Fractional-order control system design can be used for systems with non-local dynamics involving long-term memory effects. However, implementation of a fractional-order controller in industrial systems is complicated, because of the excessive demand for computational power. The following paper presents the step-by-step design procedure, parameter tuning, and experimental evaluation of the fractional order proportional-integral-derivative (FOPID) controller. The control algorithm is based on the Continued Fraction Expansion approximation of the fractional-order operators. It is implemented on a standard industrial Programmable Logic Controller. The FOPID control system is verified and evaluated in terms of efficiency and robustness using a new laboratory benchmark of a temperature control in the pipeline. The proposed solution shows increased efficiency in terms of robustness compared to the standard PID closed-loop control.

分数阶控制系统设计可用于具有长期记忆效应的非局部动力学的系统。然而，由于对计算能力的过度需求，在工业系统中实现分数阶控制器是复杂的。下面的论文介绍了分数阶比例积分微分（FOPID）控制器的分步设计过程，参数调整和实验评估。控制算法基于分数阶算子的连续分数展开近似。它在标准的工业可编程逻辑控制器上实现。使用新的管道温度控制实验室基准，对FOPID控制系统的效率和坚固性进行了验证和评估。