表明, 与整数阶PI-PD控制器相比, 分数阶PI^λ-PD^μ控制器的抗干扰性较强, 能更好地满足系统的动态响应要求.     

一种分数阶内模TIλDemμ控制器设计方法

针对整数阶、 分数阶被控对象,提出了一种分数阶内模TI^λD^μ控制器的设计方法．首先对原被控模型进行降阶处理,得到二阶分数阶延时系统模型．然后将内模控制思想引入到降阶模型,设计内模控制器G_IMC（s）．最后将G_IMC（s）与所提的新型TI^λD^μ控制器进行参数对照,能够清晰地得出参数间的对应关系,从而得出分数阶TI^λD^μ的各参数．仿真结果表明,TI^λD^μ控制器能够获得良好的控制品质和鲁棒性．     

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.     

基于分数阶内模控制的风力机叶片颤振研究

针对风力机叶片颤振系统,提出了一种结合分数阶(Fractional Order)控制与内模控制(Internal Model Control,IMC)的新型颤振控制方法.利用分数阶滤波器设计了分数阶内模控制器,基于闭环动态特性指标,如相位裕量和截止频率,实现对控制器参数的自整定.通过仿真实验对比证明,针对风力机叶片颤振控制,所设计的控制方法优于传统PID、内模PID控制方法,不仅减少了控制参数,而且提高了动态特性和鲁棒性.     

基于分数阶(PID)~γ控制器的中频感应电炉温度控制

针对中频感应电炉炉温控制中存在的大惯性、非线性、模型不确定性等特点,提出了一种分数阶(PID)~γ控制器设计方法。该控制器基于内模控制(Internal Model Control,IMC)及分数阶滤波器推导得出,仅包含两个可调节参数,有利于控制器参数的整定,并基于控制系统的相位裕量和截止频率,实现了分数阶(PID)~γ控制器的参数整定。所提方法不仅可以使温控系统具有较好的设定值跟踪和干扰抑制特性,而且当系统参数摄动时表现出更好的鲁棒性,仿真结果证明了本文方法的有效性。     

Fractional Order PI‐PD Control of Liquid Level in Coupled Two Tank System and its Experimental Validation

This paper presents a level control problem of a coupled two tank single input single output (SISO) system. A cascade control strategy is adopted having a fractional order proportional integral (FOPI) controller and fractional order proportional derivative (FOPD) controller in the outer and the inner loops, respectively. Cascaded integer order proportional integral (IOPI) and integer order proportional derivative (IOPD) controllers are also designed to compare the performances. A frequency domain approach is followed to design all the controllers. It is mathematically shown that the FOPI and FOPD controllers can achieve less steady state error and consume less energy than that of the IOPI and IOPD controllers while meeting the same phase margin and gain crossover frequency. All propositions are validated on an experimental setup.     

Relay feedback tuning of robust PID controllers with iso-damping property.

A new tuning method for proportional-integral-derivative (PID) controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PID controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given frequency called the "tangent frequency" so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. At the "tangent frequency," the Nyquist curve tangentially touches the sensitivity circle. Several relay feedback tests are used to identify the plant gain and phase at the tangent frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PID controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PID controller design. Only several relay tests are needed. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for robust PID controller design with an iso-damping property.     

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k_p, k_i, k_d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.     

基于期望系统的PID频域逼近设计

为了能在时域和频域同时具有期望的系统性能,提出了一种基于期望系统的频域逼近设计方法：在开环幅相频率特性的低频段,待设计系统频率特性模型的实部与虚部分别逼近期望开环频率特性模型的实部与虚部,从而得到PID控制器的比例增益Kp和积分增益Ki;在开环幅相频率特性的中频段,以高于期望稳定裕度的幅值条件,获得微分增益Kd的置信区间,从而确保PID控制系统的稳定性。纯滞后系统和非最小相位系统的仿真研究表明,该方法能够获得与期望系统更近的时域跟踪性能以及不低于期望系统的频域稳定裕度;同时,与其它三种PID设计方法进行了频域性能对比和时域阶跃响应测试,结果表明所提出的PID设计方法能够获得更好的性能指标。液位控制实验显示：采用所提出的方法可以实现超调量为0,系统响应速度为被控对象开环响应的的4~5倍。     

Fractional Order Modeling And Nonlinear Fractional Order Pi‐Type Control For PMLSM System

In this paper, firstly a fractional order (FO) model is proposed for the speed control of a permanent magnet linear synchronous motor (PMLSM) servo system. To identify the parameters of the FO model, a practical modeling algorithm is presented. The algorithm is based on a pattern search method and its effectiveness is verified by real experimental results. Second, a new fractional order proportional integral type controller, that is, (PI^μ)^λ or FO[FOPI], is introduced. Then a tuning methodology is presented for the FO[FOPI] controller. In this tuning method, the controller is designed to satisfy four design specifications: stability requirement, specified gain crossover frequency, specified phase margin, flat phase constraint, and minimum integral absolute error. Both set point tracking and load disturbance rejection cases are considered. The advantages of the tuning method are that it fully considers the stability requirement and avoids solving a complex nonlinear optimization problem. Simulations are conducted to verify the effectiveness of the proposed FO[FOPI] controller over classical FOPI and FO[PI] controllers.     

Robustness analysis and design of fractional order Iλ Dμ controllers using the small gain theorem

ABSTRACT

In this paper, a simple method is proposed to tune the parameters of Fractional Integral-Fractional Derivative (FIFE) I^λ D^μ controllers based on the Bode diagram. The proposed technique provides a practical approach for tuning FIFE controllers to compensate stable plants. Using the small gain theorem and based on the sensitivity functions analysis, it is proved that by applying the designed FIFE controller the robustness of the compensated system in the presence of plant uncertainties is improved in comparison to the PI controller in a similar structure. Moreover, the closed-loop phase margin and gain crossover frequency are adjustable by tuning the free controller parameters. Simulation results are presented to demonstrate the simplicity of application and effectiveness of the tuned controller.     

Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time (FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results, it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.      

Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

For all the stable first order plus time delay (FOPTD) systems, a fractional order proportional integral (FOPI) or a traditional integer order proportional integral derivative (IOPID) controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously: gain crossover frequency and phase margin. In this paper, a guideline for choosing two feasible or achievable specifications, and a new FOPI/IOPID controller synthesis are proposed for all the stable FOPTD systems. Using this synthesis scheme, the complete feasible region of two specifications can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of two specifications can be verified before the controller design. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID and FOPI controllers. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. A simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller compared with the optimized integer order PI controller and the IOPID controller designed following the same synthesis for the FOPI in this paper.     

倾转旋翼机平均驻留时间切换鲁棒H∞跟踪控制

针对倾转旋翼飞行器模态转换阶段的飞行控制问题,本文给出了倾转旋翼机纵向运动飞行控制系统模型和一种基于参考模型的鲁棒跟踪控制方法.为了保证闭环系统在切换过程中稳定并同时满足指定的鲁棒H∞性能指标,利用状态观测器对系统不可观测状态进行估计,结合模型依赖平均驻留时间方法提出了一种倾转旋翼机切换鲁棒H∞跟踪控制方法,通过求解线性矩阵不等式得到控制器增益,并分析了系统的鲁棒稳定性.仿真结果表明,所提出的方法能够使飞行器系统准确跟踪指令,且对于控制器切换具有鲁棒性.     

A graphical tuning method of fractional order proportional integral derivative controllers for interval fractional order plant

In this paper, a novel graphical tuning method of fractional order proportional integral derivative (FOPID) controllers is proposed for a given interval fractional order plant family. Firstly, an approach is presented to solve the problem of robustly stabilizing the interval fractional order plant using FOPID controller. Moreover, some alternative methods are developed to reduce the computational burden of the presented approach. The results obtained here are general and strict proofs are given on these results. Secondly, a new approach is presented to calculate the complete sets of FOPID controller parameters which guarantee the specified H_∞-norm constraint for the interval fractional order plant. The developed approach is convenient and flexible. Finally, a unified design framework is proposed. The aim of the unified design is to compute the biggest region which can simultaneously provide internal stability, maintain the classical gain and phase margin and guarantee the modern H_∞-norm constraint for the interval fractional order plant. Examples are followed to illustrate the design procedure.