Magnitude Optimum Design of PID Control Loop with Delay

The paper deals with a magnitude-optimum based synthesis of PID control loops with respect to the disturbance rejection. To obtain as general as possible formulation of the control synthesis the dimensional analysis is applied resulting in the use of similarity numbers of the so-called swingability and laggardness of the time delay plant. Just this approach has made it possible to work with the transcendental form of the optimized magnitude function. From the meromorphic description of the control loop with delay the PID setting then can be evaluated by means of Levenberg-Marquardt iteration method. The obtained PID settings are systematically compared from the viewpoint of the dominant modes of the control loop responses.