Leveraging PID Gain Selection Towards Adaptive Backstepping Control for a Class of Second-Order Systems

In this work, we establish a convenient similarity between an adaptive backstepping control law and a standard proportional-integral-derivative (PID) controller for a class of second-order systems. The extracted similarity provides a deeper understanding of the adaptive backstepping design from a performance perspective via an intuitive method to select its otherwise abstract controller gains, on top of its traditional stability perspective. Such a similarity analysis opens the door for researchers to use well-established PID tuning methods to predict the performance of Lyapunov stability-based controllers. At the same time, the obtained formulation reveals how the corresponding PID control law can be linked to Lyapunov stability theory.