Maximum sensitivity based fractional IMC–PID controller design for non-integer order system with time delay

A simple approach with a small number of tuning parameters is a key goal in fractional order controller design. Recently there have been a number of limited attempts to bring about improvements in these areas. In this paper, a new design method for a fractional order PID controller based on internal model control (IMC) is proposed to handle non-integer order systems with time delay. In order to reduce the number of tuning parameters and mitigate the impact of time delay, the fractional order internal model control scheme is used. Considering the robustness of the control system with respect to process variations and model uncertainty, maximum sensitivity is applied to the tuning of the parameters. The resulting controller has the structure of a fractional order PID which is cascaded with a filter. This is named a fractional IMC–PID controller. Numerical results are given to show the efficiency of the proposed controller.     

Fractional Control of a Humanoid Robot Reduced Model with Model Disturbances

There is an open discussion between those who defend mass-distributed models for humanoid robots and those in favor of simple concentrated models. Even though each of them has its advantages and disadvantages, little research has been conducted analyzing the control performance due to the mismatch between the model and the real robot, and how the simplifications affect the controller’s output. In this article we address this problem by combining a reduced model of the humanoid robot, which has an easier mathematical formulation and implementation, with a fractional order controller, which is robust to changes in the model parameters. This controller is a generalization of the well-known proportional–integral–derivative (PID) structure obtained from the application of Fractional Calculus for control, as will be discussed in this article. This control strategy guarantees the robustness of the system, minimizing the effects from the assumption that the robot has a simple mass distribution. The humanoid robot is modeled and identified as a triple inverted pendulum and, using a gain scheduling strategy, the performances of a classical PID controller and a fractional order PID controller are compared, tuning the controller parameters with a genetic algorithm.     

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.     

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

The extended state observer (ESO) based controller has been used successfully with integer‐order systems involving large uncertainties. In this paper, the robust control of uncertain multi‐order fractional‐order (FO) systems based on ESO is investigated. First, we transform the multi‐order FO system into an equivalent system in the form of a same‐order state‐space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded‐input and bounded‐output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology.     

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.     

直线一级倒立摆分数阶控制器设计及仿真

针对直线一级倒立摆的稳定控制问题,设计了分数阶比例积分(FOPI和FO[PI])控制器。首先,根据Newton力学方法建立了倒立摆系统的数学模型。然后,采用基于向量的增益鲁棒性分数阶控制器参数求解简化算法,设计了分数阶比例积分控制器。最后,在MATLAB环境下进行了分数阶比例积分控制器参数整定方法的有效性验证,并且对倒立摆系统分别采用分数阶比例积分控制器和整数阶PID(IOPID)控制器进行了稳定控制仿真实验,并将得到的摆杆角度响应曲线进行了对比分析。结果表明:分数阶比例积分控制器对系统的稳定控制效果优于IOPID控制器,且在分数阶比例积分控制器中,FO[PI]控制器对系统稳定控制最好,响应时间较快、振荡幅值较小且具有鲁棒性。     

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。     

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.     

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.     

A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices

A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been proposed in this paper which works on the closed loop error and its fractional derivative as the input and has a fractional integrator in its output. The fractional order differ-integrations in the proposed fuzzy logic controller (FLC) are kept as design variables along with the input–output scaling factors (SF) and are optimized with Genetic Algorithm (GA) while minimizing several integral error indices along with the control signal as the objective function. Simulations studies are carried out to control a delayed nonlinear process and an open loop unstable process with time delay. The closed loop performances and controller efforts in each case are compared with conventional PID, fuzzy PID and PI^λD^μ controller subjected to different integral performance indices. Simulation results show that the proposed fractional order fuzzy PID controller outperforms the others in most cases.     

Tuning fractional order proportional integral controllers for fractional order systems

In this paper, two fractional order proportional integral controllers are proposed and designed for a class of fractional order systems. For fair comparison, the proposed fractional order proportional integral (FOPI), fractional order [proportional integral] (FO[PI]) and the traditional integer order PID (IOPID) controllers are all designed following the same set of the imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of the controllers design for the considered class of fractional order plants. From the simulation and experimental results presented, both of the two designed fractional order controllers work efficiently, with improved performance comparing with the designed stabilizing integer order PID controller by the observation. Moreover, it is interesting to observe that the designed FO[PI] controller outperforms the designed FOPI controller following the proposed design schemes for the class of fractional order systems considered.     

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。     

A memetic algorithm applied to trajectory control by tuning of Fractional Order Proportional-Integral-Derivative controllers

This paper introduces a novel memetic algorithm namely Fractional Particle Swarm Optimization-based Memetic Algorithm (FPSOMA) to solve optimization problem using fractional calculus concept. The FC illustrates a potential for interpreting progression of the algorithm by controlling its convergence. The FPSOMA accomplishes global search over the whole search space through PSO whereas local search is performed by PSO with fractional order velocity to alter the memory of best location of the particles. To assess the performance of the proposed algorithm, firstly an empirical comparison study is presented for solving different test functions adopted from literature. Comparisons demonstrate the preference of FPSOMA than other related algorithms. Subsequently, experiments are conducted to achieve optimal gains of Fractional Order Proportional-Integral-Derivative (FO PID) controller in solving tracking problem. Results verify the efficiency of the proposed algorithm.     

Bode 理想传递函数在分数阶控制中的应用

本文将Bode 理想传递函数应用于分数阶控制器的设计和分数阶PID 控制器参数整定中．所得控制器 可以在满足系统要求的截止频率和相角裕度的前提下,使补偿后系统Bode 图的相频特性曲线在截止频率附近有一 个水平区域,即闭环系统对增益的变化具有鲁棒性．它不仅适合于分数阶对象,也适用于整数阶对象,并能够提高 系统的控制品质．仿真结果证明了上述方法的有效性．     

A robust fractional-order PID controller design based on active queue management for TCP network

In this paper, a robust fractional-order controller is designed to control the congestion in transmission control protocol (TCP) networks with time-varying parameters. Fractional controllers can increase the stability and robustness. Regardless of advantages of fractional controllers, they are still not common in congestion control in TCP networks. The network parameters are time-varying, so the robust stability is important in congestion controller design. Therefore, we focused on the robust controller design. The fractional PID controller is developed based on active queue management (AQM). D-partition technique is used. The most important property of designed controller is the robustness to the time-varying parameters of the TCP network. The vertex quasi-polynomials of the closed-loop characteristic equation are obtained, and the stability boundaries are calculated for each vertex quasi-polynomial. The intersection of all stability regions is insensitive to network parameter variations, and results in robust stability of TCP/AQM system. NS-2 simulations show that the proposed algorithm provides a stable queue length. Moreover, simulations show smaller oscillations of the queue length and less packet drop probability for FPID compared to PI and PID controllers. We can conclude from NS-2 simulations that the average packet loss probability variations are negligible when the network parameters change.     

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.     

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

Stability and stabilization analysis of fractional‐order linear time‐invariant (FO‐LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single‐order equivalent system for the given different‐order system is introduced by which a new stability condition is obtained that is easier to check in practice than the conditions known up to now. Then the stabilization problem of fractional‐order linear systems with different fractional orders via a dynamic output feedback controller with a predetermined order is investigated, utilizing the proposed stability criterion. The proposed stability and stabilization theorems are applicable to FO‐LTI systems with different fractional orders in one or both of 0 <  α  < 1 and 1 ≤  α  < 2 intervals. Finally, some numerical examples are presented to confirm the obtained analytical results.     

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.     

基于模糊自适应分数阶PIλ的APFC控制策略研究及仿真

为解决不间断电源中整流环节对电网产生的谐波污染问题,提高网侧功率因数,基于Boost型单相功率因数校正电路,将分数阶理论、模糊控制理论与传统PID控制器相结合,应用到有源功率因数校正(APFC)系统中,使其具有更好的鲁棒性和较快的动态响应速度。在MATLAB环境下对APFC电路进行搭建,并利用Simulink库中的Fuzzy单元设计模糊控制器。通过系统仿真对控制效果进行验证,结果表明:引入模糊和分数阶控制的APFC系统具有总谐波畸变率(THD)低,动、静态性能良好等优点。     

基于分数阶PID控制器的智能车控制

针对智能车高速行驶下对目标轨迹的快速跟踪要求,结合预瞄跟随理论设计了分数阶PID控制器(FOPID).分数阶PID比传统PID控制器多两个参数自由度,所以在设计过程中有更大的灵活性.利用改进Oustaloup数字实现算法,框图化实现分数阶PID控制器,通过遗传算法对IAE性能指标寻优整定FOC参数并应用于智能车被控系统...