改进的粒子群优化算法优化分数阶PID控制器参数
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摘要
为了提高分数阶比例积分微分(FOPID)控制器的控制效果,针对FOPID控制器参数整定的范围广、复杂性高等特点,提出改进的粒子群优化(PSO)算法优化FOPID控制器参数的方法。该算法对PSO中惯权重系数的上下限设定范围并随迭代次数以伽玛函数方式非线性下降,同时粒子的惯性权重系数和学习因子根据粒子的适应度值大小动态调整,使粒子保持合理运动惯性和学习能力,提高粒子的自适应能力。仿真实验表明,改进的PSO算法优化FOPID控制器的参数较标准PSO算法具有收敛速度快和收敛精度高等优点,使FOPID控制器得到较优的综合性能。
Aiming at poor control effect of Fractional Order Proportional-Integral-Derivative(FOPID) controller and the characteristics of wide range and high complexity of parameter tuning for FOPID controller, an improved Particle Swarm Optimization(PSO) method was proposed to optimize the parameters of FOPID controller. In the proposed algorithm, the upper and lower limits of inertial weight coefficients in PSO were defined and decreased nonlinearly with the iteration times in form of Gamma function, meanwhile, the inertia weight coefficients and learning factors of particles were dynamically adjusted according to the fitness value of particles, making the particles keep reasonable motion inertia and learning ability, and improving self-adaptive ability of the particles. Simulation experiments show that the improved PSO algorithm has faster convergence rate and higher convergence accuracy than the standard PSO algorithm in optimizing the parameters of FOPID controller, which makes the FOPID controller obtain better comprehensive performance.
Aiming at poor control effect of Fractional Order Proportional-Integral-Derivative(FOPID) controller and the characteristics of wide range and high complexity of parameter tuning for FOPID controller, an improved Particle Swarm Optimization(PSO) method was proposed to optimize the parameters of FOPID controller. In the proposed algorithm, the upper and lower limits of inertial weight coefficients in PSO were defined and decreased nonlinearly with the iteration times in form of Gamma function, meanwhile, the inertia weight coefficients and learning factors of particles were dynamically adjusted according to the fitness value of particles, making the particles keep reasonable motion inertia and learning ability, and improving self-adaptive ability of the particles. Simulation experiments show that the improved PSO algorithm has faster convergence rate and higher convergence accuracy than the standard PSO algorithm in optimizing the parameters of FOPID controller, which makes the FOPID controller obtain better comprehensive performance.
引文
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[18]赵远东,方正华.带有权重函数学习因子的粒子群算法[J].计算机应用,2013,33(8):2265-2268.(ZHAO Y D,FANG Z H.Particle swarm optimization algorithm with weight function's learning factor[J].Journal of Computer Applications,2013,33(8):2265-2268.)
[2]PETRAS I.The fractional-order controllers:methods for their synthesis and application[EB/OL].[2018-07-03].https://arxiv.org/pdf/math/0004064v1.pdf.
[3]MONJE C A,CALDERON A J,VINAGRE B M,et al.On fractional PIλcontrollers:some tuning rules for robustness to plant uncertainties[J].Nonlilnear Dynamics,2004,38(1/2/3/4):369-381.
[4]李新波,付云博,姜良旭,等.神经网络分数阶PIμDλ在压电叠堆控制中的应用[J].光学精密工程,2015,23(12):3439-3445.(LI X B,FU Y B,JIANG L X,et al.Application of neural network fractional order PIμDλto piezoelectric stack control[J].Optics and Precision Engineering,2015,23(12):3439-3445.)
[5]ZHANG F,YANG C,ZHOU X,et al.Fractional-order PID controller tuning using continuous state transition algorithm[J].Neural Computing and Applications,2018,29(10):795-804.
[6]张欣,仲崇权.基于量子粒子群优化设计的分数阶PIλDμ控制器[J].控制工程,2018,25(3):493-498.(ZHANG X,ZHONG CQ.Fractional order PIλDμcontroller design based on quantum particle swarm optimization[J].Control Engineering of China,2018,25(3):493-498.)
[7]AGHABABA M P.Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm[J].Soft Computing,2016,20(10):4055-4067.
[8]DAS S,PAN I,DAS S.Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes[J].ISA Transactions,2015,58:35-49.
[9]高嵩,王磊,陈超波,等.一种改进粒子群优化的分数阶PID参数整定[J].控制工程,2017,24(10):2010-2015.(GAO S,WANGL,CHEN C B,et al.An improved particle swarm optimization algorithm for fractional order PID parameter tuning[J].Control Engineering of China,2017,24(10):2010-2015.)
[10]滕志军,吕金玲,郭力文,等.基于动态加速因子的粒子群优化算法研究[J].微电子学与计算机,2017,34(12):125-129.(TENG Z J,LYU J L,GUO L W,et al.Research on particle swarm optimization based on dynamic acceleration coefficients[J].Microelectronics and Computer,2017,34(12):125-129.)
[11]ZHANG S,MA S,SONG N,et al.Fuzzy sliding mode control based on PSO for magnetic levitation positioning stage[J].IEEETransactions on Electrical and Electronic Engineering,2018,13(10):1492-1500.
[12]LIU Z-H,WEI H-L,ZHONG Q-C,et al.Parameter estimation for VSI-fed PMSM based on a dynamic PSO with learning strategies[J].IEEE Transactions on Power Electronics,2017,32(4):3154-3165.
[13]KHIABANI A G,BABAZADEH R.Design of robust fractional-order lead-lag controller for uncertain systems[J].IET Control Theory and Applications,2016,10(18):2447-2455.
[14]OUSTALOUP A,LEVRON F,MATHIEU B,et al.Frequencyband complex noninteger differentiator:characterization and synthesis[J].IEEE Transactions on Circuit and Systems-I:Fundamental Theory and Applications,2000,47(1):25-39.
[15]麻荣永,杨磊磊,张智超.基于粒子迭代位移和轨迹的粒子群算法C1、C2参数特性分析[J].数学计算,2013,2(4):109-115.(MA R Y,YANG L L,ZHANG Z C.Analysis the characteristic of C1,C2 based on the PSO of iterative shift and trajectory of particle[J].Mathematical Computation,2013,2(4):109-115.)
[16]赵延龙,滑楠,于振华.基于二次搜索的改进粒子群算法[J].计算机应用,2017,37(9):2541-2546.(ZHAO Y L,HUA N,YUZ H.Improved particle swarm optimization algorithm based on twice search[J].Journal of Computer Applications,2017,37(9):2541-2546.)
[17]SHAO Z,KLAVZAR S,LI Z,et al.On the signed Roman k-domination:complexity and thin torus graphs[J].Discrete Applied Mathematics,2017,233:175-186.
[18]赵远东,方正华.带有权重函数学习因子的粒子群算法[J].计算机应用,2013,33(8):2265-2268.(ZHAO Y D,FANG Z H.Particle swarm optimization algorithm with weight function's learning factor[J].Journal of Computer Applications,2013,33(8):2265-2268.)