Development of a PID Controller for Unknown Single-Input Single-Output System with RLS-Based Gain Auto-Tuning

This study describes a PID controller for an unknown single-input single-output system with gain auto-tuning based on recursive least squares. The PID controller has been widely used as an industrial controller because of its mathematical simplicity and reasonable performance on unknown systems with proper gains. If the gains are not determined properly or control conditions are changed unexpectedly, the performance of the PID controller can result in degradation. To address this issue, this study proposes a PID gain auto-tuning method based on the Lyapunov direct approach and recursive least squares(RLS) with forgetting factor. The equivalent error dynamics has been designed with the derivative term, and the coefficient in the equation has been estimated by using RLS. An adaptation rule for proportional and integral gains has been derived based on the estimated coefficient and the Lyapunov approach. The performance evaluation of the proposed algorithm was conducted by using Matlab/Simulink and an actual DC motor platform.