Disturbance Observer in PID Controllers for First-Order Time-Delayed Systems

Abstract

The article shows that the stabilizing P, PD, or PDA controllers for time-delayed first-order systems extended by automatic reset (disturbance reconstruction and compensation) established by evaluating the steady state output values of the controller, yield series PI, PID or PIDA controllers. By comparing the parameters of the given controllers tuned by the method of multiple real dominant pole, it can be shown that the obtained values of the integration time constant are many times larger than the time constants of the transients of the equivalent circuits with the stabilizing controller. The proposed interpretation of the functionality of disturbance observer included in controllers with disturbance compensation significantly helps in understanding principles of their optimal tuning, can also be used for further modifications of their operation taking into account various other limitations and establishes a unique educational framework covering most of the existing traditional, modern and postmodern controllers.