Data-Driven Retrospective-Cost-Based Adaptive Digital PID Control

This paper develops an adaptive digital controller for sampled-data systems with unknown dynamics. The adaptive digital PID controller is based on data-driven retrospective cost adaptive control (DDRCAC) with online closed-loop system identification. Online system identification is based on recursive least squares (RLS) with variable-rate forgetting (VRF), which is used to construct a target model that provides the controller based on retrospective cost adaptive control (RCAC) with the required modeling information. For SISO plants, this modeling information includes the sign of the leading numerator coefficient as well as nonminimum-phase (NMP) zeros. The present paper illustrates the performance of DDRCAC-based digital PID control on a first-order linear plant with unknown gain sign, a NMP second-order linear plant, and a multicopter with unknown dynamics.