Send-on-Delta PI Control

This chapter presents the analysis of event-based control structures which are based on the use of a PID controller and send-on-delta sampling. The proposed structures correspond to two cases frequently used in wireless control systems. The problem of the limit cycles that may appear in this kind of systems is stated, discussing a mathematical framework to analyze their properties, such as the frequency and amplitude of oscillations. In particular, an algorithm is proposed to compute the properties of possible limit cycles in a given process when it is controlled by the considered event-based structures. Finally, the implementation of the algorithm is tested in simulation with a set of linear models commonly used in industrial processes, and with a real process: a distributed solar collector field.