New design relations for 2-DOF PID-like control systems

Self-regulating processes can be controlled by internal model control systems where the usual three-parameter model of the process is transformed into a rational model via a parametrized first-order approximant of the apparent dead time. Using feedback and feedforward compensators leads to 2-DOF PID controllers whose time constants cancel that of the rational model. To obtain the desired sensitivity of the actual control loop, the model adaptation parameter and a gain tuning factor in the control system are determined by functions of the normalized dead time. The response to setpoint changes is selected by means of the feedforward compensator or via a prefilter. Plots of the sensitivity and the simulation of step responses to changes in the controller setpoint or to disturbances, show the validity of these design relations for transfer functions representative of typical industrial processes.