Identification of process transfer function parameters in event-based PI control loops

Abstract

This paper presents a method to estimate the parameters of first and second order systems with time delays with different accuracy levels for autotuning of event-based PI control loops. In particular, the event-based sampling condition applied in this work is based on the sampling strategy known as symmetric-send-on-delta (SSOD). The method is based on forcing the system to enter into a limit cycle and on using the information achieved from the oscillation to estimate the transfer function parameters. By manipulating the PI controller, the system can reach different limit cycles as a consequence of the intersections of the Nyquist map of the process with the describing function reciprocal of the event-based sampler. The frequency and amplitude of the limit cycle selected to apply the method define the quality of the estimations, avoiding the inaccuracy that relay identification methods based on describing function produce. Simulation results demonstrate that the estimations can be as accurate as those obtained with relay identification methods for time-driven control systems based on other approaches (state-space, curve fitting, Laplace transform, etc.).

Keywords: Describing function; Estimation; Event-based control; Limit cycle; Send-on-delta.