Robust PI controller design for a laboratory time delay process

The paper presents an approach to robust PI controller design for systems with interval parametric uncertainty and time delay. It is supposed that the controlled system is described by a transfer function with parameters lying in certain intervals and with a time delay term. The transfer function of the controlled system is modified by approximation of the time delay term by its Pade expansion. The area of all PI controller parameters kp, ki, that are able to assure the robust stability of the feedback closed loop, is found by the method, which is based on plotting the stability boundary locus in the (kp, ki)-plane. Then the pole-placement method is used to specify those controller parameters from the robust stability area, which assure quality of the control performance prescribed by a choice of closed loop poles or relative damping or natural undamped frequency of the control response. The contribution presents theoretical results confirmed by practical experiments in laboratory conditions. Robust PI controllers are found using designed approach for control of an electronic equipment with varying time delay. Designed robust PI controllers are realized using the PLC SIMATIC S7–300.