改进的粒子群优化算法优化分数阶PID控制器参数

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。

Optimization of fractional PID controller parameters based on improved PSO algorithm

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.