This work is focused on the study of limit cycles that appear in a control scheme which is based on the use of a PI controller with an event-based send-on-delta sampling (SOD). The processes investigated are integrator processes plus time delay (IPTD) and first and second order processes plus time delay, which are of interest because they are frequently used to model many industrial processes. The SOD sampling is characterized as a non-linearity of n levels with hysteresis. An algorithm to calculate the limit cycles properties is proposed, and then the results obtained in simulations are compared with experiments performed on a real plant, a distributed solar collector field at the Solar Platform of Almeria (PSA, Spain). (C) 2013 Elsevier Ltd. All rights reserved.