Fractional order PID control for steer-by-wire system of emergency rescue vehicle based on genetic algorithm

Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of the ECV.The overall structure and mathematical model of the SBW system are described at length.The fractional order proportional-integral-derivative(FOPID)controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system.The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation.Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error(ITAE),peak overshoot,as well as settling time.The time-domain simulations are implemented to identify the performance of the raised FOPID controller.The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative(PID)controller on the part of transient response,tracking capability and robustness.

Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay, the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results. © 2017 Chinese Association of Automation.

Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay

It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system's parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony ABC algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method. © 2014 Chinese Association of Automation.

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

Stable Model Order Reduction Method for Fractional-Order Systems Based on Unsymmetric Lanczos Algorithm

This study explores a stable model order reduction method for fractional-order systems. Using the unsymmetric Lanczos algorithm, the reduced order system with a certain number of matched moments is generated. To obtain a stable reduced order system, the stable model order reduction procedure is discussed. By the revised operation on the tridiagonal matrix produced by the unsymmetric Lanczos algorithm, we propose a reduced order modeling method for a fractional-order system to achieve a satisfactory fitting effect with the original system by the matched moments in the frequency domain. Besides, the bound function of the order reduction error is offered. Two numerical examples are presented to illustrate the effectiveness of the proposed method.

Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.

Parrondo's paradox for chaos control and anticontrol of fractional-order systems

We present the generalized forms of Parrondo＇s paradox existing in fractional-order nonlinear systems. The gener- alization is implemented by applying a parameter switching （PS） algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N 〉 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words ＂winning＂ and ＂loosing＂ in the classical Parrondo＇s paradox with ＂order＂ and ＂chaos＂, respectively, the PS algorithm leads to the generalized Parrondo＇s paradox： chaos1 ＋ chaos2 ＋..- ＋ chaosN = order and order1 ＋ order2 ＋.-. ＋ orderN = chaos. Finally, the concept is well demon- strated with the results based on the fractional-order Chen system.

WFRFT modulation recognition based on HOC and optimal order searching algorithm

A hybrid carrier（HC） scheme based on weighted-type fractional Fourier transform（WFRFT） has been proposed recently.While most of the works focus on HC scheme＇s inherent characteristics, little attention is paid to the WFRFT modulation recognition.In this paper, a new theory is provided to recognize the WFRFT modulation based on higher order cumulants（HOC）. First, it is deduced that the optimal WFRFT received order can be obtained through the minimization of 4 th-order cumulants, C_（42）. Then, a combinatorial searching algorithm is designed to minimize C_（42）.Finally, simulation results show that the designed scheme has a high recognition rate and the combinatorial searching algorithm is effective and reliable.

Identification of fractional order Hammerstein models based on mixed signals

An algorithm based on mixed signals is proposed,to solve the issues of low accuracy of identification algorithm,immeasurable intermediate variables of fractional order Hammerstein model,and how to determine the magnitude of fractional order.In this paper,a special mixed input signal is designed to separate the nonlinear and linear parts of the fractional order Hammerstein model so that each part can be identified independently.The nonlinear part is fitted by the neural fuzzy network model,which avoids the limitation of polynomial fitting and broadens the application range of nonlinear models.In addition,the multi-innovation Levenberg-Marquardt(MILM)algorithm and auxiliary recursive least square algorithm are innovatively integrated into the parameter identification algorithm of the fractional order Hammerstein model to obtain more accurate identification results.A simulation example is given to verify the accuracy and effectiveness of the proposed method.

分数阶Boost变换器的混沌控制研究

基于电容电感均为分数阶的事实,对分数阶连续导通模式Boost变换器的非线性动力学特性进行分析,提出了基于优化参数共振微扰法的分数阶Boost变换器混沌控制策略。首先,采用预估-校正算法建立了峰值电流控制分数阶Boost变换器的预估-校正模型,通过分岔图详细分析了电路参数对变换器非线性动力学特性的影响。然后,采用优化参数共振微扰法对变换器进行混沌控制,推导了系统的稳定判据,计算了扰动信号的最优幅值与相位。最后,在MATLAB/Simulink中进行仿真实验。研究表明,选择合理的扰动信号,能够有效抑制变换器的混沌现象,使变换器由混沌回归稳定状态。与参数共振微扰法相比,优化后的控制策略提高了系统的鲁棒性。仿真结果验证了所提策略的有效性。

基于非线性动态重心粒子群优化的分数阶PI^(λ)D^(μ)控制器设计

针对现有Oustaloup滤波器拟合精度不佳、结构复杂的缺点,提出了最优精简Oustaloup滤波器。针对粒子群优化算法整定分数阶PI^(λ)D^(μ)控制器参数时学习能力不充分、迭代收敛乏力的问题,提出了一种改进的粒子群优化算法。该算法设计了双异步非线性动态学习因子,以提高粒子的思考能力与信息共享能力,并增加了粒子群质量重心项,用以加速收敛过程。将改进的算法结合最优精简Oustaloup滤波器应用于分数阶PI^(λ)D^(μ)控制器的设计过程,选取了2个分数阶系统模型进行仿真验证。结果表明,改进的算法收敛速度更快且不易陷入局部最优,所设计的控制系统超调量更小、调节时间更短、稳态误差更小,提高了系统的抗干扰能力。

基于预估-校正算法的分数阶Boost变换器倍周期分岔研究

基于电感电容本质是分数阶的事实,对分数阶Boost变换器的非线性动力学特性进行了深入研究。采用分数阶微积分的预估-校正算法,建立了Boost变换器的预估-校正模型,在此基础上得到了以参考电流、输入电压以及电容电感阶数为分岔参数的分岔图,研究了变换器的倍周期分岔和混沌行为,同时与整数阶Boost变换器的非线性动力学行为进行了比较。研究结果表明,在一定的工作条件下,随着变换器某些电路参数的变化,分数阶Boost变换器会出现分岔和混沌等非线性现象;在相同电路参数的条件下,整数阶和分数阶变换器的稳定参数域之间存在差异,与整数阶变换器相比,分数阶变换器的参数稳定区域更小,更真实地反映了Boost变换器的非线性动力学特性。

基于分数阶模型多新息无迹卡尔曼滤波算法的超级电容SOC估计

对超级电容的SOC估计展开了研究。首先,搭建了超级电容测试平台,用于超级电容的参数辨识,并对超级电容进行了常规性能测试;其次,在不同的环境温度和动态工况下采用多种算法进行超级电容SOC估计。结果表明,采用分数阶模型多新息无迹卡尔曼滤波(FOMIUKF)算法对超级电容SOC的估计精度最高,对超级电容的路端电压跟随情况最好,估计结果的均方根误差和平均绝对误差的最大值分别约为1.8%和1.73%。

基于改进粒子群优化算法的分数阶PID控制器

针对控制系统控制性能不稳定的问题,实践中可在控制系统里设定一种分数阶PID控制器。相比于整数阶PID控制器,分数阶PID控制器增加了λ和μ两个控制参数,这样可以让控制器在控制过程中拥有更好的性能,但同时也使得参数整定使用更加困难。为了更容易地求出控制器的参数,需要使用改良过的粒子群(PSO)优化方法来进行整定,将时间误差绝对值(ITAE)准则应用到控制器的控制过程当中,可以快捷地得出分数阶PID控制器的优化参数。通过对常规PID控制器与分数阶PID控制器的仿真结果进行对比,经过优化后的粒子群算法得到的参数在运用到控制系统中时会得到的更好的效果,说明了优化后的分数阶PID控制器的控制效果要优于整数阶PID控制器的控制效果。

基于鲁棒控制的自适应分数阶梯度优化算法设计

当目标函数是强凸函数时,一般的分数阶梯度下降法不能够使函数收敛到最小值点,只能收敛到一个包含最小值点的区域内或者是发散的.为了解决这个问题,本文提出了自适应分数阶梯度下降法(AFOGD)和自适应分数阶加速梯度下降法(AFOAGD)两种新的优化算法.受到鲁棒控制理论中二次约束和李雅普诺夫稳定性理论的启发,建立了一个线性矩阵不等式去分析所提出的算法的收敛性.当目标函数是L-光滑且m-强凸时,算法可以达到R线性收敛.最后几个数值仿真证明了算法的有效性和优越性.

基于改进分数阶快速终端滑模的APF优化控制研究

电力电子化系统的快速发展导致电网中的谐波问题日益严重。为进一步提高有源电力滤波器(activepower filter, APF)的补偿电流跟踪性能和滤波效果,提出一种基于金枪鱼群优化(tuna swarm optimization, TSO)算法的改进型分数阶快速终端滑模控制(improved fractional-order fast terminal sliding mode control, IFOFTSMC)策略。首先,搭建三相并联型APF的数学模型,并考虑其参数扰动。其次,提出一种改进的分数阶快速终端滑模控制策略,其中滑模面采用分数阶快速终端滑模与分数阶PI相结合,并进行了有限时间分析,趋近律采用指数趋近律和幂次趋近律相结合,同时以反双曲正弦函作为切换项。然后,利用TSO算法对所设计控制器的参数和阶次进行优化并获得最优解。最后,通过仿真验证了所提控制方法的有效性。此外,经与相关文献比较进一步证实了所提优化控制算法不仅可以获得最优控制参数和最优分数阶阶次,使系统在有限时间内到达稳定,还能使APF具有更好的电流跟踪性能、滤波效果和更强的鲁棒性。

分数阶移相全桥变换器的建模与优化控制

基于电路中的分抗元件具有非整数阶特性,利用分数阶微积分理论和状态空间平均法,对分数阶移相全桥变换器进行建模与优化控制分析。建立了移相全桥变换器的分数阶状态平均方程,研究电感和电容的分数阶特性对移相全桥变换器频域特性的影响。结合遗传算法的优点,得到满足误差绝对值积分的最优分数阶比例积分(PIλ)控制器参数与最优整数阶比例积分(PI)控制器参数,并搭建了分数阶移相全桥变换器的电路仿真模型与不同控制器的仿真模型,进行了不同控制器、不同工况和负载变化下电路仿真结果的比较。结果表明:相较于整数阶PI控制器,分数阶PIλ控制器能够提供更优的控制性能,使分数阶移相全桥变换器具有更快的响应速度、更好的稳态性能和更强的鲁棒性。

G-L分数导数高阶逼近算法的鲁比希生成函数系数的求解

考察G-L分数导数的逼近阶,引出高精度的数值算法,提出三种求解鲁比希高阶逼近生成函数系数的方法 .从信号处理的角度出发,采用拉格朗日插值逼近法首次在理论上严格推导出鲁比希生成函数系数的解析表达式.构造了任意阶次的生成函数,通过不同形式的生成函数等价,用数学归纳和矩阵方程两种方法对生成函数系数进行求解,验证了结果的正确性.

基于分数阶三参数模型的HTPB推进剂粘弹性力学响应分析

为拓展分数阶粘弹性模型在端羟基聚丁二烯(HTPB)推进剂中的应用,研究分数阶粘弹性模型预示推进剂频域下的动态模量变化。推导了三维下的分数阶三参数模型,并结合Grünwald-Letnikov定义编写UMAT子程序。为标定本构参数,推导了带有预加载的蠕变、松弛响应的解析解,并采用遗传算法分别标定了0.4 MPa和0.6 MPa应力下蠕变实验以及10%和30%应变下松弛实验的本构参数。计算得到的有限元数值与解析解、解析解与实验值的时程相对误差均小于5%。采用分数阶三参数模型动态模量对-5、25、60℃下的动态力学实验(DMA)结果进行拟合得到本构参数,动态模量与实验结果误差小于2%,同时随着温度升高,本构参数均减小,体现出HTPB推进剂升温软化现象。结果表明,分数阶三参数模型能精确地描述不同温度下多种频率的HTPB推进剂模量变化,结合二次开发本构,可为后续HTPB推进剂复杂边界下的力学响应的研究提供材料本构模型。