Analytical two-degree-of-freedom design method for linear processes with time delay

In this paper, an analytical two-degree-of-freedom control method is proposed for linear systems with time delay, including stable, unstable and nonminimum-phase plants of arbitrary order. The reference models for setpoint response and disturbance response are first presented, respectively, by virtue of dynamical characteristic of the control system and internal stability conditions. Then, the controllers are derived inversely. The resulting ideal controller for disturbance rejection is involved with time delay in a complex manner, and thus, the analytical controller reduction formulas are provided to reproduce it in the PID form by employing the Maclaurin expansion. This brings much convenience to the controller implementation. Moreover, quantitative performance and robust stability of the control system are discussed. The setpoint response and disturbance response can be separately regulated by tuning the corresponding control parameters. Finally, Simulation examples are included to show the effectiveness of the proposed method