PID controller design based on two-degrees-of-freedom direct synthesis

Two design methods for proportional-integral-derivative (PID) controllers are proposed based on the two-degrees-of-freedom (2-DOF) direct synthesis (DS) approach. One method specifies the closed-loop setpoint-to-output transfer function, and the other specifies the closed-loop disturbance-to-output transfer function. With appropriate DS, the 2-DOF controllers are approximated as a PID controller with setpoint weighting. Analytical expressions for the PID controllers are derived for common process models. The examples demonstrate that the proposed design methods result in very good control for a wide variety of processes, and that they can provide better performance over recent DS and internal model control methods when they are tuned to have the same degree of robustness as measured in terms of the peak sensitivity.