Abstract: Fractional order Proportional-Integral-Derivative (PID) controller is a PID controller to the fractional Proportional-Integral-Derivative controller; it can more precisely control the complicated system than the traditional PID controller. The parameter values play a decisive role in the effects of control. A new hybrid algorithm was proposed. The Bacterial Foraging Algorithm and Particle Swarm Optimization (BFA-PSO) were combined to calculate the precise fractional order controller parameter values, which used the chemotactic, reproduction and elimination-dispersal of the BFA and combined the merits of few parameter and being easy to optimize. The simulation results show that the algorithm based on the fractional order PID control is of not only non-overshoot and fast convergence but also robustness and high precision, so it can be used to control different kinds of objects and processes.

Key words: fractional order Proportional-Integral-Derivative (PID) controller, Particle Swarm Optimization (PSO), Bacterial Foraging Algorithm (BFA), parameter optimization, robustness

摘要： 分数阶比例—积分—微分(PID)控制器是一种把PID控制器的整数阶次推广到分数的比例、积分、微分控制器，它比传统的PID控制器更能精确地控制复杂的被控系统。而参数的取值对控制效果的好坏起着决定性作用，为此提出了一种混合粒子群算法BFA-PSO优化参数值。该算法将具有趋化、繁殖和驱散特点的细菌觅食算法和参数少，易于优化的粒子群算法相结合来计算出精确的分数阶PID控制器的参数值。通过对传统PID控制器和分数阶PID控制器参数优化的实验仿真，结果表明基于该算法的分数阶PID控制不仅无超调量、收敛速度快，而且鲁棒性强、收敛精度高，可用于控制不同的对象和过程。

关键词: 分数阶PID控制器, 粒子群算法, 细菌觅食算法, 参数优化, 鲁棒性