Performance Limitations of Optimal Fractional-Order PID Controllers Applied to First-Order Plus Time-Delay Processes

摘要

Since fractional order PID (FOPID) controllers have two more parameters to tune compared to the classical PID controllers, it is commonly believed that these controllers always lead to a better performance in comparison to PID controllers. In this paper, optimal FOPID controllers, which minimize the ISE performance index (corresponding to the tracking of the step command or rejection of the step disturbance) are applied to different first-order plus time-delay processes and the results are compared with those achieved by using optimal PID controllers. The results show that, in general, for tracking purposes the optimal FOPID controller has no superiority to the optimal PID controller when the normalized dead time of the process is around 2.6. It is also observed that the optimal FOPID controller becomes less effective for disturbance rejection purposes as the normalized dead time of the process is increased.