An improved tuning method of fractional order proportional differentiation (FOPD) controller for the path tracking control of tractors

• Improved parameter tuning to compensate missing parts of flat phase method.
• Enables closed-loop system with smaller integral absolute error than IOPD controller.
• Enhanced IAE performance can decrease the amount of crop crushed.

An optimal fractional order proportional differentiation (FOPD) controller is designed for path tracking control of a specified tractor by taking integral absolute error (IAE) performance index as the evaluation criterion. The controller parameters are tuned by two methods: flat phase tuning; or an improved tuning method proposed in this paper, which can compensate for the missing parts of the flat phase method caused by computation. Comparison and analysis of two tuning methods are given. Moreover, the optimal FOPD controller is compared with the optimal integer order proportion differentiation (IOPD) controller tuned by performance indexes through simulations. Simulation results demonstrate that the optimal FOPD controller enables the closed-loop system to have smaller IAE value, and enhances IAE performance allowing less crop to be crushed. The efficiency of the proposed tuning method and the advantages of the FOPD controller are presented.