Identification and Tuning Methods for PI Control Systems Based on Symmetric Send-on-delta Sampling

Two procedures for the definition of an autotuning algorithm for event-based proportional-integral (PI) control systems are proposed in this contribution. Firstly, a method for the identification of the most common transfer functions used for tuning PI controllers is explained. The rationale of the identification method is based on the limit cycles that the event-based sampler and a convenient tuning of the PI controller can produce in the closed loop. The identification method is designed for controller tuning, that is, fitting the behaviour of the process in the range of frequencies between ω-180° and ω-135°. Secondly, a new method for tuning the event-based PI controller is explained. The main control objective of the new tuning rule is to generate a set of parameters that introduces the process in a limit cycle at a user-specified inter-event time. However, by introducing an oscillation margin in the tuning rule, the method generalizes to produce controller parameters that avoid limit cycles with a certain robustness margin. Simulations demonstrate the effectiveness of the tuning rule to force the system to oscillate at a specified frequency as a consequence of the events triggered by the event-based sampler.