Proportional integral-fractional filter controller design for first order lag plus time delay system

In this work, a design approach of proportional integral-fractional filter (PI-FF) controller for first order plus time delay (FOPTD) system is proposed in order to enhance the feedback control system performances characteristics. The controller design method is drawn up such that the transfer function of the overall closed-loop system is equivalent to the transfer function of the general fractional Bagley-Torvik reference model whose behaviour ranges from relaxation to oscillation for different values of the fractional order derivative and the damping ratio-like parameter. The tuning parameters of the PI-FF controller are derived analytically from the FOPTD process model and the general fractional Bagley-Torvik reference model parameters. Illustrative examples were presented to test the effectiveness and the usefulness of the proposed PI-FF controller on the feedback control system performance characteristics enhancement.