Dynamic similarity approach to control system design: delayed PID control loop

ABSTRACTThe paper deals with a novel approach to dimensional analysis-based design of control systems. The case of delayed PID control loop is used to show the benefits of the dynamic similarity concept in providing the control with response resulting from a constrained Integral Absolute Error (IAE) optimisation. The particular aim is to achieve this response in disturbance rejection ability of the control loop. To reach a generalised description in evaluating the control loop dynamics, a dimensionless model is applied resulting from the dimensional analysis of the control loop parameters. By means of originally introduced similarity numbers of laggardness and swingability, explicit relationships between the dominant pole coordinates and the PID controller gains are obtained. The proposed optimum setting of control loop constrained in damping is referred to the ultimate oscillations of the plant.