A novel nonlinear PID controller design with adaptive gains

In this study, a novel nonlinear PID controller is developed for a class of second-order nonlinear systems subject to uncertainties and external disturbances. The proposed control architecture preserves the intuitive structure of the conventional PID framework while enhancing it through a systematically designed nonlinear adaptation mechanism. In particular, the controller gains are updated online via a newly constructed adaptive update rule with an innovative structural formulation, enabling improved performance under varying operating conditions. A rigorous stability analysis of the closed-loop system is carried out using Lyapunov-type methods specifically tailored for the proposed adaptive structure. It is formally proven that all closed-loop signals remain bounded, and semi-global uniform ultimate stability (SGUUS) of the tracking error is guaranteed. Unlike many adaptive or nonlinear PID formulations in the literature, the derived stability results are not limited solely to the adaptive case. It is emphasized that the proposed analytical framework is also directly applicable to classical constant-gain PID controllers. Therefore, this study additionally provides a novel stability analysis of PID control for second-order nonlinear systems, extending existing theoretical results. The practical applicability and robustness of the proposed control methodology are validated through extensive experimental studies conducted on a real-time platform. The experimental results demonstrate improved tracking performance, robustness against uncertainties, and effective disturbance rejection. The proposed controller reduces the average tracking errors by about 72% in pitch and 77% in roll compared with the fixed-gain PID case, thereby confirming the theoretical findings and highlighting the effectiveness of the proposed nonlinear PID design.