Improved PID tuning rules using fractional calculus

For stable systems, which are modeled with first order plus dead time (FOPDT) models, improved PID tuning rules are developed using the direct synthesis (DS) method. Considering a desired closed-loop system, a new form of fractional order transfer function is used. The control goals are good set-point response, appropriate load disturbance rejection, as well as satisfactory performance and robustness indices. To achieve these goals, two tuning parameters of the controller should appropriately be tuned. Finally, explicit simple relations for controller parameters are provided. Simulation results show that the proposed design method provides a robust PID controller that performs well for both set-point and load disturbance signals.