A Practical Guideline for Designing and Tuning Adaptive Backstepping Controllers for a Class of Second-Order Systems based on PID Similarity

This work proposes a practical guideline for designing and tuning adaptive backstepping control systems by leveraging the similarity with PID control laws for a class of second-order nonlinear systems. A complete set of mathematical formulations, visual aids, and a well-structured algorithm are provided to exploit the benefits of the established link. This aims at facilitating the adoption of advanced nonlinear control laws in more real-life and industrial applications while benefiting from the legacy of PID tuning rules. Furthermore, the proposed guideline allows for upgrading primitive PID controllers to more advanced nonlinear control system. The adaptive backstepping control law is formulated as a two degrees-of-freedom control law that combines the sum of a feedback PID control component and a feedforward model compensation component. The relationship between backstepping and PID gains is provided in the form of a third-order polynomial, and a simplified second-order one, with practical design algorithm and tuning guidelines. The proposed control law and tuning methodology are validated on a quadrotor unmanned aerial vehicle (UAV) system in both simulation and experimentally. Graphical Abstract