Online tuning of derivative order term of variable-order fractional proportional–integral–derivative controllers for the first-order time delay systems

In this study, an online tuning strategy for the fractional derivative order term of the variable-order fractional proportional–integral–derivative (PID) controller is proposed for processes with dead time. The classical step response is divided into regions, and meta-rules are developed for each region in order to improve the control performance. To achieve the goals of the meta-rules, a set of equations that are the functions of absolute error and model parameters are proposed to manipulate the fractional order derivative during the process. These equations can handle the changes in model parameters since the coefficients of these equations are functions of model parameters. On both simulation studies and experimental results on the active suspension system, we show that the proposed method improves the time domain performance criteria both in relation to reference tracking and load disturbance rejection. Moreover, the robustness of the proposed method has also been tested and analyzed for the dead time variation within the process.