Characterization of limit cycles for self-regulating and integral processes with PI control and send-on-delta sampling

• We implement and analyze two different event-based control schemes.
• The control schemes are based on a PID controller and send-on-delta sampler.
• We characterize the limit cycles that appear in the proposed control schemes.
• The local stability of the limit cycles is studied.
• The theoretical results are validated in simulation and in a real plant.

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 Almería (PSA, Spain).